Finite Group Databasebeta

← C2×#13083002 #15661464

Subgroups — C2×#13083002 #15661464

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#13083002C2132yesmaximal, direct product factor
2C2×#10623231C212yesmaximal, complemented
3C2×#10623178C212yesmaximal, complemented
4C2×#10623265C211yesmaximal, characteristic, complemented
5C2×#10623063C211yesmaximal, characteristic, complemented
6C2×#10623063C211yesmaximal, characteristic, complemented
7C2×#10623221C211yesmaximal, characteristic, complemented
8C2×#10623226C211yesmaximal, characteristic, complemented
9C2×#10623045C211yesmaximal, characteristic, complemented
10C2×#10623224C212yesmaximal, complemented
11C2×#10623258C211yesmaximal, characteristic, complemented
12C2×#10623164C212yesmaximal, complemented
13C2×#10623038C211yesmaximal, characteristic, complemented
14C2×#10623260C211yesmaximal, characteristic, complemented
15C2×#10623264C212yesmaximal, complemented
16C2×#10623171C212yesmaximal, complemented
17C2×#10623229C211yesmaximal, characteristic, complemented
18C2×#10623066C211yesmaximal, characteristic, complemented
19C2×#10623160C212yesmaximal, complemented
20C2×#10623255C212yesmaximal, complemented
21C2×#10623219C211yesmaximal, characteristic, complemented
22C2×#10623256C211yesmaximal, characteristic, complemented
23C2×#10623059C211yesmaximal, characteristic, complemented
24C2×C11×#544C211yesmaximal, characteristic, complemented
25C22×#4343C2212yes—
26C22×Q8×D11C2212yes—
27C22×#4339C2212yes—
28C11×#544C22116yescomplemented
29C2×C11×C4⋊Q8C2211yescharacteristic
30C2×C11×C4⋊Q8C2211yescharacteristic
31C2×C11×C4⋊Q8C2212yes—
32C2×C11×#125C2212yes—
33C2×C11×#125C2211yescharacteristic
34C2×C11×#125C2211yescharacteristic
35C2×C11×C22⋊Q8C2212yes—
36C2×C11×C22⋊Q8C2212yes—
37C2×C11×#117C2211yescharacteristic
38C2×C11×#117C2211yescharacteristic
39C22×C11×C4⋊C4C2211yescharacteristic
40C2×#67000C2212yes—
41C2×#67000C2212yes—
42C2×#67000C2212yes—
43C2×#66999C2212yes—
44C2×#66999C2212yes—
45C2×#66997C2212yes—
46C2×#66983C2211yescharacteristic
47C2×#66983C2212yes—
48C2×#66983C2211yescharacteristic
49C2×#66982C2212yes—
50C2×C4×C22⋊D11C2211yescharacteristic
51C2×C4×C22⋊D11C2211yescharacteristic
52C2×C4×C22⋊D11C2212yes—
53#10623265C22116yescomplemented
54#10623264C22132yescomplemented
55#10623260C22116yescomplemented
56#10623258C22116yescomplemented
57#10623256C22116yescomplemented
58#10623255C22132yescomplemented
59#10623231C22132yescomplemented
60#10623229C22116yescomplemented
61#10623226C22116yescomplemented
62#10623224C22132yescomplemented
63#10623221C22116yescomplemented
64#10623219C22116yescomplemented
65#10623178C22132yescomplemented
66#10623171C22132yescomplemented
67#10623164C22132yescomplemented
68#10623160C22132yescomplemented
69#10623066C22116yescomplemented
70#10623063C22116yescomplemented
71#10623063C22116yescomplemented
72#10623059C22116yescomplemented
73#10623045C22116yescomplemented
74C2×#66951C2212yes—
75C2×#66951C2212yes—
76C2×#66951C2211yescharacteristic
77C2×#66950C2212yes—
78C2×#66949C2212yes—
79C2×#66949C2212yes—
80C2×#66949C2211yescharacteristic
81C2×#66949C2212yes—
82C2×#66949C2212yes—
83C2×#66949C2212yes—
84C2×#66949C2212yes—
85C2×#66949C2212yes—
86C2×#66949C2212yes—
87#10623038C22116yescomplemented
88C2×#66948C2211yescharacteristic
89C2×#66948C2211yescharacteristic
90C2×#66948C2212yes—
91C2×#66948C2211yescharacteristic
92C2×#66948C2212yes—
93C2×#66948C2212yes—
94C2×#66948C2211yescharacteristic
95C2×#66948C2212yes—
96C2×#66948C2212yes—
97C2×#66947C2212yes—
98C2×#66947C2212yes—
99C2×#66947C2211yescharacteristic
100C2×#66947C2212yes—
101C2×#66947C2212yes—
102C2×#66947C2212yes—
103C2×#66947C2212yes—
104C2×#66947C2212yes—
105C2×#66946C2212yes—
106C2×#66946C2211yescharacteristic
107C2×#66946C2212yes—
108C2×#66946C2211yescharacteristic
109C2×#66946C2211yescharacteristic
110C2×#66946C2211yescharacteristic
111C2×#66945C2212yes—
112C2×#66945C2211yescharacteristic
113C2×#66945C2211yescharacteristic
114C2×#66945C2211yescharacteristic
115C2×C4⋊C4×D11C2212yes—
116C2×C4⋊C4×D11C2211yescharacteristic
117C2×#66943C2211yescharacteristic
118C2×#66942C2211yescharacteristic
119C2×#66942C2212yes—
120C2×#66941C2211yescharacteristic
121C2×#66941C2211yescharacteristic
122C2×#66941C2211yescharacteristic
123C2×#66940C2212yes—
124C2×#66940C2212yes—
125C2×#66938C2211yescharacteristic
126C2×#66938C2212yes—
127C2×#66938C2212yes—
128C2×#66937C2211yescharacteristic
129C2×#66937C2212yes—
130C2×#66937C2212yes—
131C2×#66937C2212yes—
132C2×#66937C2212yes—
133C2×#66936C2211yescharacteristic
134C2×#66932C2211yescharacteristic
135C2×#66928C2212yes—
136C2×#66928C2212yes—
137C2×#66927C2211yescharacteristic
138C2×C4×D44C2211yescharacteristic
139C2×C4×D44C2211yescharacteristic
140C2×C4×D44C2211yescharacteristic
141C2×#66925C2212yes—
142C2×#66925C2212yes—
143C2×#66925C2211yescharacteristic
144C2×C42×D11C2211yescharacteristic
145C2×#66923C2211yescharacteristic
146C2×C4×Dic22C2211yescharacteristic
147C22×Q8×C11C2312yes—
148C22×Q8×C11C2312yes—
149C23×C4×C11C2311yescharacteristic
150C23×C4×C11C2312yes—
151C22×C22⋊D11C2311yescharacteristic
152C22×C22⋊D11C2311yescharacteristic
153C22×C22⋊D11C2312yes—
154C22×C22⋊D11C2312yes—
155C2×#4343—48no—
156C2×#4343C23116yes—
157C2×Q8×D11—48no—
158C2×Q8×D11C23116yes—
159C2×#4339—48no—
160C2×#4339C23116yes—
161C22×D44C2311yescharacteristic
162C22×D44C2311yescharacteristic
163C22×D44C2311yescharacteristic
164C22×D44C2312yes—
165C22×D44C2312yes—
166C22×D44C2312yes—
167C22×D44C2312yes—
168C22×D44C2312yes—
169C22×D44C2312yes—
170C22×C4×D11C2311yescharacteristic
171C22×C4×D11C2311yescharacteristic
172C22×C4×D11C2311yescharacteristic
173C22×C4×D11C2312yes—
174C22×C4×D11C2312yes—
175C22×C4×D11C2311yescharacteristic
176C22×C4×D11C2312yes—
177C22×C4×D11C2312yes—
178C22×C4×D11C2312yes—
179C22×C4×D11C2312yes—
180C22×C4×D11C2312yes—
181C22×Dic22C2311yescharacteristic
182C22×Dic22C2312yes—
183C22×Dic22C2312yes—
184C22×Dic22C2312yes—
185C11×C4⋊Q8C23116yes—
186C11×C4⋊Q8C2318yes—
187C11×C4⋊Q8C2318yes—
188C11×#125C2318yes—
189C11×#125C2318yes—
190C11×#125C23116yes—
191C11×C22⋊Q8C23116yes—
192C11×C22⋊Q8C23116yes—
193C11×#117C2318yes—
194C11×#117C2318yes—
195C2×C11×C4⋊C4C2312yes—
196C2×C11×C4⋊C4C2312yes—
197C2×C11×C4⋊C4C2311yescharacteristic
198C2×C11×C4⋊C4C2311yescharacteristic
199C2×C11×C4⋊C4C2311yescharacteristic
200C2×C11×C4⋊C4C2312yes—
201C2×C11×C4⋊C4C2311yescharacteristic
202C2×C11×C4⋊C4C2311yescharacteristic
203C2×C11×C4⋊C4C2312yes—
204C2×C11×C4⋊C4C2312yes—
205C2×C11×C4⋊C4C2312yes—
206C2×C11×C4⋊C4C2312yes—
207C2×C11×C4⋊C4C2311yescharacteristic
208C2×C11×C4⋊C4C2318yes—
209C2×C11×C22⋊C4C2311yescharacteristic
210C2×C11×C22⋊C4C2311yescharacteristic
211C2×C11×C22⋊C4C2312yes—
212C2×C42×C11C2311yescharacteristic
213C2×C42×C11C2311yescharacteristic
214C2×C42×C11C2312yes—
215C2×C22⋊Dic11C2311yescharacteristic
216C2×C22⋊Dic11C2311yescharacteristic
217#67000C23116yes—
218#67000C23116yes—
219#67000C23116yes—
220#66999C23116yes—
221#66999C23116yes—
222#66997C23116yes—
223#66983C2318yes—
224#66983C2318yes—
225#66983C23116yes—
226#66982C23116yes—
227C4×C22⋊D11C2318yes—
228C4×C22⋊D11C2318yes—
229C4×C22⋊D11C23116yes—
230C2×(C2×D11)⋊C4C2312yes—
231C2×(C2×D11)⋊C4C2312yes—
232C2×(C2×D11)⋊C4C2311yescharacteristic
233C2×(C2×D11)⋊C4C2312yes—
234C2×(C2×D11)⋊C4C2312yes—
235C2×(C2×D11)⋊C4C2311yescharacteristic
236C2×(C2×D11)⋊C4C2311yescharacteristic
237C2×(C2×D11)⋊C4C2312yes—
238C2×(C2×D11)⋊C4C2312yes—
239C2×(C2×D11)⋊C4C2311yescharacteristic
240C2×(C2×D11)⋊C4C2311yescharacteristic
241C2×(C2×D11)⋊C4C2311yescharacteristic
242C2×(C2×D11)⋊C4C2312yes—
243C2×(C2×D11)⋊C4C2312yes—
244C2×(C2×D11)⋊C4C2312yes—
245C2×(C2×D11)⋊C4C2312yes—
246C2×(C2×D11)⋊C4C2312yes—
247C2×(C2×D11)⋊C4C2312yes—
248C2×(C2×D11)⋊C4C2312yes—
249C2×(C2×D11)⋊C4C2312yes—
250C2×(C2×D11)⋊C4C2312yes—
251C2×C4⋊Dic11C2311yescharacteristic
252C2×C4⋊Dic11C2311yescharacteristic
253C2×C4⋊Dic11C2311yescharacteristic
254C2×C4⋊Dic11C2311yescharacteristic
255C2×C4⋊Dic11C2312yes—
256C2×Dic11⋊C4C2311yescharacteristic
257C2×Dic11⋊C4C2311yescharacteristic
258C2×Dic11⋊C4C2312yes—
259C2×Dic11⋊C4C2312yes—
260C2×Dic11⋊C4C2311yescharacteristic
261C2×Dic11⋊C4C2311yescharacteristic
262C2×Dic11⋊C4C2311yescharacteristic
263C2×Dic11⋊C4C2311yescharacteristic
264C2×Dic11⋊C4C2312yes—
265C2×Dic11⋊C4C2312yes—
266C2×Dic11⋊C4C2312yes—
267C2×Dic11⋊C4C2312yes—
268C2×Dic11⋊C4C2312yes—
269C2×C4×Dic11C2311yescharacteristic
270C2×C4×Dic11C2311yescharacteristic
271C2×C4×Dic11C2311yescharacteristic
272C2×C4×Dic11C2311yescharacteristic
273C2×C4×Dic11C2312yes—
274C2×C4×Dic11C2312yes—
275C2×C4×Dic11C2312yes—
276#66951C2318yes—
277#66951C23116yes—
278#66951C23116yes—
279#66950C23116yes—
280#66949C2318yes—
281#66949C23116yes—
282#66949C23116yes—
283#66949C23116yes—
284#66949C23116yes—
285#66949C23116yes—
286#66949C23116yes—
287#66949C23116yes—
288#66949C23116yes—
289#66948C2318yes—
290#66948C2318yes—
291#66948C23116yes—
292#66948C23116yes—
293#66948C2318yes—
294#66948C23116yes—
295#66948C2318yes—
296#66948C23116yes—
297#66948C23116yes—
298#66947C23116yes—
299#66947C23116yes—
300#66947C23116yes—
301#66947C23116yes—
302#66947C23116yes—
303#66947C2318yes—
304#66947C23116yes—
305#66947C23116yes—
306#66946C2318yes—
307#66946C2318yes—
308#66946C23116yes—
309#66946C2318yes—
310#66946C23116yes—
311#66946C2318yes—
312#66945C2318yes—
313#66945C2318yes—
314#66945C23116yes—
315#66945C2318yes—
316C4⋊C4×D11C2318yes—
317C4⋊C4×D11C23116yes—
318#66943C2318yes—
319#66942C23116yes—
320#66942C2318yes—
321#66941C2318yes—
322#66941C2318yes—
323#66941C2318yes—
324#66940C23116yes—
325#66940C23116yes—
326#66938C2318yes—
327#66938C23116yes—
328#66938C23116yes—
329#66937C2318yes—
330#66937C23116yes—
331#66937C23116yes—
332#66937C23116yes—
333#66937C23116yes—
334#66936C2318yes—
335#66932C2318yes—
336#66928C23116yes—
337#66928C23116yes—
338#66927C2318yes—
339C4×D44C2318yes—
340C4×D44C2318yes—
341C4×D44C2318yes—
342#66925C23116yes—
343#66925C2318yes—
344#66925C23116yes—
345C42×D11C2318yes—
346#66923C2318yes—
347C4×Dic22C2318yes—
348C2×#3547—111nomaximal, Sylow
349C24×C11C2411yescharacteristic
350C23×D11C2412yes—
351C23×D11C2411yescharacteristic
352C23×D11C2412yes—
353C23×D11C2411yescharacteristic
354C2×Q8×C11—44no—
355C2×Q8×C11—44no—
356C2×Q8×C11C2418yes—
357C2×Q8×C11C2418yes—
358C22×C4×C11—24no—
359C22×C4×C11—44no—
360C22×C4×C11C2411yescharacteristic
361C22×C4×C11C2411yescharacteristic
362C22×C4×C11C2412yes—
363C22×C4×C11C2412yes—
364C22×C4×C11C2412yes—
365C22×C4×C11C2411yescharacteristic
366C22×C4×C11C2412yes—
367C22×C4×C11C2411yescharacteristic
368C22×C4×C11C2411yescharacteristic
369C22×C4×C11C2414yes—
370C22×C4×C11C2418yes—
371C22×C4×C11C2411yescharacteristic
372C2×C22⋊D11—24no—
373C2×C22⋊D11—44no—
374C2×C22⋊D11—42no—
375C2×C22⋊D11—44no—
376C2×C22⋊D11C2414yes—
377C2×C22⋊D11C2414yes—
378C2×C22⋊D11C2418yes—
379C2×C22⋊D11C2418yes—
380C22×Dic11C2411yescharacteristic
381C22×Dic11C2411yescharacteristic
382C22×Dic11C2412yes—
383C22×Dic11C2411yescharacteristic
384C22×Dic11C2411yescharacteristic
385C22×Dic11C2412yes—
386C22×Dic11C2411yescharacteristic
387C22×Dic11C2411yescharacteristic
388#4343—432no—
389Q8×D11—432no—
390#4339—432no—
391C2×D44—24no—
392C2×D44—24no—
393C2×D44—44no—
394C2×D44—42no—
395C2×D44—44no—
396C2×D44—44no—
397C2×D44—44no—
398C2×D44—44no—
399C2×D44—44no—
400C2×D44C2414yes—
401C2×D44C2414yes—
402C2×D44C2414yes—
403C2×D44C2418yes—
404C2×D44C2418yes—
405C2×D44C2418yes—
406C2×D44C2418yes—
407C2×D44C2418yes—
408C2×D44C2418yes—
409C2×C4×D11—28no—
410C2×C4×D11—28no—
411C2×C4×D11—24no—
412C2×C4×D11—24no—
413C2×C4×D11—24no—
414C2×C4×D11—44no—
415C2×C4×D11—44no—
416C2×C4×D11—42no—
417C2×C4×D11—44no—
418C2×C4×D11—44no—
419C2×C4×D11—44no—
420C2×C4×D11C2414yes—
421C2×C4×D11C2414yes—
422C2×C4×D11C2414yes—
423C2×C4×D11C2418yes—
424C2×C4×D11C2418yes—
425C2×C4×D11C2414yes—
426C2×C4×D11C2418yes—
427C2×C4×D11C2418yes—
428C2×C4×D11C2418yes—
429C2×C4×D11C2418yes—
430C2×C4×D11C2418yes—
431C2×Dic22—28no—
432C2×Dic22—24no—
433C2×Dic22—44no—
434C2×Dic22—44no—
435C2×Dic22C2414yes—
436C2×Dic22C2418yes—
437C2×Dic22C2418yes—
438C2×Dic22C2418yes—
439C11×C4⋊C4C2418yes—
440C11×C4⋊C4C2418yes—
441C11×C4⋊C4C2414yes—
442C11×C4⋊C4C2414yes—
443C11×C4⋊C4C2414yes—
444C11×C4⋊C4C2418yes—
445C11×C4⋊C4C2414yes—
446C11×C4⋊C4C2414yes—
447C11×C4⋊C4C2418yes—
448C11×C4⋊C4C2418yes—
449C11×C4⋊C4C2418yes—
450C11×C4⋊C4C2418yes—
451C11×C4⋊C4C2414yes—
452C11×C22⋊C4C2414yes—
453C11×C22⋊C4C2414yes—
454C11×C22⋊C4C2418yes—
455C42×C11C2414yes—
456C42×C11C2414yes—
457C42×C11C2418yes—
458C22⋊Dic11C2414yes—
459C22⋊Dic11C2414yes—
460(C2×D11)⋊C4C2418yes—
461(C2×D11)⋊C4C2418yes—
462(C2×D11)⋊C4C2414yes—
463(C2×D11)⋊C4C2418yes—
464(C2×D11)⋊C4C2418yes—
465(C2×D11)⋊C4C2414yes—
466(C2×D11)⋊C4C2414yes—
467(C2×D11)⋊C4C2418yes—
468(C2×D11)⋊C4C2418yes—
469(C2×D11)⋊C4C2414yes—
470(C2×D11)⋊C4C2414yes—
471(C2×D11)⋊C4C2414yes—
472(C2×D11)⋊C4C2418yes—
473(C2×D11)⋊C4C2418yes—
474(C2×D11)⋊C4C2418yes—
475(C2×D11)⋊C4C2418yes—
476(C2×D11)⋊C4C2418yes—
477(C2×D11)⋊C4C2418yes—
478(C2×D11)⋊C4C2418yes—
479(C2×D11)⋊C4C2418yes—
480(C2×D11)⋊C4C2418yes—
481C4⋊Dic11C2414yes—
482C4⋊Dic11C2414yes—
483C4⋊Dic11C2414yes—
484C4⋊Dic11C2414yes—
485C4⋊Dic11C2418yes—
486Dic11⋊C4C2414yes—
487Dic11⋊C4C2414yes—
488Dic11⋊C4C2418yes—
489Dic11⋊C4C2418yes—
490Dic11⋊C4C2414yes—
491Dic11⋊C4C2414yes—
492Dic11⋊C4C2414yes—
493Dic11⋊C4C2414yes—
494Dic11⋊C4C2418yes—
495Dic11⋊C4C2418yes—
496Dic11⋊C4C2418yes—
497Dic11⋊C4C2418yes—
498Dic11⋊C4C2418yes—
499C4×Dic11C2414yes—
500C4×Dic11C2414yes—
501C4×Dic11C2414yes—
502C4×Dic11C2414yes—
503C4×Dic11C2418yes—
504C4×Dic11C2418yes—
505C4×Dic11C2418yes—
506#3547—1132no—
507C2×#562—112no—
508C2×#562—112no—
509C2×#555—111no—
510C2×#555—111no—
511C2×#555—111no—
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×#544D1111yescharacteristic, complemented
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—22no—
532C23×C11—22no—
533C23×C11C2512yes—
534C23×C11C2511yescharacteristic
535C22×D11—24no—
536C22×D11—22no—
537C22×D11—24no—
538C22×D11—22no—
539C22×D11—22no—
540C22×D11—22no—
541C22×D11—24no—
542C22×D11—24no—
543C22×D11—24no—
544C22×D11—22no—
545C22×D11—22no—
546C22×D11—24no—
547C22×D11C2514yes—
548C22×D11C2512yes—
549C22×D11C2514yes—
550C22×D11C2512yes—
551Q8×C11—48no—
552Q8×C11—48no—
553C2×C4×C11—22no—
554C2×C4×C11—24no—
555C2×C4×C11—24no—
556C2×C4×C11—24no—
557C2×C4×C11—22no—
558C2×C4×C11—22no—
559C2×C4×C11—24no—
560C2×C4×C11—22no—
561C2×C4×C11—22no—
562C2×C4×C11—28no—
563C2×C4×C11—48no—
564C2×C4×C112−1+414yes—
565C2×C4×C11C2512yes—
566C2×C4×C11C2512yes—
567C2×C4×C11C2514yes—
568C2×C4×C11C2514yes—
569C2×C4×C11C2514yes—
570C2×C4×C11C2512yes—
571C2×C4×C11C2514yes—
572C2×C4×C11C2512yes—
573C2×C4×C11C2512yes—
574C2×C4×C11C2512yes—
575C22⋊D11—28no—
576C22⋊D11—48no—
577C22⋊D11—48no—
578C22⋊D11—44no—
579C2×Dic11—22no—
580C2×Dic11—24no—
581C2×Dic11—22no—
582C2×Dic11—22no—
583C2×Dic11—22no—
584C2×Dic11—24no—
585C2×Dic11—22no—
586C2×Dic11H(5,𝔽2)14yes—
587C2×Dic11C2512yes—
588C2×Dic11C2512yes—
589C2×Dic11C2514yes—
590C2×Dic11C2512yes—
591C2×Dic11C2512yes—
592C2×Dic11C2514yes—
593C2×Dic11C2512yes—
594C2×Dic11C2512yes—
595D44—28no—
596D44—28no—
597D44—48no—
598D44—44no—
599D44—48no—
600D44—48no—
601D44—48no—
602D44—48no—
603D44—48no—
604C4×D11—28no—
605C4×D11—28no—
606C4×D11—216no—
607C4×D11—216no—
608C4×D11—28no—
609C4×D11—44no—
610C4×D11—48no—
611C4×D11—48no—
612C4×D11—48no—
613C4×D11—48no—
614C4×D11—48no—
615Dic22—216no—
616Dic22—28no—
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#555—1116no—
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#544C2×D11116yescomplemented
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⋊Q8C2×D1111yescharacteristic
649C2×C4⋊Q8C2×D1112yes—
650C2×C4⋊Q8C2×D1111yescharacteristic
651C2×#127—111no—
652#529—1116no—
653C2×#126—111no—
654C2×#126—112no—
655C2×#126—112no—
656C2×#126—111no—
657C2×#125—111no—
658C2×#125—112no—
659C2×#125—111no—
660C2×#125—111no—
661C2×#125C2×D1111yescharacteristic
662C2×#125C2×D1112yes—
663C2×#125C2×D1111yescharacteristic
664C2×#124—112no—
665C2×#124—112no—
666C2×#124—112no—
667C2×#124—111no—
668C2×#124—112no—
669C2×#124—112no—
670C2×#124—112no—
671C2×#124—112no—
672C2×#123—112no—
673C2×#123—111no—
674C2×#123—112no—
675C2×#123—112no—
676C2×#123—112no—
677C2×#123—112no—
678C2×#123—112no—
679C2×#123—112no—
680C2×#123—112no—
681C2×#123—111no—
682C2×C22⋊Q8—112no—
683C2×C22⋊Q8—112no—
684C2×C22⋊Q8—111no—
685C2×C22⋊Q8—112no—
686C2×C22⋊Q8—112no—
687C2×C22⋊Q8—112no—
688C2×C22⋊Q8—112no—
689C2×C22⋊Q8—112no—
690C2×C22⋊Q8—112no—
691C2×C22⋊Q8—112no—
692C2×C22⋊Q8—112no—
693C2×C22⋊Q8—112no—
694C2×C22⋊Q8C2×D1112yes—
695C2×C22⋊Q8C2×D1112yes—
696C2×#121—112no—
697C2×#121—111no—
698C2×#121—111no—
699C2×#121—111no—
700C2×#121—111no—
701C2×#121—112no—
702C2×#121—112no—
703C2×#121—112no—
704C2×#121—112no—
705C2×#121—111no—
706C2×#121—112no—
707C2×#121—111no—
708C2×#121—111no—
709C2×#121—112no—
710C2×#121—112no—
711C2×#121—112no—
712C2×#121—112no—
713C2×C4×Q8—112no—
714C2×C4×Q8—112no—
715C2×C4×Q8—111no—
716C2×C4×D4—111no—
717C2×C4×D4—111no—
718C2×C4×D4—112no—
719C2×C4×D4—111no—
720C2×C4×D4—112no—
721C2×C4×D4—111no—
722C2×C4×D4—111no—
723C2×C4×D4—111no—
724C2×C4×D4—112no—
725C2×C4×D4—111no—
726C2×C4×D4—111no—
727C2×C4×D4—111no—
728C2×#117—111no—
729C2×#117—111no—
730C2×#117—112no—
731C2×#117—111no—
732C2×#117—111no—
733C2×#117—112no—
734C2×#117—112no—
735C2×#117C2×D1111yescharacteristic
736C2×#117C2×D1111yescharacteristic
737C22×C4⋊C4—112no—
738C22×C4⋊C4—111no—
739C22×C4⋊C4C2×D1111yescharacteristic
740C22×C42—111no—
741C22×C11—22no—
742C22×C11—22no—
743C22×C11—22no—
744C22×C11—44no—
745C22×C11C2×H(5,𝔽2)12yes—
746C22×C11C2×2−1+412yes—
747C22×C11#58512yes—
748C22×C11C2611yescharacteristic
749C2×D11—24no—
750C2×D11—22no—
751C2×D11—24no—
752C2×D11—22no—
753C2×D11—22no—
754C2×D11—22no—
755C2×D11—24no—
756C2×D11—24no—
757C2×D11—24no—
758C2×D11—22no—
759C2×D11—22no—
760C2×D11—24no—
761C2×D11—48no—
762C2×D11—44no—
763C2×D11—48no—
764C2×D11—44no—
765C4×C11—24no—
766C4×C11—24no—
767C4×C11—22no—
768C4×C11—24no—
769C4×C11—22no—
770C4×C11—22no—
771C4×C11—24no—
772C4×C11—22no—
773C4×C11—22no—
774C4×C11C2×2−1+414yes—
775Dic11—22no—
776Dic11—24no—
777Dic11—22no—
778Dic11—22no—
779Dic11—22no—
780Dic11—24no—
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—448no—
793C22×Q8C22×D1112yes—
794C22×Q8C22×D1112yes—
795C22×D4—111no—
796C22×D4—111no—
797C22×D4—112no—
798C22×D4—112no—
799C22×D4—111no—
800C22×D4—111no—
801C22×D4—111no—
802C22×D4—112no—
803C22×D4—112no—
804C22×D4—112no—
805C22×D4—112no—
806C22×D4—112no—
807C22×D4—112no—
808C23×C4—111no—
809C23×C4—112no—
810C23×C4—111no—
811C23×C4—112no—
812C23×C4—111no—
813C23×C4—112no—
814C23×C4—112no—
815C23×C4—112no—
816C23×C4—112no—
817C23×C4—112no—
818C23×C4—111no—
819C23×C4C22×D1111yescharacteristic
820C23×C4C22×D1112yes—
821C4⋊Q8—1116no—
822C4⋊Q8—118no—
823C4⋊Q8—118no—
824C4⋊Q8—118no—
825C4⋊Q8C22×D1118yes—
826C4⋊Q8C22×D11116yes—
827C4⋊Q8C22×D1118yes—
828#127—118no—
829#126—118no—
830#126—1116no—
831#126—1116no—
832#126—118no—
833#125—118no—
834#125—1116no—
835#125—118no—
836#125—118no—
837#125C22×D1118yes—
838#125C22×D11116yes—
839#125C22×D1118yes—
840#124—1116no—
841#124—1116no—
842#124—1116no—
843#124—118no—
844#124—1116no—
845#124—1116no—
846#124—1116no—
847#124—1116no—
848#123—1116no—
849#123—118no—
850#123—1116no—
851#123—1116no—
852#123—1116no—
853#123—1116no—
854#123—1116no—
855#123—1116no—
856#123—1116no—
857#123—118no—
858C22⋊Q8—1116no—
859C22⋊Q8—1116no—
860C22⋊Q8—118no—
861C22⋊Q8—1116no—
862C22⋊Q8—1116no—
863C22⋊Q8—1116no—
864C22⋊Q8—1116no—
865C22⋊Q8—1116no—
866C22⋊Q8—1116no—
867C22⋊Q8—1116no—
868C22⋊Q8—1116no—
869C22⋊Q8—1116no—
870C22⋊Q8C22×D11116yes—
871C22⋊Q8C22×D11116yes—
872#121—1116no—
873#121—118no—
874#121—118no—
875#121—118no—
876#121—118no—
877#121—1116no—
878#121—1116no—
879#121—1116no—
880#121—1116no—
881#121—118no—
882#121—1116no—
883#121—118no—
884#121—118no—
885#121—1116no—
886#121—1116no—
887#121—1116no—
888#121—1116no—
889C4×Q8—1116no—
890C4×Q8—1116no—
891C4×Q8—118no—
892C4×D4—118no—
893C4×D4—118no—
894C4×D4—1116no—
895C4×D4—118no—
896C4×D4—1116no—
897C4×D4—118no—
898C4×D4—118no—
899C4×D4—118no—
900C4×D4—1116no—
901C4×D4—118no—
902C4×D4—118no—
903C4×D4—118no—
904#117—118no—
905#117—118no—
906#117—1116no—
907#117—118no—
908#117—118no—
909#117—1116no—
910#117—1116no—
911#117C22×D1118yes—
912#117C22×D1118yes—
913C2×C4⋊C4—111no—
914C2×C4⋊C4—111no—
915C2×C4⋊C4—112no—
916C2×C4⋊C4—112no—
917C2×C4⋊C4—112no—
918C2×C4⋊C4—111no—
919C2×C4⋊C4—111no—
920C2×C4⋊C4—111no—
921C2×C4⋊C4—111no—
922C2×C4⋊C4—112no—
923C2×C4⋊C4—111no—
924C2×C4⋊C4—111no—
925C2×C4⋊C4—112no—
926C2×C4⋊C4—112no—
927C2×C4⋊C4—112no—
928C2×C4⋊C4—111no—
929C2×C4⋊C4—111no—
930C2×C4⋊C4—112no—
931C2×C4⋊C4—1116no—
932C2×C4⋊C4—118no—
933C2×C4⋊C4C22×D1111yescharacteristic
934C2×C4⋊C4C22×D1112yes—
935C2×C4⋊C4C22×D1111yescharacteristic
936C2×C4⋊C4C22×D1112yes—
937C2×C4⋊C4C22×D1118yes—
938C2×C4⋊C4C22×D1111yescharacteristic
939C2×C4⋊C4C22×D1111yescharacteristic
940C2×C4⋊C4C22×D1112yes—
941C2×C4⋊C4C22×D1111yescharacteristic
942C2×C4⋊C4C22×D1111yescharacteristic
943C2×C4⋊C4C22×D1112yes—
944C2×C4⋊C4C22×D1112yes—
945C2×C4⋊C4C22×D1112yes—
946C2×C4⋊C4C22×D1112yes—
947C2×C22⋊C4—111no—
948C2×C22⋊C4—111no—
949C2×C22⋊C4—112no—
950C2×C22⋊C4—111no—
951C2×C22⋊C4—112no—
952C2×C22⋊C4—111no—
953C2×C22⋊C4—112no—
954C2×C22⋊C4—112no—
955C2×C22⋊C4—112no—
956C2×C22⋊C4—112no—
957C2×C22⋊C4—112no—
958C2×C22⋊C4—112no—
959C2×C22⋊C4—112no—
960C2×C22⋊C4—111no—
961C2×C22⋊C4—112no—
962C2×C22⋊C4—112no—
963C2×C22⋊C4—112no—
964C2×C22⋊C4—112no—
965C2×C22⋊C4—112no—
966C2×C22⋊C4—112no—
967C2×C22⋊C4—111no—
968C2×C22⋊C4—111no—
969C2×C22⋊C4—111no—
970C2×C22⋊C4C22×D1111yescharacteristic
971C2×C22⋊C4C22×D1111yescharacteristic
972C2×C22⋊C4C22×D1112yes—
973C2×C42—112no—
974C2×C42—112no—
975C2×C42—112no—
976C2×C42—111no—
977C2×C42—111no—
978C2×C42—111no—
979C2×C42—111no—
980C2×C42—118no—
981C2×C42C22×D1112yes—
982C2×C42C22×D1111yescharacteristic
983C2×C42C22×D1111yescharacteristic
984C2×C11—42no—
985C2×C11#354714yescomplemented
986C2×C11C22×H(5,𝔽2)11yescharacteristic
987C2×C11C22×2−1+411yescharacteristic
988C2×C11C2×#58511yescharacteristic
989D11—44no—
990D11—42no—
991D11—44no—
992D11—42no—
993C24—111no—
994C24—111no—
995C24—112no—
996C24—112no—
997C24C23×D1111yescharacteristic
998#41—4432no—
999#41—4432no—
1000C2×Q8—44no—
1001C2×Q8—44no—
1002C2×Q8—114no—
1003C2×Q8—118no—
1004C2×Q8—118no—
1005C2×Q8—118no—
1006C2×Q8—224no—
1007C2×Q8—228no—
1008C2×Q8—444no—
1009C2×Q8—444no—
1010C2×Q8—4432no—
1011C2×Q8C23×D1118yes—
1012C2×Q8C23×D1118yes—
1013C2×D4—114no—
1014C2×D4—114no—
1015C2×D4—118no—
1016C2×D4—118no—
1017C2×D4—114no—
1018C2×D4—114no—
1019C2×D4—114no—
1020C2×D4—118no—
1021C2×D4—118no—
1022C2×D4—118no—
1023C2×D4—118no—
1024C2×D4—118no—
1025C2×D4—118no—
1026C2×D4—224no—
1027C2×D4—224no—
1028C2×D4—224no—
1029C2×D4—444no—
1030C2×D4—444no—
1031C2×D4—444no—
1032C2×D4—444no—
1033C2×D4—442no—
1034C2×D4—444no—
1035C2×D4—444no—
1036C2×D4—444no—
1037C2×D4—442no—
1038C2×D4—444no—
1039C22×C4—24no—
1040C22×C4—44no—
1041C22×C4—111no—
1042C22×C4—111no—
1043C22×C4—111no—
1044C22×C4—111no—
1045C22×C4—112no—
1046C22×C4—111no—
1047C22×C4—111no—
1048C22×C4—112no—
1049C22×C4—114no—
1050C22×C4—114no—
1051C22×C4—114no—
1052C22×C4—118no—
1053C22×C4—118no—
1054C22×C4—114no—
1055C22×C4—118no—
1056C22×C4—118no—
1057C22×C4—118no—
1058C22×C4—118no—
1059C22×C4—118no—
1060C22×C4—228no—
1061C22×C4—228no—
1062C22×C4—224no—
1063C22×C4—224no—
1064C22×C4—224no—
1065C22×C4—444no—
1066C22×C4—444no—
1067C22×C4—444no—
1068C22×C4—444no—
1069C22×C4—442no—
1070C22×C4—444no—
1071C22×C4C23×D1114yes—
1072C22×C4C23×D1112yes—
1073C22×C4C23×D1112yes—
1074C22×C4C23×D1111yescharacteristic
1075C22×C4C23×D1111yescharacteristic
1076C22×C4C23×D1112yes—
1077C22×C4C23×D1111yescharacteristic
1078C22×C4C23×D1111yescharacteristic
1079C22×C4C23×D1111yescharacteristic
1080C22×C4C23×D1112yes—
1081C22×C4C23×D1118yes—
1082C22×C4C23×D1111yescharacteristic
1083C4⋊C4—114no—
1084C4⋊C4—114no—
1085C4⋊C4—118no—
1086C4⋊C4—118no—
1087C4⋊C4—118no—
1088C4⋊C4—114no—
1089C4⋊C4—114no—
1090C4⋊C4—114no—
1091C4⋊C4—114no—
1092C4⋊C4—118no—
1093C4⋊C4—114no—
1094C4⋊C4—114no—
1095C4⋊C4—118no—
1096C4⋊C4—118no—
1097C4⋊C4—118no—
1098C4⋊C4—114no—
1099C4⋊C4—114no—
1100C4⋊C4—118no—
1101C4⋊C4C23×D1114yes—
1102C4⋊C4C23×D1118yes—
1103C4⋊C4C23×D1114yes—
1104C4⋊C4C23×D1118yes—
1105C4⋊C4C23×D1114yes—
1106C4⋊C4C23×D1114yes—
1107C4⋊C4C23×D1118yes—
1108C4⋊C4C23×D1114yes—
1109C4⋊C4C23×D1114yes—
1110C4⋊C4C23×D1118yes—
1111C4⋊C4C23×D1118yes—
1112C4⋊C4C23×D1118yes—
1113C4⋊C4C23×D1118yes—
1114C22⋊C4—114no—
1115C22⋊C4—114no—
1116C22⋊C4—118no—
1117C22⋊C4—114no—
1118C22⋊C4—118no—
1119C22⋊C4—114no—
1120C22⋊C4—118no—
1121C22⋊C4—118no—
1122C22⋊C4—118no—
1123C22⋊C4—118no—
1124C22⋊C4—118no—
1125C22⋊C4—118no—
1126C22⋊C4—118no—
1127C22⋊C4—114no—
1128C22⋊C4—118no—
1129C22⋊C4—118no—
1130C22⋊C4—118no—
1131C22⋊C4—118no—
1132C22⋊C4—118no—
1133C22⋊C4—118no—
1134C22⋊C4—114no—
1135C22⋊C4—114no—
1136C22⋊C4—114no—
1137C22⋊C4C23×D1114yes—
1138C22⋊C4C23×D1114yes—
1139C22⋊C4C23×D1118yes—
1140C42—114no—
1141C42—114no—
1142C42—114no—
1143C42—118no—
1144C42—118no—
1145C42—118no—
1146C42—114no—
1147C42C23×D1114yes—
1148C42C23×D1118yes—
1149C42C23×D1114yes—
1150C11C2×#354711yescharacteristic, complemented, Sylow
1151C23—22no—
1152C23—22no—
1153C23—22no—
1154C23—114no—
1155C23—112no—
1156C23—114no—
1157C23—112no—
1158C23—222no—
1159C23—222no—
1160C23—224no—
1161C23—224no—
1162C23—224no—
1163C23—222no—
1164C23—224no—
1165C23—222no—
1166C23—224no—
1167C23—222no—
1168C23—222no—
1169C23—224no—
1170C23C24×D1112yes—
1171C23C24×D1111yescharacteristic
1172Q8—48no—
1173Q8—48no—
1174Q8—228no—
1175Q8—2216no—
1176Q8—448no—
1177Q8—448no—
1178D4—228no—
1179D4—228no—
1180D4—228no—
1181D4—448no—
1182D4—448no—
1183D4—448no—
1184D4—448no—
1185D4—444no—
1186D4—448no—
1187D4—448no—
1188D4—448no—
1189D4—444no—
1190D4—448no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—28no—
1201C2×C4—48no—
1202C2×C4—114no—
1203C2×C4—112no—
1204C2×C4—112no—
1205C2×C4—112no—
1206C2×C4—112no—
1207C2×C4—114no—
1208C2×C4—112no—
1209C2×C4—112no—
1210C2×C4—114no—
1211C2×C4—2216no—
1212C2×C4—2216no—
1213C2×C4—228no—
1214C2×C4—222no—
1215C2×C4—222no—
1216C2×C4—224no—
1217C2×C4—222no—
1218C2×C4—222no—
1219C2×C4—224no—
1220C2×C4—222no—
1221C2×C4—228no—
1222C2×C4—228no—
1223C2×C4—448no—
1224C2×C4—448no—
1225C2×C4—448no—
1226C2×C4—448no—
1227C2×C4—444no—
1228C2×C4—448no—
1229C2×C4#6704014yes—
1230C2×C4C24×D1114yes—
1231C2×C4C24×D1114yes—
1232C2×C4C24×D1112yes—
1233C2×C4C24×D1112yes—
1234C2×C4C24×D1114yes—
1235C2×C4C24×D1112yes—
1236C2×C4C24×D1112yes—
1237C2×C4C24×D1112yes—
1238C2×C4C24×D1114yes—
1239C2×C4C24×D1112yes—
1240C22—22no—
1241C22—22no—
1242C22—22no—
1243C22—44no—
1244C22—224no—
1245C22—222no—
1246C22—224no—
1247C22—222no—
1248C22—222no—
1249C22—222no—
1250C22—224no—
1251C22—224no—
1252C22—224no—
1253C22—222no—
1254C22—222no—
1255C22—224no—
1256C22—444no—
1257C22—444no—
1258C22—448no—
1259C22—448no—
1260C22C2×#6704012yes—
1261C22D11×H(5,𝔽2)12yes—
1262C22#1062345712yes—
1263C22C25×D1111yescharacteristic
1264C4—24no—
1265C4—24no—
1266C4—22no—
1267C4—24no—
1268C4—22no—
1269C4—22no—
1270C4—22no—
1271C4—22no—
1272C4—24no—
1273C4—114no—
1274C4—224no—
1275C4—222no—
1276C4—222no—
1277C4—222no—
1278C4—222no—
1279C4—224no—
1280C4—222no—
1281C4C2×#6704014yes—
1282C2—42no—
1283C2—444no—
1284C2—442no—
1285C2—444no—
1286C2—442no—
1287C2#1308300214yesdirect product factor
1288C2C2×D11×H(5,𝔽2)11yescharacteristic
1289C2C22×#6704011yescharacteristic
1290C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#544C2
socleC23×C11C25
hypercenterC2×#544D11
hypocenterC11C2×#3547
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #13083002C2direct (N × H)
2. C2×#10623231C2semidirect
3. C2×#10623178C2semidirect
4. C2×#10623265C2semidirect
5. C2×#10623063C2semidirect
6. C2×#10623063C2semidirect
7. C2×#10623221C2semidirect
8. C2×#10623226C2semidirect
9. C2×#10623045C2semidirect
10. C2×#10623224C2semidirect
11. C2×#10623258C2semidirect
12. C2×#10623164C2semidirect
13. C2×#10623038C2semidirect
14. C2×#10623260C2semidirect
15. C2×#10623264C2semidirect
16. C2×#10623171C2semidirect
17. C2×#10623229C2semidirect
18. C2×#10623066C2semidirect
19. C2×#10623160C2semidirect
20. C2×#10623255C2semidirect
21. C2×#10623219C2semidirect
22. C2×#10623256C2semidirect
23. C2×#10623059C2semidirect
24. C2×C11×#544C2semidirect
28. C11×#544C22semidirect
53. #10623265C22semidirect
54. #10623264C22semidirect
55. #10623260C22semidirect
56. #10623258C22semidirect
57. #10623256C22semidirect
58. #10623255C22semidirect
59. #10623231C22semidirect
60. #10623229C22semidirect
61. #10623226C22semidirect
62. #10623224C22semidirect
63. #10623221C22semidirect
64. #10623219C22semidirect
65. #10623178C22semidirect
66. #10623171C22semidirect
67. #10623164C22semidirect
68. #10623160C22semidirect
69. #10623066C22semidirect
70. #10623063C22semidirect
71. #10623063C22semidirect
72. #10623059C22semidirect
73. #10623045C22semidirect
87. #10623038C22semidirect
520. C2×#544D11semidirect
635. #544C2×D11semidirect
985. C2×C11#3547semidirect
1150. C11C2×#3547semidirect
1287. C2#13083002direct (N × H)

Maximal subgroups

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

subgroupindex
#130830022
C2×#106232312
C2×#106231782
C2×#106232652
C2×#106230632
C2×#106232212
C2×#106232262
C2×#106230452
C2×#106232242
C2×#106232582
C2×#106231642
C2×#106230382
C2×#106232602
C2×#106232642
C2×#106231712
C2×#106232292
C2×#106230662
C2×#106231602
C2×#106232552
C2×#106232192
C2×#106232562
C2×#106230592
C2×C11×#5442
C2×#354711