Finite Group Databasebeta

← C2×#13082992 #15661461

Subgroups — C2×#13082992 #15661461

Order 2816.

7182 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082992C2132yesmaximal, direct product factor
2C2×#10623152C212yesmaximal, complemented
3C2×#10623215C212yesmaximal, complemented
4C2×#10623147C211yesmaximal, characteristic, complemented
5C2×#10623063C211yesmaximal, characteristic, complemented
6C2×#10623070C211yesmaximal, characteristic, complemented
7C2×#10623096C211yesmaximal, characteristic, complemented
8C2×#10623061C211yesmaximal, characteristic, complemented
9C2×#10623062C212yesmaximal, complemented
10C2×#10623258C211yesmaximal, characteristic, complemented
11C2×#10623208C212yesmaximal, complemented
12C2×#10623142C211yesmaximal, characteristic, complemented
13C2×#10623050C211yesmaximal, characteristic, complemented
14C2×#10623260C211yesmaximal, characteristic, complemented
15C2×#10623065C212yesmaximal, complemented
16C2×#10623200C212yesmaximal, complemented
17C2×#10623150C211yesmaximal, characteristic, complemented
18C2×#10623093C211yesmaximal, characteristic, complemented
19C2×#10623128C212yesmaximal, complemented
20C2×#10623206C212yesmaximal, complemented
21C2×#10623048C211yesmaximal, characteristic, complemented
22C2×#10623127C211yesmaximal, characteristic, complemented
23C2×#10623069C211yesmaximal, characteristic, complemented
24C2×C11×#555C211yesmaximal, characteristic, complemented
25C22×Q8×D11C2212yes—
26C22×#4341C2212yes—
27C22×#4341C2212yes—
28C11×#555C22116yescomplemented
29C2×C11×C4⋊Q8C2211yescharacteristic
30C2×C11×#124C2212yes—
31C2×C11×#124C2212yes—
32C2×C11×#121C2211yescharacteristic
33C2×C11×#121C2212yes—
34C2×C11×#121C2211yescharacteristic
35C2×C4×D4×C11C2211yescharacteristic
36C2×C4×D4×C11C2211yescharacteristic
37C2×C11×#117C2212yes—
38C2×C11×#117C2211yescharacteristic
39C2×C11×#117C2211yescharacteristic
40C2×#66999C2212yes—
41C2×#66999C2212yes—
42C2×#66997C2212yes—
43C2×#66993C2211yescharacteristic
44C2×#66992C2211yescharacteristic
45C2×#66992C2212yes—
46C2×#66992C2212yes—
47C2×#66992C2212yes—
48C2×#66992C2212yes—
49C2×#66991C2211yescharacteristic
50C2×#66991C2212yes—
51C2×#66989C2212yes—
52C2×#66988C2211yescharacteristic
53C2×#66988C2212yes—
54C2×D4×Dic11C2211yescharacteristic
55C2×D4×Dic11C2211yescharacteristic
56C2×#66983C2211yescharacteristic
57C2×#66983C2211yescharacteristic
58C2×#66983C2212yes—
59C2×#66982C2212yes—
60C2×C4×C22⋊D11C2211yescharacteristic
61C2×C4×C22⋊D11C2211yescharacteristic
62C2×#66979C2211yescharacteristic
63C2×#66979C2211yescharacteristic
64C22×C4⋊Dic11C2211yescharacteristic
65C2×#66977C2212yes—
66C22×Dic11⋊C4C2212yes—
67C22×C4×Dic11C2211yescharacteristic
68#10623260C22116yescomplemented
69#10623258C22116yescomplemented
70#10623215C22132yescomplemented
71#10623208C22132yescomplemented
72#10623206C22132yescomplemented
73#10623200C22132yescomplemented
74#10623152C22132yescomplemented
75#10623150C22116yescomplemented
76#10623147C22116yescomplemented
77#10623142C22116yescomplemented
78#10623128C22132yescomplemented
79#10623127C22116yescomplemented
80#10623096C22116yescomplemented
81#10623093C22116yescomplemented
82#10623070C22116yescomplemented
83#10623069C22116yescomplemented
84#10623065C22132yescomplemented
85#10623063C22116yescomplemented
86#10623062C22132yescomplemented
87#10623061C22116yescomplemented
88#10623050C22116yescomplemented
89#10623048C22116yescomplemented
90C2×#66951C2212yes—
91C2×#66951C2211yescharacteristic
92C2×#66949C2212yes—
93C2×#66949C2212yes—
94C2×#66949C2212yes—
95C2×#66948C2211yescharacteristic
96C2×#66946C2211yescharacteristic
97C2×#66946C2211yescharacteristic
98C2×#66945C2211yescharacteristic
99C2×C4⋊C4×D11C2211yescharacteristic
100C2×#66943C2211yescharacteristic
101C2×#66943C2211yescharacteristic
102C2×#66943C2211yescharacteristic
103C2×#66942C2211yescharacteristic
104C2×#66942C2212yes—
105C2×#66941C2211yescharacteristic
106C2×#66941C2211yescharacteristic
107C2×#66941C2211yescharacteristic
108C2×#66941C2211yescharacteristic
109C2×#66939C2212yes—
110C2×#66939C2211yescharacteristic
111C2×#66938C2211yescharacteristic
112C2×#66938C2212yes—
113C2×#66938C2212yes—
114C2×#66938C2212yes—
115C2×#66937C2212yes—
116C2×#66937C2212yes—
117C2×#66937C2212yes—
118C2×#66936C2212yes—
119C2×#66936C2212yes—
120C2×#66936C2212yes—
121C2×#66936C2212yes—
122C2×#66936C2212yes—
123C2×(C22⋊D11)⋊C4C2212yes—
124C2×(C22⋊D11)⋊C4C2212yes—
125C2×#66932C2211yescharacteristic
126C2×#66931C2212yes—
127C2×#66931C2211yescharacteristic
128C2×#66931C2212yes—
129C2×#66931C2212yes—
130C2×#66931C2212yes—
131C2×#66931C2212yes—
132C2×#66931C2212yes—
133C2×#66931C2212yes—
134C2×#66930C2212yes—
135C2×#66929C2212yes—
136C2×#66928C2212yes—
137C2×C4×D44C2212yes—
138C2×C4×D44C2211yescharacteristic
139C2×#66925C2212yes—
140C2×#66925C2211yescharacteristic
141C2×#66923C2212yes—
142C2×#66923C2211yescharacteristic
143C2×#66922C2212yes—
144C2×C4×Dic22C2212yes—
145C2×C4×Dic22C2211yescharacteristic
146C2×C4×Dic22C2212yes—
147C22×Q8×C11C2312yes—
148C22×D4×C11C2311yescharacteristic
149C22×D4×C11C2312yes—
150C22×D4×C11C2311yescharacteristic
151C22×D4×C11C2312yes—
152C23×C4×C11C2311yescharacteristic
153C23×C4×C11C2311yescharacteristic
154C23×C4×C11C2312yes—
155C22×C22⋊D11C2311yescharacteristic
156C22×C22⋊D11C2312yes—
157C22×C22⋊D11C2312yes—
158C22×C22⋊D11C2312yes—
159C22×C22⋊D11C2312yes—
160C22×C22⋊D11C2312yes—
161C22×C22⋊D11C2311yescharacteristic
162C23×Dic11C2311yescharacteristic
163C23×Dic11C2312yes—
164C23×Dic11C2312yes—
165C23×Dic11C2312yes—
166C23×Dic11C2311yescharacteristic
167C2×Q8×D11—48no—
168C2×Q8×D11C23116yes—
169C2×#4341—48no—
170C2×#4341—48no—
171C2×#4341C23116yes—
172C2×#4341C23116yes—
173C22×D44C2311yescharacteristic
174C22×D44C2312yes—
175C22×C4×D11C2312yes—
176C22×C4×D11C2311yescharacteristic
177C22×C4×D11C2312yes—
178C22×C4×D11C2312yes—
179C22×C4×D11C2312yes—
180C22×Dic22C2311yescharacteristic
181C22×Dic22C2312yes—
182C22×Dic22C2312yes—
183C22×Dic22C2312yes—
184C22×Dic22C2312yes—
185C11×C4⋊Q8C2318yes—
186C11×#124C23116yes—
187C11×#124C23116yes—
188C11×#121C2318yes—
189C11×#121C23116yes—
190C11×#121C2318yes—
191C4×D4×C11C2318yes—
192C4×D4×C11C2318yes—
193C11×#117C2318yes—
194C11×#117C2318yes—
195C11×#117C23116yes—
196C2×C11×C4⋊C4C2311yescharacteristic
197C2×C11×C4⋊C4C2311yescharacteristic
198C2×C11×C4⋊C4C2311yescharacteristic
199C2×C11×C4⋊C4C2312yes—
200C2×C11×C4⋊C4C2311yescharacteristic
201C2×C11×C22⋊C4C2312yes—
202C2×C11×C22⋊C4C2312yes—
203C2×C11×C22⋊C4C2312yes—
204C2×C11×C22⋊C4C2312yes—
205C2×C11×C22⋊C4C2312yes—
206C2×C11×C22⋊C4C2311yescharacteristic
207C2×C11×C22⋊C4C2311yescharacteristic
208C2×C42×C11C2312yes—
209C2×C42×C11C2311yescharacteristic
210C2×C42×C11C2312yes—
211C2×C22⋊Dic11C2312yes—
212C2×C22⋊Dic11C2311yescharacteristic
213C2×C22⋊Dic11C2312yes—
214C2×C22⋊Dic11C2311yescharacteristic
215C2×C22⋊Dic11C2311yescharacteristic
216C2×C22⋊Dic11C2312yes—
217C2×C22⋊Dic11C2312yes—
218C2×C22⋊Dic11C2311yescharacteristic
219#66999C23116yes—
220#66999C23116yes—
221#66997C23116yes—
222#66993C2318yes—
223#66992C2318yes—
224#66992C23116yes—
225#66992C23116yes—
226#66992C23116yes—
227#66992C23116yes—
228#66991C2318yes—
229#66991C23116yes—
230#66989C23116yes—
231#66988C2318yes—
232#66988C23116yes—
233D4×Dic11C2318yes—
234D4×Dic11C2318yes—
235#66983C2318yes—
236#66983C2318yes—
237#66983C23116yes—
238#66982C23116yes—
239C4×C22⋊D11C2318yes—
240C4×C22⋊D11C2318yes—
241C2×(C2×D11)⋊C4C2312yes—
242C2×(C2×D11)⋊C4C2312yes—
243C2×(C2×D11)⋊C4C2311yescharacteristic
244C2×(C2×D11)⋊C4C2311yescharacteristic
245C2×(C2×D11)⋊C4C2311yescharacteristic
246C2×(C2×D11)⋊C4C2312yes—
247C2×(C2×D11)⋊C4C2312yes—
248C2×(C2×D11)⋊C4C2311yescharacteristic
249C2×(C2×D11)⋊C4C2312yes—
250C2×(C2×D11)⋊C4C2312yes—
251C2×(C2×D11)⋊C4C2312yes—
252#66979C2318yes—
253#66979C2318yes—
254C2×C4⋊Dic11C2312yes—
255C2×C4⋊Dic11C2311yescharacteristic
256C2×C4⋊Dic11C2312yes—
257C2×C4⋊Dic11C2311yescharacteristic
258C2×C4⋊Dic11C2312yes—
259C2×C4⋊Dic11C2312yes—
260C2×C4⋊Dic11C2311yescharacteristic
261C2×C4⋊Dic11C2311yescharacteristic
262C2×C4⋊Dic11C2311yescharacteristic
263C2×C4⋊Dic11C2311yescharacteristic
264C2×C4⋊Dic11C2318yes—
265#66977C23116yes—
266C2×Dic11⋊C4C2312yes—
267C2×Dic11⋊C4C2312yes—
268C2×Dic11⋊C4C2312yes—
269C2×Dic11⋊C4C2312yes—
270C2×Dic11⋊C4C2311yescharacteristic
271C2×Dic11⋊C4C2311yescharacteristic
272C2×Dic11⋊C4C2312yes—
273C2×Dic11⋊C4C2312yes—
274C2×Dic11⋊C4C2312yes—
275C2×Dic11⋊C4C2312yes—
276C2×Dic11⋊C4C2312yes—
277C2×Dic11⋊C4C2311yescharacteristic
278C2×Dic11⋊C4C2311yescharacteristic
279C2×Dic11⋊C4C2311yescharacteristic
280C2×Dic11⋊C4C2311yescharacteristic
281C2×Dic11⋊C4C2312yes—
282C2×Dic11⋊C4C23116yes—
283C2×C4×Dic11C2312yes—
284C2×C4×Dic11C2311yescharacteristic
285C2×C4×Dic11C2311yescharacteristic
286C2×C4×Dic11C2311yescharacteristic
287C2×C4×Dic11C2311yescharacteristic
288C2×C4×Dic11C2312yes—
289C2×C4×Dic11C2311yescharacteristic
290C2×C4×Dic11C2318yes—
291#66951C23116yes—
292#66951C2318yes—
293#66949C23116yes—
294#66949C23116yes—
295#66949C23116yes—
296#66948C2318yes—
297#66946C2318yes—
298#66946C2318yes—
299#66945C2318yes—
300C4⋊C4×D11C2318yes—
301#66943C2318yes—
302#66943C2318yes—
303#66943C2318yes—
304#66942C23116yes—
305#66942C2318yes—
306#66941C2318yes—
307#66941C2318yes—
308#66941C2318yes—
309#66941C2318yes—
310#66939C23116yes—
311#66939C2318yes—
312#66938C23116yes—
313#66938C23116yes—
314#66938C23116yes—
315#66938C2318yes—
316#66937C23116yes—
317#66937C23116yes—
318#66937C23116yes—
319#66936C23116yes—
320#66936C23116yes—
321#66936C23116yes—
322#66936C23116yes—
323#66936C23116yes—
324(C22⋊D11)⋊C4C23116yes—
325(C22⋊D11)⋊C4C23116yes—
326#66932C2318yes—
327#66931C23116yes—
328#66931C23116yes—
329#66931C23116yes—
330#66931C23116yes—
331#66931C23116yes—
332#66931C2318yes—
333#66931C23116yes—
334#66931C23116yes—
335#66930C23116yes—
336#66929C23116yes—
337#66928C23116yes—
338C4×D44C2318yes—
339C4×D44C23116yes—
340#66925C2318yes—
341#66925C23116yes—
342#66923C2318yes—
343#66923C23116yes—
344#66922C23116yes—
345C4×Dic22C2318yes—
346C4×Dic22C23116yes—
347C4×Dic22C23116yes—
348C2×#3547—111nomaximal, Sylow
349C24×C11C2411yescharacteristic
350C24×C11C2412yes—
351C24×C11C2411yescharacteristic
352C23×D11C2412yes—
353C23×D11C2411yescharacteristic
354C2×Q8×C11—44no—
355C2×Q8×C11C2418yes—
356C2×D4×C11—24no—
357C2×D4×C11—44no—
358C2×D4×C11—44no—
359C2×D4×C11—42no—
360C2×D4×C11C2414yes—
361C2×D4×C11C2418yes—
362C2×D4×C11C2414yes—
363C2×D4×C11C2418yes—
364C22×C4×C11—24no—
365C22×C4×C11—24no—
366C22×C4×C11—44no—
367C22×C4×C11C2411yescharacteristic
368C22×C4×C11C2414yes—
369C22×C4×C11C2412yes—
370C22×C4×C11C2411yescharacteristic
371C22×C4×C11C2412yes—
372C22×C4×C11C2411yescharacteristic
373C22×C4×C11C2412yes—
374C22×C4×C11C2411yescharacteristic
375C22×C4×C11C2414yes—
376C22×C4×C11C2418yes—
377C22×C4×C11C2411yescharacteristic
378C2×C22⋊D11—24no—
379C2×C22⋊D11—44no—
380C2×C22⋊D11—44no—
381C2×C22⋊D11—44no—
382C2×C22⋊D11—42no—
383C2×C22⋊D11—44no—
384C2×C22⋊D11—44no—
385C2×C22⋊D11C2414yes—
386C2×C22⋊D11C2418yes—
387C2×C22⋊D11C2418yes—
388C2×C22⋊D11C2418yes—
389C2×C22⋊D11C2418yes—
390C2×C22⋊D11C2418yes—
391C2×C22⋊D11C2414yes—
392C22×Dic11—24no—
393C22×Dic11—28no—
394C22×Dic11—44no—
395C22×Dic11—44no—
396C22×Dic11—42no—
397C22×Dic11C2414yes—
398C22×Dic11C2418yes—
399C22×Dic11C2411yescharacteristic
400C22×Dic11C2411yescharacteristic
401C22×Dic11C2412yes—
402C22×Dic11C2411yescharacteristic
403C22×Dic11C2411yescharacteristic
404C22×Dic11C2411yescharacteristic
405C22×Dic11C2412yes—
406C22×Dic11C2411yescharacteristic
407C22×Dic11C2412yes—
408C22×Dic11C2418yes—
409C22×Dic11C2418yes—
410C22×Dic11C2414yes—
411C22×Dic11C2411yescharacteristic
412Q8×D11—432no—
413#4341—432no—
414#4341—432no—
415C2×D44—24no—
416C2×D44—44no—
417C2×D44C2414yes—
418C2×D44C2418yes—
419C2×C4×D11—28no—
420C2×C4×D11—24no—
421C2×C4×D11—44no—
422C2×C4×D11—44no—
423C2×C4×D11—44no—
424C2×C4×D11C2418yes—
425C2×C4×D11C2414yes—
426C2×C4×D11C2418yes—
427C2×C4×D11C2418yes—
428C2×C4×D11C2418yes—
429C2×Dic22—28no—
430C2×Dic22—24no—
431C2×Dic22—44no—
432C2×Dic22—44no—
433C2×Dic22—44no—
434C2×Dic22C2414yes—
435C2×Dic22C2418yes—
436C2×Dic22C2418yes—
437C2×Dic22C2418yes—
438C2×Dic22C2418yes—
439C11×C4⋊C4C2414yes—
440C11×C4⋊C4C2414yes—
441C11×C4⋊C4C2414yes—
442C11×C4⋊C4C2418yes—
443C11×C4⋊C4C2414yes—
444C11×C22⋊C4C2418yes—
445C11×C22⋊C4C2418yes—
446C11×C22⋊C4C2418yes—
447C11×C22⋊C4C2418yes—
448C11×C22⋊C4C2418yes—
449C11×C22⋊C4C2414yes—
450C11×C22⋊C4C2414yes—
451C42×C11C2418yes—
452C42×C11C2414yes—
453C42×C11C2418yes—
454C22⋊Dic11C2418yes—
455C22⋊Dic11C2414yes—
456C22⋊Dic11C2418yes—
457C22⋊Dic11C2414yes—
458C22⋊Dic11C2414yes—
459C22⋊Dic11C2418yes—
460C22⋊Dic11C2418yes—
461C22⋊Dic11C2414yes—
462(C2×D11)⋊C4C2418yes—
463(C2×D11)⋊C4C2418yes—
464(C2×D11)⋊C4C2414yes—
465(C2×D11)⋊C4C2414yes—
466(C2×D11)⋊C4C2414yes—
467(C2×D11)⋊C4C2418yes—
468(C2×D11)⋊C4C2418yes—
469(C2×D11)⋊C4C2414yes—
470(C2×D11)⋊C4C2418yes—
471(C2×D11)⋊C4C2418yes—
472(C2×D11)⋊C4C2418yes—
473C4⋊Dic11C2418yes—
474C4⋊Dic11C2414yes—
475C4⋊Dic11C2418yes—
476C4⋊Dic11C2414yes—
477C4⋊Dic11C2418yes—
478C4⋊Dic11C2418yes—
479C4⋊Dic11C2414yes—
480C4⋊Dic11C2414yes—
481C4⋊Dic11C2414yes—
482C4⋊Dic11C2414yes—
483Dic11⋊C4C2418yes—
484Dic11⋊C4C2418yes—
485Dic11⋊C4C2418yes—
486Dic11⋊C4C2418yes—
487Dic11⋊C4C2414yes—
488Dic11⋊C4C2414yes—
489Dic11⋊C4C2418yes—
490Dic11⋊C4C2418yes—
491Dic11⋊C4C2418yes—
492Dic11⋊C4C2418yes—
493Dic11⋊C4C2418yes—
494Dic11⋊C4C2414yes—
495Dic11⋊C4C2414yes—
496Dic11⋊C4C2414yes—
497Dic11⋊C4C2414yes—
498Dic11⋊C4C2418yes—
499C4×Dic11C2418yes—
500C4×Dic11C2414yes—
501C4×Dic11C2414yes—
502C4×Dic11C2414yes—
503C4×Dic11C2414yes—
504C4×Dic11C2418yes—
505C4×Dic11C2414yes—
506#3547—1132no—
507C2×#562—112no—
508C2×#562—112no—
509C2×#555—111no—
510C2×#555—111no—
511C2×#555D1111yescharacteristic, complemented
512C2×#554—111no—
513C2×#553—111no—
514C2×#553—111no—
515C2×#552—112no—
516C2×D4×Q8—111no—
517C2×#548—112no—
518C2×#547—111no—
519C2×#544—111no—
520C2×#544—111no—
521C2×#542—112no—
522C2×#542—112no—
523C2×#540—111no—
524C2×#540—111no—
525C2×#537—112no—
526C2×#536—112no—
527C2×#533—111no—
528C2×#532—111no—
529C2×#529—111no—
530C23×C11—22no—
531C23×C11—24no—
532C23×C11—22no—
533C23×C11—22no—
534C23×C11—22no—
535C23×C11—24no—
536C23×C11—24no—
537C23×C11—22no—
538C23×C11—22no—
539C23×C11C2512yes—
540C23×C11C2514yes—
541C23×C11C2512yes—
542C23×C11C2511yescharacteristic
543C22×D11—24no—
544C22×D11—22no—
545C22×D11—22no—
546C22×D11—24no—
547C22×D11—22no—
548C22×D11—24no—
549C22×D11C2514yes—
550C22×D11C2512yes—
551Q8×C11—48no—
552D4×C11—28no—
553D4×C11—48no—
554D4×C11—48no—
555D4×C11—44no—
556C2×C4×C11—24no—
557C2×C4×C11—22no—
558C2×C4×C11—24no—
559C2×C4×C11—22no—
560C2×C4×C11—22no—
561C2×C4×C11—24no—
562C2×C4×C11—22no—
563C2×C4×C11—28no—
564C2×C4×C11—28no—
565C2×C4×C11—48no—
566C2×C4×C112−1+414yes—
567C2×C4×C11C2512yes—
568C2×C4×C11C2514yes—
569C2×C4×C11C2512yes—
570C2×C4×C11C2514yes—
571C2×C4×C11C2512yes—
572C2×C4×C11C2514yes—
573C2×C4×C11C2512yes—
574C2×C4×C11C2512yes—
575C22⋊D11—28no—
576C22⋊D11—48no—
577C22⋊D11—48no—
578C22⋊D11—48no—
579C22⋊D11—48no—
580C22⋊D11—44no—
581C22⋊D11—48no—
582C2×Dic11—22no—
583C2×Dic11—24no—
584C2×Dic11—22no—
585C2×Dic11—24no—
586C2×Dic11—22no—
587C2×Dic11—22no—
588C2×Dic11—24no—
589C2×Dic11—22no—
590C2×Dic11—22no—
591C2×Dic11—28no—
592C2×Dic11—216no—
593C2×Dic11—48no—
594C2×Dic11—44no—
595C2×Dic11—48no—
596C2×Dic11H(5,𝔽2)14yes—
597C2×Dic11C2512yes—
598C2×Dic11C2512yes—
599C2×Dic11C2514yes—
600C2×Dic11C2512yes—
601C2×Dic11C2512yes—
602C2×Dic11C2512yes—
603C2×Dic11C2514yes—
604C2×Dic11C2512yes—
605C2×Dic11C2514yes—
606C2×Dic11C2512yes—
607D44—28no—
608D44—48no—
609C4×D11—28no—
610C4×D11—216no—
611C4×D11—48no—
612C4×D11—48no—
613C4×D11—48no—
614Dic22—216no—
615Dic22—28no—
616Dic22—48no—
617Dic22—48no—
618Dic22—48no—
619C22×#41—112no—
620C22×#41—112no—
621C23×Q8—112no—
622#562—1132no—
623#562—1132no—
624#555—1116no—
625#555—1116no—
626#555C2×D11116yescomplemented
627#554—1116no—
628#553—1116no—
629#553—1116no—
630#552—1132no—
631D4×Q8—1116no—
632#548—1132no—
633#547—1116no—
634#544—1116no—
635#544—1116no—
636#542—1132no—
637#542—1132no—
638#540—1116no—
639#540—1116no—
640#537—1132no—
641#536—1132no—
642#533—1116no—
643#532—1116no—
644C2×C4⋊Q8—112no—
645C2×C4⋊Q8—111no—
646C2×C4⋊Q8—111no—
647C2×C4⋊Q8—111no—
648C2×C4⋊Q8—111no—
649C2×C4⋊Q8—112no—
650C2×C4⋊Q8C2×D1111yescharacteristic
651C2×#127—111no—
652#529—1116no—
653C2×#126—111no—
654C2×#126—112no—
655C2×#126—111no—
656C2×#126—112no—
657C2×#125—111no—
658C2×#125—112no—
659C2×#125—111no—
660C2×#125—111no—
661C2×#125—111no—
662C2×#125—112no—
663C2×#125—111no—
664C2×#124—112no—
665C2×#124—111no—
666C2×#124—112no—
667C2×#124—112no—
668C2×#124—112no—
669C2×#124—112no—
670C2×#124C2×D1112yes—
671C2×#124C2×D1112yes—
672C2×#123—111no—
673C2×#123—112no—
674C2×#123—112no—
675C2×#123—112no—
676C2×#123—112no—
677C2×#123—112no—
678C2×#123—112no—
679C2×#123—112no—
680C2×#123—111no—
681C2×#123—112no—
682C2×C22⋊Q8—112no—
683C2×C22⋊Q8—112no—
684C2×C22⋊Q8—112no—
685C2×C22⋊Q8—112no—
686C2×C22⋊Q8—112no—
687C2×C22⋊Q8—112no—
688C2×C22⋊Q8—111no—
689C2×C22⋊Q8—112no—
690C2×C22⋊Q8—112no—
691C2×C22⋊Q8—112no—
692C2×C22⋊Q8—112no—
693C2×C22⋊Q8—112no—
694C2×C22⋊Q8—112no—
695C2×C22⋊Q8—112no—
696C2×#121—111no—
697C2×#121—112no—
698C2×#121—111no—
699C2×#121—112no—
700C2×#121—112no—
701C2×#121—112no—
702C2×#121—112no—
703C2×#121—111no—
704C2×#121—112no—
705C2×#121—111no—
706C2×#121—111no—
707C2×#121—112no—
708C2×#121—112no—
709C2×#121—112no—
710C2×#121C2×D1111yescharacteristic
711C2×#121C2×D1112yes—
712C2×#121C2×D1111yescharacteristic
713C2×C4×Q8—111no—
714C2×C4×Q8—112no—
715C2×C4×Q8—112no—
716C2×C4×D4—111no—
717C2×C4×D4—111no—
718C2×C4×D4—111no—
719C2×C4×D4—111no—
720C2×C4×D4—111no—
721C2×C4×D4—111no—
722C2×C4×D4—112no—
723C2×C4×D4—112no—
724C2×C4×D4—111no—
725C2×C4×D4—112no—
726C2×C4×D4C2×D1111yescharacteristic
727C2×C4×D4C2×D1111yescharacteristic
728C2×#117—111no—
729C2×#117—111no—
730C2×#117—111no—
731C2×#117—112no—
732C2×#117—111no—
733C2×#117—112no—
734C2×#117C2×D1111yescharacteristic
735C2×#117C2×D1112yes—
736C2×#117C2×D1111yescharacteristic
737C22×C4⋊C4—112no—
738C22×C4⋊C4—111no—
739C22×C4⋊C4—111no—
740C22×C42—111no—
741C22×C11—22no—
742C22×C11—24no—
743C22×C11—22no—
744C22×C11—22no—
745C22×C11—22no—
746C22×C11—24no—
747C22×C11—24no—
748C22×C11—22no—
749C22×C11—22no—
750C22×C11—44no—
751C22×C11—48no—
752C22×C11—44no—
753C22×C11C2×H(5,𝔽2)12yes—
754C22×C11C2×2−1+412yes—
755C22×C11#58512yes—
756C22×C11C2611yescharacteristic
757C2×D11—24no—
758C2×D11—22no—
759C2×D11—22no—
760C2×D11—24no—
761C2×D11—22no—
762C2×D11—24no—
763C2×D11—48no—
764C2×D11—44no—
765C4×C11—24no—
766C4×C11—24no—
767C4×C11—22no—
768C4×C11—22no—
769C4×C11—22no—
770C4×C11—22no—
771C4×C11—24no—
772C4×C11C2×2−1+414yes—
773Dic11—22no—
774Dic11—24no—
775Dic11—22no—
776Dic11—24no—
777Dic11—22no—
778Dic11—22no—
779Dic11—24no—
780Dic11—22no—
781Dic11—22no—
782Dic11C2×H(5,𝔽2)14yes—
783C2×#41—1116no—
784C2×#41—1116no—
785C2×#41—448no—
786C2×#41—448no—
787C22×Q8—1116no—
788C22×Q8—111no—
789C22×Q8—112no—
790C22×Q8—112no—
791C22×Q8—112no—
792C22×Q8—112no—
793C22×Q8—448no—
794C22×Q8C22×D1112yes—
795C22×D4—111no—
796C22×D4—111no—
797C22×D4—112no—
798C22×D4—112no—
799C22×D4—112no—
800C22×D4—112no—
801C22×D4—112no—
802C22×D4—111no—
803C22×D4—112no—
804C22×D4C22×D1111yescharacteristic
805C22×D4C22×D1111yescharacteristic
806C22×D4C22×D1112yes—
807C22×D4C22×D1112yes—
808C23×C4—112no—
809C23×C4—111no—
810C23×C4—112no—
811C23×C4—112no—
812C23×C4—111no—
813C23×C4—111no—
814C23×C4—112no—
815C23×C4—112no—
816C23×C4—112no—
817C23×C4—112no—
818C23×C4C22×D1111yescharacteristic
819C23×C4C22×D1111yescharacteristic
820C23×C4C22×D1112yes—
821C4⋊Q8—1116no—
822C4⋊Q8—118no—
823C4⋊Q8—118no—
824C4⋊Q8—118no—
825C4⋊Q8—118no—
826C4⋊Q8—1116no—
827C4⋊Q8C22×D1118yes—
828#127—118no—
829#126—118no—
830#126—1116no—
831#126—118no—
832#126—1116no—
833#125—118no—
834#125—118no—
835#125—118no—
836#125—1116no—
837#125—118no—
838#125—1116no—
839#125—118no—
840#124—1116no—
841#124—118no—
842#124—1116no—
843#124—1116no—
844#124—1116no—
845#124—1116no—
846#124C22×D11116yes—
847#124C22×D11116yes—
848#123—118no—
849#123—1116no—
850#123—1116no—
851#123—118no—
852#123—1116no—
853#123—1116no—
854#123—1116no—
855#123—1116no—
856#123—1116no—
857#123—1116no—
858C22⋊Q8—1116no—
859C22⋊Q8—1116no—
860C22⋊Q8—1116no—
861C22⋊Q8—1116no—
862C22⋊Q8—1116no—
863C22⋊Q8—1116no—
864C22⋊Q8—118no—
865C22⋊Q8—1116no—
866C22⋊Q8—1116no—
867C22⋊Q8—1116no—
868C22⋊Q8—1116no—
869C22⋊Q8—1116no—
870C22⋊Q8—1116no—
871C22⋊Q8—1116no—
872#121—118no—
873#121—1116no—
874#121—1116no—
875#121—1116no—
876#121—1116no—
877#121—118no—
878#121—1116no—
879#121—118no—
880#121—1116no—
881#121—118no—
882#121—118no—
883#121—1116no—
884#121—1116no—
885#121—1116no—
886#121C22×D1118yes—
887#121C22×D11116yes—
888#121C22×D1118yes—
889C4×Q8—118no—
890C4×Q8—1116no—
891C4×Q8—1116no—
892C4×D4—118no—
893C4×D4—118no—
894C4×D4—118no—
895C4×D4—118no—
896C4×D4—118no—
897C4×D4—118no—
898C4×D4—1116no—
899C4×D4—1116no—
900C4×D4—118no—
901C4×D4—1116no—
902C4×D4C22×D1118yes—
903C4×D4C22×D1118yes—
904#117—118no—
905#117—118no—
906#117—118no—
907#117—1116no—
908#117—118no—
909#117—1116no—
910#117C22×D1118yes—
911#117C22×D11116yes—
912#117C22×D1118yes—
913C2×C4⋊C4—111no—
914C2×C4⋊C4—111no—
915C2×C4⋊C4—111no—
916C2×C4⋊C4—112no—
917C2×C4⋊C4—112no—
918C2×C4⋊C4—112no—
919C2×C4⋊C4—112no—
920C2×C4⋊C4—112no—
921C2×C4⋊C4—1116no—
922C2×C4⋊C4—118no—
923C2×C4⋊C4—111no—
924C2×C4⋊C4—111no—
925C2×C4⋊C4—111no—
926C2×C4⋊C4—112no—
927C2×C4⋊C4—111no—
928C2×C4⋊C4—111no—
929C2×C4⋊C4—111no—
930C2×C4⋊C4—111no—
931C2×C4⋊C4—112no—
932C2×C4⋊C4—112no—
933C2×C4⋊C4—112no—
934C2×C4⋊C4—112no—
935C2×C4⋊C4—112no—
936C2×C4⋊C4—112no—
937C2×C4⋊C4—112no—
938C2×C4⋊C4—111no—
939C2×C4⋊C4—111no—
940C2×C4⋊C4—112no—
941C2×C4⋊C4—118no—
942C2×C4⋊C4C22×D1111yescharacteristic
943C2×C4⋊C4C22×D1111yescharacteristic
944C2×C4⋊C4C22×D1111yescharacteristic
945C2×C4⋊C4C22×D1111yescharacteristic
946C2×C4⋊C4C22×D1112yes—
947C2×C22⋊C4—111no—
948C2×C22⋊C4—112no—
949C2×C22⋊C4—111no—
950C2×C22⋊C4—112no—
951C2×C22⋊C4—112no—
952C2×C22⋊C4—112no—
953C2×C22⋊C4—111no—
954C2×C22⋊C4—111no—
955C2×C22⋊C4—111no—
956C2×C22⋊C4—111no—
957C2×C22⋊C4—112no—
958C2×C22⋊C4—112no—
959C2×C22⋊C4—112no—
960C2×C22⋊C4—112no—
961C2×C22⋊C4—111no—
962C2×C22⋊C4—112no—
963C2×C22⋊C4—112no—
964C2×C22⋊C4—112no—
965C2×C22⋊C4—111no—
966C2×C22⋊C4C22×D1112yes—
967C2×C22⋊C4C22×D1112yes—
968C2×C22⋊C4C22×D1112yes—
969C2×C22⋊C4C22×D1112yes—
970C2×C22⋊C4C22×D1111yescharacteristic
971C2×C22⋊C4C22×D1112yes—
972C2×C22⋊C4C22×D1111yescharacteristic
973C2×C42—112no—
974C2×C42—112no—
975C2×C42—111no—
976C2×C42—111no—
977C2×C42—111no—
978C2×C42—111no—
979C2×C42—111no—
980C2×C42—118no—
981C2×C42C22×D1112yes—
982C2×C42C22×D1111yescharacteristic
983C2×C42C22×D1112yes—
984C2×C11—42no—
985C2×C11—44no—
986C2×C11—42no—
987C2×C11#354714yescomplemented
988C2×C11C22×H(5,𝔽2)11yescharacteristic
989C2×C11C22×2−1+411yescharacteristic
990C2×C11C2×#58511yescharacteristic
991D11—44no—
992D11—42no—
993C24—111no—
994C24—112no—
995C24C23×D1111yescharacteristic
996C24C23×D1111yescharacteristic
997C24C23×D1112yes—
998#41—4432no—
999#41—4432no—
1000C2×Q8—44no—
1001C2×Q8—114no—
1002C2×Q8—118no—
1003C2×Q8—118no—
1004C2×Q8—118no—
1005C2×Q8—118no—
1006C2×Q8—224no—
1007C2×Q8—228no—
1008C2×Q8—444no—
1009C2×Q8—444no—
1010C2×Q8—444no—
1011C2×Q8—4432no—
1012C2×Q8C23×D1118yes—
1013C2×D4—24no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—42no—
1017C2×D4—114no—
1018C2×D4—114no—
1019C2×D4—118no—
1020C2×D4—118no—
1021C2×D4—118no—
1022C2×D4—118no—
1023C2×D4—118no—
1024C2×D4—114no—
1025C2×D4—118no—
1026C2×D4—224no—
1027C2×D4—224no—
1028C2×D4—444no—
1029C2×D4—444no—
1030C2×D4—444no—
1031C2×D4—444no—
1032C2×D4—442no—
1033C2×D4—444no—
1034C2×D4—444no—
1035C2×D4C23×D1114yes—
1036C2×D4C23×D1114yes—
1037C2×D4C23×D1118yes—
1038C2×D4C23×D1118yes—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—44no—
1042C22×C4—111no—
1043C22×C4—114no—
1044C22×C4—118no—
1045C22×C4—111no—
1046C22×C4—111no—
1047C22×C4—112no—
1048C22×C4—111no—
1049C22×C4—111no—
1050C22×C4—111no—
1051C22×C4—111no—
1052C22×C4—112no—
1053C22×C4—112no—
1054C22×C4—114no—
1055C22×C4—118no—
1056C22×C4—118no—
1057C22×C4—114no—
1058C22×C4—118no—
1059C22×C4—118no—
1060C22×C4—118no—
1061C22×C4—118no—
1062C22×C4—228no—
1063C22×C4—228no—
1064C22×C4—224no—
1065C22×C4—224no—
1066C22×C4—444no—
1067C22×C4—444no—
1068C22×C4—444no—
1069C22×C4—444no—
1070C22×C4—444no—
1071C22×C4—442no—
1072C22×C4C23×D1114yes—
1073C22×C4C23×D1114yes—
1074C22×C4C23×D1111yescharacteristic
1075C22×C4C23×D1112yes—
1076C22×C4C23×D1111yescharacteristic
1077C22×C4C23×D1112yes—
1078C22×C4C23×D1111yescharacteristic
1079C22×C4C23×D1111yescharacteristic
1080C22×C4C23×D1112yes—
1081C22×C4C23×D1118yes—
1082C22×C4C23×D1111yescharacteristic
1083C4⋊C4—114no—
1084C4⋊C4—114no—
1085C4⋊C4—114no—
1086C4⋊C4—118no—
1087C4⋊C4—118no—
1088C4⋊C4—118no—
1089C4⋊C4—118no—
1090C4⋊C4—118no—
1091C4⋊C4—114no—
1092C4⋊C4—114no—
1093C4⋊C4—114no—
1094C4⋊C4—118no—
1095C4⋊C4—114no—
1096C4⋊C4—114no—
1097C4⋊C4—114no—
1098C4⋊C4—114no—
1099C4⋊C4—118no—
1100C4⋊C4—118no—
1101C4⋊C4—118no—
1102C4⋊C4—118no—
1103C4⋊C4—118no—
1104C4⋊C4—118no—
1105C4⋊C4—118no—
1106C4⋊C4—114no—
1107C4⋊C4—114no—
1108C4⋊C4—118no—
1109C4⋊C4C23×D1114yes—
1110C4⋊C4C23×D1114yes—
1111C4⋊C4C23×D1114yes—
1112C4⋊C4C23×D1114yes—
1113C4⋊C4C23×D1118yes—
1114C22⋊C4—114no—
1115C22⋊C4—118no—
1116C22⋊C4—114no—
1117C22⋊C4—118no—
1118C22⋊C4—118no—
1119C22⋊C4—118no—
1120C22⋊C4—114no—
1121C22⋊C4—114no—
1122C22⋊C4—114no—
1123C22⋊C4—114no—
1124C22⋊C4—118no—
1125C22⋊C4—118no—
1126C22⋊C4—118no—
1127C22⋊C4—118no—
1128C22⋊C4—114no—
1129C22⋊C4—118no—
1130C22⋊C4—118no—
1131C22⋊C4—118no—
1132C22⋊C4—114no—
1133C22⋊C4C23×D1118yes—
1134C22⋊C4C23×D1118yes—
1135C22⋊C4C23×D1118yes—
1136C22⋊C4C23×D1118yes—
1137C22⋊C4C23×D1114yes—
1138C22⋊C4C23×D1118yes—
1139C22⋊C4C23×D1114yes—
1140C42—114no—
1141C42—114no—
1142C42—114no—
1143C42—114no—
1144C42—118no—
1145C42—118no—
1146C42—114no—
1147C42C23×D1118yes—
1148C42C23×D1114yes—
1149C42C23×D1118yes—
1150C11C2×#354711yescharacteristic, complemented, Sylow
1151C23—22no—
1152C23—22no—
1153C23—24no—
1154C23—24no—
1155C23—22no—
1156C23—22no—
1157C23—22no—
1158C23—24no—
1159C23—22no—
1160C23—114no—
1161C23—112no—
1162C23—222no—
1163C23—224no—
1164C23—222no—
1165C23—224no—
1166C23—224no—
1167C23—222no—
1168C23C24×D1112yes—
1169C23C24×D1114yes—
1170C23C24×D1112yes—
1171C23C24×D1111yescharacteristic
1172Q8—48no—
1173Q8—228no—
1174Q8—2216no—
1175Q8—448no—
1176Q8—448no—
1177Q8—448no—
1178D4—28no—
1179D4—44no—
1180D4—48no—
1181D4—48no—
1182D4—228no—
1183D4—228no—
1184D4—448no—
1185D4—448no—
1186D4—448no—
1187D4—448no—
1188D4—444no—
1189D4—448no—
1190D4—448no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—28no—
1199C2×C4—28no—
1200C2×C4—48no—
1201C2×C4—114no—
1202C2×C4—112no—
1203C2×C4—112no—
1204C2×C4—112no—
1205C2×C4—114no—
1206C2×C4—112no—
1207C2×C4—112no—
1208C2×C4—112no—
1209C2×C4—112no—
1210C2×C4—114no—
1211C2×C4—114no—
1212C2×C4—2216no—
1213C2×C4—2216no—
1214C2×C4—228no—
1215C2×C4—222no—
1216C2×C4—222no—
1217C2×C4—222no—
1218C2×C4—224no—
1219C2×C4—222no—
1220C2×C4—224no—
1221C2×C4—222no—
1222C2×C4—224no—
1223C2×C4—222no—
1224C2×C4—228no—
1225C2×C4—448no—
1226C2×C4—448no—
1227C2×C4—448no—
1228C2×C4—448no—
1229C2×C4—448no—
1230C2×C4—444no—
1231C2×C4#6704314yes—
1232C2×C4C24×D1112yes—
1233C2×C4C24×D1114yes—
1234C2×C4C24×D1112yes—
1235C2×C4C24×D1114yes—
1236C2×C4C24×D1112yes—
1237C2×C4C24×D1112yes—
1238C2×C4C24×D1114yes—
1239C2×C4C24×D1112yes—
1240C22—22no—
1241C22—24no—
1242C22—22no—
1243C22—22no—
1244C22—22no—
1245C22—24no—
1246C22—24no—
1247C22—22no—
1248C22—22no—
1249C22—44no—
1250C22—44no—
1251C22—48no—
1252C22—224no—
1253C22—222no—
1254C22—222no—
1255C22—224no—
1256C22—222no—
1257C22—224no—
1258C22—444no—
1259C22—448no—
1260C22C2×#6704312yes—
1261C22#1062345312yes—
1262C22D11×H(5,𝔽2)12yes—
1263C22C25×D1111yescharacteristic
1264C4—24no—
1265C4—24no—
1266C4—22no—
1267C4—22no—
1268C4—22no—
1269C4—22no—
1270C4—24no—
1271C4—114no—
1272C4—224no—
1273C4—222no—
1274C4—224no—
1275C4—222no—
1276C4—222no—
1277C4—222no—
1278C4—222no—
1279C4—224no—
1280C4—222no—
1281C4C2×#6704314yes—
1282C2—42no—
1283C2—44no—
1284C2—42no—
1285C2—444no—
1286C2—442no—
1287C2#1308299214yesdirect product factor
1288C2C2×D11×H(5,𝔽2)11yescharacteristic
1289C2C22×#6704311yescharacteristic
1290C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#555C2
socleC23×C11C25
hypercenterC2×#555D11
hypocenterC11C2×#3547
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#555

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13082992C2direct (N × H)
2. C2×#10623152C2semidirect
3. C2×#10623215C2semidirect
4. C2×#10623147C2semidirect
5. C2×#10623063C2semidirect
6. C2×#10623070C2semidirect
7. C2×#10623096C2semidirect
8. C2×#10623061C2semidirect
9. C2×#10623062C2semidirect
10. C2×#10623258C2semidirect
11. C2×#10623208C2semidirect
12. C2×#10623142C2semidirect
13. C2×#10623050C2semidirect
14. C2×#10623260C2semidirect
15. C2×#10623065C2semidirect
16. C2×#10623200C2semidirect
17. C2×#10623150C2semidirect
18. C2×#10623093C2semidirect
19. C2×#10623128C2semidirect
20. C2×#10623206C2semidirect
21. C2×#10623048C2semidirect
22. C2×#10623127C2semidirect
23. C2×#10623069C2semidirect
24. C2×C11×#555C2semidirect
28. C11×#555C22semidirect
68. #10623260C22semidirect
69. #10623258C22semidirect
70. #10623215C22semidirect
71. #10623208C22semidirect
72. #10623206C22semidirect
73. #10623200C22semidirect
74. #10623152C22semidirect
75. #10623150C22semidirect
76. #10623147C22semidirect
77. #10623142C22semidirect
78. #10623128C22semidirect
79. #10623127C22semidirect
80. #10623096C22semidirect
81. #10623093C22semidirect
82. #10623070C22semidirect
83. #10623069C22semidirect
84. #10623065C22semidirect
85. #10623063C22semidirect
86. #10623062C22semidirect
87. #10623061C22semidirect
88. #10623050C22semidirect
89. #10623048C22semidirect
511. C2×#555D11semidirect
626. #555C2×D11semidirect
987. C2×C11#3547semidirect
1150. C11C2×#3547semidirect
1287. C2#13082992direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130829922
C2×#106231522
C2×#106232152
C2×#106231472
C2×#106230632
C2×#106230702
C2×#106230962
C2×#106230612
C2×#106230622
C2×#106232582
C2×#106232082
C2×#106231422
C2×#106230502
C2×#106232602
C2×#106230652
C2×#106232002
C2×#106231502
C2×#106230932
C2×#106231282
C2×#106232062
C2×#106230482
C2×#106231272
C2×#106230692
C2×C11×#5552
C2×#354711