Finite Group Databasebeta

← C2×#13082395 #15662182

Subgroups — C2×#13082395 #15662182

Order 2816.

11126 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67043C212yesmaximal, complemented
2#13082395C2132yesmaximal, direct product factor
3C2×D4×Dic22C211yesmaximal, characteristic, complemented
4C2×#10623258C211yesmaximal, characteristic, complemented
5C2×#10623163C212yesmaximal, complemented
6C2×#10623086C211yesmaximal, characteristic, complemented
7C2×#10623038C212yesmaximal, complemented
8C2×#10623142C212yesmaximal, complemented
9C2×#10623355C212yesmaximal, complemented
10C2×#10623186C214yesmaximal, complemented
11C2×#10623159C212yesmaximal, complemented
12C2×#10623179C214yesmaximal, complemented
13C2×#10623079C211yesmaximal, characteristic, complemented
14C2×#10623127C212yesmaximal, complemented
15C22×#66941C212yesmaximal, complemented
16C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
17C2×C4×#4341C211yesmaximal, characteristic, complemented
18C2×C11×#547C211yesmaximal, characteristic, complemented
19C22×C11×#41C2212yes—
20C2×#67043—232no—
21C2×#67043C22132yescomplemented
22C22×Q8×D11C2212yes—
23C22×Q8×D11C2212yes—
24C22×#4341C2214yes—
25C22×#4341C2214yes—
26C22×#4341C2212yes—
27C22×#4341C2211yescharacteristic
28C22×#4339C2212yes—
29C22×#4339C2214yes—
30C23×Dic22C2214yes—
31C23×Dic22C2212yes—
32C11×#547C22116yescomplemented
33C2×C11×C4⋊Q8C2211yescharacteristic
34C2×C11×#123C2214yes—
35C2×C11×C22⋊Q8C2212yes—
36C2×C11×#121C2212yes—
37C2×C4×D4×C11C2211yescharacteristic
38C2×C4×D4×C11C2211yescharacteristic
39C22×C11×C4⋊C4C2212yes—
40#10623355C22132yescomplemented
41C2×#66999C2212yes—
42C2×#66997C2212yes—
43C2×#66993C2211yescharacteristic
44C2×#66992C2214yes—
45C2×#66991C2211yescharacteristic
46C2×#66988C2214yes—
47C2×D4×Dic11C2212yes—
48C2×D4×Dic11C2211yescharacteristic
49C2×#66983C2212yes—
50C2×#66982C2214yes—
51C2×C4×C22⋊D11C2212yes—
52C2×C4×C22⋊D11C2212yes—
53C22×C4⋊Dic11C2212yes—
54C2×#66977C2212yes—
55C22×Dic11⋊C4C2214yes—
56C22×C4×Dic11C2212yes—
57#10623258C22116yescomplemented
58D11×C4⋊Q8C22116yescomplemented
59#10623186C22164yescomplemented
60#10623179C22164yescomplemented
61#10623163C22132yescomplemented
62#10623159C22132yescomplemented
63#10623142C22132yescomplemented
64#10623127C22132yescomplemented
65#10623086C22116yescomplemented
66#10623079C22116yescomplemented
67D4×Dic22C22116yescomplemented
68C4×#4341C22116yescomplemented
69C2×#66950C2212yes—
70C2×#66949C2214yes—
71C2×#66949C2214yes—
72#10623038C22132yescomplemented
73C2×#66948C2211yescharacteristic
74C2×#66947C2214yes—
75C2×#66946C2212yes—
76C2×#66945C2211yescharacteristic
77C2×C4⋊C4×D11C2212yes—
78C2×C4⋊C4×D11C2212yes—
79C2×#66941C2212yes—
80C2×#66941C2212yes—
81C2×#66941C2211yescharacteristic
82C2×#66941C2214yes—
83C2×#66941C2214yes—
84C2×#66941C2212yes—
85C2×#66941C2212yes—
86C2×#66941C22132yescomplemented
87C2×#66940C2211yescharacteristic
88C2×#66939C2214yes—
89C2×#66938C2214yes—
90C2×#66938C2212yes—
91C2×#66937C2212yes—
92C2×#66936C2214yes—
93C2×(C22⋊D11)⋊C4C2214yes—
94C2×(C22⋊D11)⋊C4C2212yes—
95C2×#66931C2214yes—
96C2×#66931C2214yes—
97C2×#66930C2212yes—
98C2×C4×D44C2211yescharacteristic
99C2×C42×D11C2211yescharacteristic
100C2×#66922C2211yescharacteristic
101C2×C4×Dic22C2211yescharacteristic
102C2×C11×#41—216no—
103C2×C11×#41C23116yes—
104C22×Q8×C11C2312yes—
105C22×D4×C11C2311yescharacteristic
106C22×D4×C11C2314yes—
107C22×D4×C11C2311yescharacteristic
108C23×C4×C11C2312yes—
109C23×C4×C11C2314yes—
110C23×C4×C11C2312yes—
111C22×C22⋊D11C2312yes—
112C22×C22⋊D11C2312yes—
113C22×C22⋊D11C2312yes—
114C22×C22⋊D11C2314yes—
115C22×C22⋊D11C2312yes—
116C23×Dic11C2314yes—
117C23×Dic11C2312yes—
118C23×Dic11C2314yes—
119C23×Dic11C2312yes—
120#67043—2256no—
121C2×Q8×D11—216no—
122C2×Q8×D11—216no—
123C2×Q8×D11C23116yes—
124C2×Q8×D11C23116yes—
125C2×#4341—216no—
126C2×#4341—232no—
127C2×#4341—232no—
128C2×#4341D4116yescomplemented
129C2×#4341C23116yes—
130C2×#4341C23132yes—
131C2×#4341C23132yes—
132C2×#4341C2318yes—
133C2×#4339—232no—
134C2×#4339—216no—
135C2×#4339C23132yes—
136C2×#4339C23116yes—
137C22×D44C2311yescharacteristic
138C22×D44C2312yes—
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2312yes—
142C22×C4×D11C2314yes—
143C22×C4×D11C2314yes—
144C22×C4×D11C2311yescharacteristic
145C22×Dic22—232no—
146C22×Dic22—216no—
147C22×Dic22C2312yes—
148C22×Dic22C2314yes—
149C22×Dic22C2314yes—
150C22×Dic22C2312yes—
151C22×Dic22C2314yes—
152C22×Dic22C23132yes—
153C22×Dic22C23116yes—
154C22×Dic22C2311yescharacteristic
155C11×C4⋊Q8C2318yes—
156C11×#123C23132yes—
157C11×C22⋊Q8C23116yes—
158C11×#121C23116yes—
159C4×D4×C11C2318yes—
160C4×D4×C11C2318yes—
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2312yes—
164C2×C11×C4⋊C4C2314yes—
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C4⋊C4C23116yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2314yes—
170C2×C42×C11C2311yescharacteristic
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2314yes—
174#66999C23116yes—
175#66997C23116yes—
176#66993C2318yes—
177#66992C23132yes—
178#66991C2318yes—
179#66988C23132yes—
180D4×Dic11C2318yes—
181D4×Dic11C23116yes—
182#66983C23116yes—
183#66982C23132yes—
184C4×C22⋊D11C23116yes—
185C4×C22⋊D11C23116yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2314yes—
189C2×(C2×D11)⋊C4C2314yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×C4⋊Dic11C2311yescharacteristic
192C2×C4⋊Dic11C2312yes—
193C2×C4⋊Dic11C2312yes—
194C2×C4⋊Dic11C2311yescharacteristic
195C2×C4⋊Dic11C2314yes—
196C2×C4⋊Dic11C23116yes—
197#66977C23116yes—
198C2×Dic11⋊C4C2312yes—
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2314yes—
201C2×Dic11⋊C4C2314yes—
202C2×Dic11⋊C4C2314yes—
203C2×Dic11⋊C4C2314yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C23132yes—
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C23116yes—
213#66950C23116yes—
214#66949C23132yes—
215#66949C23132yes—
216#66948C2318yes—
217#66947C23132yes—
218#66946C23116yes—
219#66945C2318yes—
220C4⋊C4×D11C23116yes—
221C4⋊C4×D11C23116yes—
222#66941C23116yes—
223#66941C23116yes—
224#66941C23116yes—
225#66941C2318yes—
226#66941C23116yes—
227#66941C23132yes—
228#66941C23132yes—
229#66940C2318yes—
230#66939C23132yes—
231#66938C23116yes—
232#66938C23132yes—
233#66937C23116yes—
234#66936C23132yes—
235(C22⋊D11)⋊C4C23116yes—
236(C22⋊D11)⋊C4C23132yes—
237#66931C23132yes—
238#66931C23132yes—
239#66930C23116yes—
240C4×D44C2318yes—
241C42×D11C2318yes—
242#66922C2318yes—
243C4×Dic22C2318yes—
244C2×#3499—111nomaximal, Sylow
245C24×C11C2412yes—
246C24×C11C2412yes—
247C23×D11C2412yes—
248C23×D11C2411yescharacteristic
249C11×#41—264no—
250C2×Q8×C11—28no—
251C2×Q8×C11C2418yes—
252C2×D4×C11—216no—
253C2×D4×C11—24no—
254C2×D4×C11C2×D418yes—
255C2×D4×C11C2414yes—
256C2×D4×C11C24116yes—
257C2×D4×C11C2414yes—
258C22×C4×C11—216no—
259C22×C4×C11—28no—
260C22×C4×C11—28no—
261C22×C4×C11C2412yes—
262C22×C4×C11C2418yes—
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2412yes—
265C22×C4×C11C2414yes—
266C22×C4×C11C24116yes—
267C22×C4×C11C2418yes—
268C22×C4×C11C2411yescharacteristic
269C22×C4×C11C2411yescharacteristic
270C2×C22⋊D11—28no—
271C2×C22⋊D11—28no—
272C2×C22⋊D11—216no—
273C2×C22⋊D11—28no—
274C2×C22⋊D11C2×D4116yes—
275C2×C22⋊D11C2418yes—
276C2×C22⋊D11C2418yes—
277C2×C22⋊D11C2418yes—
278C2×C22⋊D11C24116yes—
279C2×C22⋊D11C2418yes—
280C22×Dic11—216no—
281C22×Dic11—28no—
282C22×Dic11—216no—
283C22×Dic11C2×D4116yes—
284C22×Dic11C24116yes—
285C22×Dic11C2418yes—
286C22×Dic11C24116yes—
287C22×Dic11C2411yescharacteristic
288C22×Dic11C2412yes—
289C22×Dic11C2414yes—
290C22×Dic11C2412yes—
291C22×Dic11C2418yes—
292C22×Dic11C2411yescharacteristic
293C22×Dic11C2412yes—
294C22×Dic11C2411yescharacteristic
295Q8×D11—264no—
296Q8×D11—264no—
297#4341—2128no—
298#4341—2128no—
299#4341—264no—
300#4341C2×D4164yescomplemented
301#4339—2128no—
302#4339—264no—
303C2×D44—28no—
304C2×D44—24no—
305C2×D44C2414yes—
306C2×D44C2418yes—
307C2×C4×D11—216no—
308C2×C4×D11—24no—
309C2×C4×D11—216no—
310C2×C4×D11—28no—
311C2×C4×D11—24no—
312C2×C4×D11C2×D418yes—
313C2×C4×D11C2414yes—
314C2×C4×D11C2414yes—
315C2×C4×D11C2418yes—
316C2×C4×D11C24116yes—
317C2×C4×D11C24116yes—
318C2×C4×D11C2414yes—
319C2×Dic22—28no—
320C2×Dic22—216no—
321C2×Dic22—216no—
322C2×Dic22—216no—
323C2×Dic22—2128no—
324C2×Dic22—264no—
325C2×Dic22—28no—
326C2×Dic22C2×D418yes—
327C2×Dic22C2418yes—
328C2×Dic22C24116yes—
329C2×Dic22C24116yes—
330C2×Dic22C2418yes—
331C2×Dic22C24116yes—
332C2×Dic22C2414yes—
333C11×C4⋊C4C2414yes—
334C11×C4⋊C4C2414yes—
335C11×C4⋊C4C2418yes—
336C11×C4⋊C4C24116yes—
337C11×C4⋊C4C2418yes—
338C11×C22⋊C4C2418yes—
339C11×C22⋊C4C2418yes—
340C11×C22⋊C4C24116yes—
341C42×C11C2414yes—
342C22⋊Dic11C2418yes—
343C22⋊Dic11C2418yes—
344C22⋊Dic11C24116yes—
345(C2×D11)⋊C4C2418yes—
346(C2×D11)⋊C4C2418yes—
347(C2×D11)⋊C4C24116yes—
348(C2×D11)⋊C4C24116yes—
349(C2×D11)⋊C4C2418yes—
350C4⋊Dic11C2414yes—
351C4⋊Dic11C2418yes—
352C4⋊Dic11C2418yes—
353C4⋊Dic11C2414yes—
354C4⋊Dic11C24116yes—
355Dic11⋊C4C2418yes—
356Dic11⋊C4C2418yes—
357Dic11⋊C4C24116yes—
358Dic11⋊C4C24116yes—
359Dic11⋊C4C24116yes—
360Dic11⋊C4C24116yes—
361Dic11⋊C4C2418yes—
362C4×Dic11C2418yes—
363C4×Dic11C2414yes—
364C4×Dic11C2414yes—
365C4×Dic11C2414yes—
366C4×Dic11C2418yes—
367C4×Dic11C2418yes—
368C22×2−1+4—112no—
369#3499—1132no—
370C2×D4×Q8—111no—
371C2×D4×Q8—112no—
372C2×D4×Q8—111no—
373C2×#547—112no—
374C2×#547—114no—
375C2×#547—112no—
376C2×#547—111no—
377C2×#547—112no—
378C2×#547D1111yescharacteristic, complemented
379C2×#536—114no—
380C2×#536—112no—
381C2×#532—112no—
382C2×#532—111no—
383C22×C4⋊Q8—111no—
384C22×C4⋊Q8—112no—
385C2×C4×#41—111no—
386C23×C11—24no—
387C23×C11—24no—
388C23×C11—24no—
389C23×C11—24no—
390C23×C11—24no—
391C23×C11C22×D418yes—
392C23×C11C2514yes—
393C23×C11C2514yes—
394C23×C11C2511yescharacteristic
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—24no—
398C22×D11—24no—
399C22×D11—24no—
400C22×D11C22×D414yes—
401C22×D11C2514yes—
402C22×D11C2512yes—
403Q8×C11—216no—
404D4×C11—232no—
405D4×C11—28no—
406D4×C11C22×D4116yes—
407C2×C4×C11—24no—
408C2×C4×C11—28no—
409C2×C4×C11—232no—
410C2×C4×C11—22no—
411C2×C4×C11—24no—
412C2×C4×C11—216no—
413C2×C4×C11—216no—
414C2×C4×C11C22×D414yes—
415C2×C4×C112−1+414yescomplemented
416C2×C4×C11C2514yes—
417C2×C4×C11C2512yes—
418C2×C4×C11C2514yes—
419C2×C4×C11C2518yes—
420C2×C4×C11C2512yes—
421C2×C4×C11C2512yes—
422C22⋊D11—232no—
423C22⋊D11—216no—
424C22⋊D11—216no—
425C22⋊D11—216no—
426C22⋊D11C22×D4132yes—
427C2×Dic11—24no—
428C2×Dic11—28no—
429C2×Dic11—232no—
430C2×Dic11—22no—
431C2×Dic11—24no—
432C2×Dic11—232no—
433C2×Dic11—216no—
434C2×Dic11C22×D414yes—
435C2×Dic11C22×D418yes—
436C2×Dic11C22×D4132yes—
437C2×Dic112−1+414yescomplemented
438C2×Dic11C2512yes—
439C2×Dic11C2514yes—
440C2×Dic11C2518yes—
441C2×Dic11C2514yes—
442C2×Dic11C2512yes—
443C2×Dic11C2514yes—
444C2×Dic11C2512yes—
445D44—216no—
446D44—28no—
447C4×D11—232no—
448C4×D11—216no—
449C4×D11—28no—
450C4×D11—232no—
451C4×D11—28no—
452C4×D11C22×D4116yes—
453Dic22—216no—
454Dic22—216no—
455Dic22—232no—
456Dic22—232no—
457Dic22—232no—
458Dic22C22×D4116yes—
459C2×2−1+4—1132no—
460C2×2−1+4—2232no—
461C22×#41—111no—
462C22×#41—114no—
463C22×#41—112no—
464C22×#41—114no—
465C22×#41—112no—
466C22×#41—114no—
467C22×#41C2×D1112yes—
468C23×Q8—112no—
469C23×Q8—112no—
470C23×Q8—114no—
471C23×Q8—112no—
472D4×Q8—1116no—
473D4×Q8—1132no—
474D4×Q8—1116no—
475#547—1132no—
476#547—1164no—
477#547—1132no—
478#547—1116no—
479#547—1132no—
480#547C2×D11116yescomplemented
481#536—1164no—
482#536—1132no—
483#532—1132no—
484#532—1116no—
485C2×C4⋊Q8—112no—
486C2×C4⋊Q8—1116no—
487C2×C4⋊Q8—112no—
488C2×C4⋊Q8—111no—
489C2×C4⋊Q8—112no—
490C2×C4⋊Q8—114no—
491C2×C4⋊Q8—114no—
492C2×C4⋊Q8—112no—
493C2×C4⋊Q8—112no—
494C2×C4⋊Q8—1132no—
495C2×C4⋊Q8—111no—
496C2×C4⋊Q8C2×D1111yescharacteristic
497C2×#127—111no—
498C2×#124—114no—
499C2×#124—112no—
500C2×#123—114no—
501C2×#123—114no—
502C2×#123—114no—
503C2×#123—114no—
504C2×#123—114no—
505C2×#123C2×D1114yes—
506C2×C22⋊Q8—112no—
507C2×C22⋊Q8—112no—
508C2×C22⋊Q8—114no—
509C2×C22⋊Q8—114no—
510C2×C22⋊Q8—112no—
511C2×C22⋊Q8—114no—
512C2×C22⋊Q8—114no—
513C2×C22⋊Q8C2×D1112yes—
514C2×#121—111no—
515C2×#121—114no—
516C2×#121—112no—
517C2×#121—111no—
518C2×#121—112no—
519C2×#121C2×D1112yes—
520C4×#41—1116no—
521C2×C4×Q8—111no—
522C2×C4×Q8—111no—
523C2×C4×D4—111no—
524C2×C4×D4—112no—
525C2×C4×D4—112no—
526C2×C4×D4—112no—
527C2×C4×D4—112no—
528C2×C4×D4—112no—
529C2×C4×D4—114no—
530C2×C4×D4—111no—
531C2×C4×D4C2×D1111yescharacteristic
532C2×C4×D4C2×D1111yescharacteristic
533C2×#117—111no—
534C2×#117—112no—
535C22×C4⋊C4—114no—
536C22×C4⋊C4—112no—
537C22×C4⋊C4—112no—
538C22×C4⋊C4—112no—
539C22×C4⋊C4C2×D1112yes—
540C22×C42—112no—
541C22×C42—111no—
542C22×C11—24no—
543C22×C11—24no—
544C22×C11—216no—
545C22×C11—24no—
546C22×C11—24no—
547C22×C11—24no—
548C22×C11—48no—
549C22×C11C23×D418yes—
550C22×C11C23×D412yes—
551C22×C11C2×2−1+412yes—
552C22×C11C2×2−1+412yes—
553C22×C11C2611yescharacteristic
554C2×D11—22no—
555C2×D11—22no—
556C2×D11—28no—
557C2×D11—24no—
558C2×D11—24no—
559C2×D11—24no—
560C2×D11—48no—
561C2×D11C23×D414yes—
562C4×C11—24no—
563C4×C11—28no—
564C4×C11—24no—
565C4×C11—22no—
566C4×C11C23×D414yes—
567C4×C11C2×2−1+414yescomplemented
568Dic11—28no—
569Dic11—24no—
570Dic11—22no—
571Dic11—24no—
572Dic11C23×D414yes—
573Dic11C23×D418yes—
574Dic11C2×2−1+414yescomplemented
5752−1+4—22256no—
576C2×#41—216no—
577C2×#41—1116no—
578C2×#41—118no—
579C2×#41—1132no—
580C2×#41—1116no—
581C2×#41—1132no—
582C2×#41—1116no—
583C2×#41—1132no—
584C2×#41—2216no—
585C2×#41—2232no—
586C2×#41—2232no—
587C2×#41—2232no—
588C2×#41—2216no—
589C2×#41C22×D11116yes—
590C22×Q8—1116no—
591C22×Q8—1116no—
592C22×Q8—111no—
593C22×Q8—114no—
594C22×Q8—114no—
595C22×Q8—112no—
596C22×Q8—114no—
597C22×Q8—112no—
598C22×Q8—1132no—
599C22×Q8—1116no—
600C22×Q8—2232no—
601C22×Q8—2216no—
602C22×Q8—2216no—
603C22×Q8—2216no—
604C22×Q8C22×D1112yes—
605C22×D4—112no—
606C22×D4—112no—
607C22×D4—112no—
608C22×D4—114no—
609C22×D4—112no—
610C22×D4—111no—
611C22×D4—112no—
612C22×D4C22×D1111yescharacteristic
613C22×D4C22×D1114yes—
614C22×D4C22×D1111yescharacteristic
615C23×C4—112no—
616C23×C4—111no—
617C23×C4—112no—
618C23×C4—114no—
619C23×C4—114no—
620C23×C4—111no—
621C23×C4—111no—
622C23×C4—114no—
623C23×C4—114no—
624C23×C4—112no—
625C23×C4C22×D1112yes—
626C23×C4C22×D1114yes—
627C23×C4C22×D1112yes—
628C4⋊Q8—1116no—
629C4⋊Q8—1116no—
630C4⋊Q8—118no—
631C4⋊Q8—1116no—
632C4⋊Q8—1132no—
633C4⋊Q8—1132no—
634C4⋊Q8—1116no—
635C4⋊Q8—1116no—
636C4⋊Q8—118no—
637C4⋊Q8C22×D1118yes—
638#127—118no—
639#124—1132no—
640#124—1116no—
641#123—1132no—
642#123—1132no—
643#123—1132no—
644#123—1132no—
645#123—1132no—
646#123C22×D11132yes—
647C22⋊Q8—1116no—
648C22⋊Q8—1116no—
649C22⋊Q8—1132no—
650C22⋊Q8—1132no—
651C22⋊Q8—1116no—
652C22⋊Q8—1132no—
653C22⋊Q8—1132no—
654C22⋊Q8C22×D11116yes—
655#121—118no—
656#121—1132no—
657#121—1116no—
658#121—118no—
659#121—1116no—
660#121C22×D11116yes—
661C4×Q8—118no—
662C4×Q8—118no—
663C4×D4—118no—
664C4×D4—1116no—
665C4×D4—1116no—
666C4×D4—1116no—
667C4×D4—1116no—
668C4×D4—1116no—
669C4×D4—1132no—
670C4×D4—118no—
671C4×D4C22×D1118yes—
672C4×D4C22×D1118yes—
673#117—118no—
674#117—1116no—
675C2×C4⋊C4—114no—
676C2×C4⋊C4—112no—
677C2×C4⋊C4—111no—
678C2×C4⋊C4—112no—
679C2×C4⋊C4—114no—
680C2×C4⋊C4—114no—
681C2×C4⋊C4—114no—
682C2×C4⋊C4—114no—
683C2×C4⋊C4—112no—
684C2×C4⋊C4—1132no—
685C2×C4⋊C4—1116no—
686C2×C4⋊C4—112no—
687C2×C4⋊C4—112no—
688C2×C4⋊C4—111no—
689C2×C4⋊C4—1116no—
690C2×C4⋊C4—1116no—
691C2×C4⋊C4C22×D1112yes—
692C2×C4⋊C4C22×D1112yes—
693C2×C4⋊C4C22×D1111yescharacteristic
694C2×C4⋊C4C22×D1114yes—
695C2×C4⋊C4C22×D11116yes—
696C2×C4⋊C4C22×D1111yescharacteristic
697C2×C22⋊C4—112no—
698C2×C22⋊C4—114no—
699C2×C22⋊C4—112no—
700C2×C22⋊C4—112no—
701C2×C22⋊C4—114no—
702C2×C22⋊C4—112no—
703C2×C22⋊C4—114no—
704C2×C22⋊C4—112no—
705C2×C22⋊C4C22×D1112yes—
706C2×C22⋊C4C22×D1114yes—
707C2×C22⋊C4C22×D1112yes—
708C2×C42—112no—
709C2×C42—111no—
710C2×C42—112no—
711C2×C42—111no—
712C2×C42—112no—
713C2×C42—1116no—
714C2×C42—111no—
715C2×C42—118no—
716C2×C42C22×D1111yescharacteristic
717C2×C11—28no—
718C2×C11—44no—
719C2×C11#349914yescomplemented
720C2×C11C24×D411yescharacteristic
721C2×C11C22×2−1+411yescharacteristic
722C2×C11C22×2−1+411yescharacteristic
723D11—24no—
724D11—44no—
725C24—111no—
726C24—112no—
727C24C23×D1112yes—
728C24C23×D1112yes—
729#41—264no—
730#41—1164no—
731#41—2264no—
732#41—22128no—
733#41—22128no—
734#41—22128no—
735#41—2264no—
736C2×Q8—28no—
737C2×Q8—118no—
738C2×Q8—114no—
739C2×Q8—1116no—
740C2×Q8—1116no—
741C2×Q8—118no—
742C2×Q8—1116no—
743C2×Q8—118no—
744C2×Q8—228no—
745C2×Q8—2216no—
746C2×Q8—2216no—
747C2×Q8—2216no—
748C2×Q8—22128no—
749C2×Q8—2264no—
750C2×Q8—2264no—
751C2×Q8—2264no—
752C2×Q8—228no—
753C2×Q8C23×D1118yes—
754C2×D4—216no—
755C2×D4—24no—
756C2×D4—1116no—
757C2×D4—118no—
758C2×D4—118no—
759C2×D4—118no—
760C2×D4—1116no—
761C2×D4—118no—
762C2×D4—114no—
763C2×D4—118no—
764C2×D4—228no—
765C2×D4—228no—
766C2×D4—228no—
767C2×D4—228no—
768C2×D4—2216no—
769C2×D4—224no—
770C2×D4D4×D1118yes—
771C2×D4C23×D1114yes—
772C2×D4C23×D11116yes—
773C2×D4C23×D1114yes—
774C22×C4—216no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—1116no—
778C22×C4—118no—
779C22×C4—111no—
780C22×C4—111no—
781C22×C4—112no—
782C22×C4—118no—
783C22×C4—114no—
784C22×C4—118no—
785C22×C4—1116no—
786C22×C4—1116no—
787C22×C4—111no—
788C22×C4—112no—
789C22×C4—112no—
790C22×C4—114no—
791C22×C4—114no—
792C22×C4—114no—
793C22×C4—1116no—
794C22×C4—1116no—
795C22×C4—118no—
796C22×C4—2216no—
797C22×C4—224no—
798C22×C4—2216no—
799C22×C4—2216no—
800C22×C4—228no—
801C22×C4—2216no—
802C22×C4—228no—
803C22×C4—224no—
804C22×C4C23×D1118yes—
805C22×C4C23×D11116yes—
806C22×C4C23×D1118yes—
807C22×C4C23×D1112yes—
808C22×C4C23×D1111yescharacteristic
809C22×C4C23×D1114yes—
810C22×C4C23×D1112yes—
811C22×C4C23×D1111yescharacteristic
812C22×C4C23×D1111yescharacteristic
813C4⋊C4—1116no—
814C4⋊C4—118no—
815C4⋊C4—114no—
816C4⋊C4—118no—
817C4⋊C4—1116no—
818C4⋊C4—1116no—
819C4⋊C4—1116no—
820C4⋊C4—1116no—
821C4⋊C4—118no—
822C4⋊C4—118no—
823C4⋊C4—118no—
824C4⋊C4—114no—
825C4⋊C4C23×D1118yes—
826C4⋊C4C23×D1118yes—
827C4⋊C4C23×D1114yes—
828C4⋊C4C23×D11116yes—
829C4⋊C4C23×D1114yes—
830C22⋊C4—118no—
831C22⋊C4—1116no—
832C22⋊C4—118no—
833C22⋊C4—118no—
834C22⋊C4—1116no—
835C22⋊C4—118no—
836C22⋊C4—1116no—
837C22⋊C4—118no—
838C22⋊C4C23×D1118yes—
839C22⋊C4C23×D11116yes—
840C22⋊C4C23×D1118yes—
841C42—114no—
842C42—118no—
843C42—114no—
844C42—118no—
845C42—114no—
846C42—118no—
847C42C23×D1114yes—
848C11C2×#349911yescharacteristic, complemented, Sylow
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—114no—
855C23—112no—
856C23—114no—
857C23—222no—
858C23—222no—
859C23—224no—
860C23—224no—
861C23—224no—
862C23C2×D4×D1118yes—
863C23C24×D1114yes—
864C23C24×D1114yes—
865C23C24×D1111yescharacteristic
866Q8—216no—
867Q8—1116no—
868Q8—2216no—
869Q8—2232no—
870Q8—2232no—
871Q8—2232no—
872Q8—2216no—
873D4—232no—
874D4—28no—
875D4—1132no—
876D4—2216no—
877D4—2216no—
878D4—2216no—
879D4—2216no—
880D4—2232no—
881D4—228no—
882D4C2×D4×D11116yes—
883C2×C4—24no—
884C2×C4—28no—
885C2×C4—232no—
886C2×C4—24no—
887C2×C4—22no—
888C2×C4—216no—
889C2×C4—216no—
890C2×C4—114no—
891C2×C4—118no—
892C2×C4—1132no—
893C2×C4—114no—
894C2×C4—112no—
895C2×C4—112no—
896C2×C4—114no—
897C2×C4—1116no—
898C2×C4—114no—
899C2×C4—112no—
900C2×C4—114no—
901C2×C4—118no—
902C2×C4—2232no—
903C2×C4—228no—
904C2×C4—2232no—
905C2×C4—2232no—
906C2×C4—2216no—
907C2×C4—228no—
908C2×C4—224no—
909C2×C4—2232no—
910C2×C4—222no—
911C2×C4—224no—
912C2×C4—2216no—
913C2×C4—228no—
914C2×C4C2×D4×D1114yes—
915C2×C4#6704314yescomplemented
916C2×C4C24×D1114yes—
917C2×C4C24×D1112yes—
918C2×C4C24×D1118yes—
919C2×C4C24×D1114yes—
920C2×C4C24×D1112yes—
921C2×C4C24×D1112yes—
922C22—216no—
923C22—24no—
924C22—24no—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—48no—
929C22—114no—
930C22—228no—
931C22—222no—
932C22—222no—
933C22—224no—
934C22—224no—
935C22—224no—
936C22—448no—
937C22C22×D4×D1118yes—
938C22C22×D4×D1112yes—
939C22C2×#6704312yes—
940C22D11×2−1+412yes—
941C22C25×D1111yescharacteristic
942C4—24no—
943C4—28no—
944C4—22no—
945C4—24no—
946C4—114no—
947C4—118no—
948C4—114no—
949C4—228no—
950C4—224no—
951C4—224no—
952C4—222no—
953C4C22×D4×D1114yes—
954C4C2×#6704314yescomplemented
955C2—28no—
956C2—44no—
957C2—224no—
958C2—444no—
959C2#1308239514yesdirect product factor
960C2C23×D4×D1111yescharacteristic
961C2C2×D11×2−1+411yescharacteristic
962C2C22×#6704311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#547C2
socleC23×C11C25
hypercenterC2×#547D11
hypocenterC11C2×#3499
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C22×#67043C2semidirect
2. #13082395C2direct (N × H)
3. C2×D4×Dic22C2semidirect
4. C2×#10623258C2semidirect
5. C2×#10623163C2semidirect
6. C2×#10623086C2semidirect
7. C2×#10623038C2semidirect
8. C2×#10623142C2semidirect
9. C2×#10623355C2semidirect
10. C2×#10623186C2semidirect
11. C2×#10623159C2semidirect
12. C2×#10623179C2semidirect
13. C2×#10623079C2semidirect
14. C2×#10623127C2semidirect
15. C22×#66941C2semidirect
16. C2×D11×C4⋊Q8C2semidirect
17. C2×C4×#4341C2semidirect
18. C2×C11×#547C2semidirect
21. C2×#67043C22semidirect
32. C11×#547C22semidirect
40. #10623355C22semidirect
57. #10623258C22semidirect
58. D11×C4⋊Q8C22semidirect
59. #10623186C22semidirect
60. #10623179C22semidirect
61. #10623163C22semidirect
62. #10623159C22semidirect
63. #10623142C22semidirect
64. #10623127C22semidirect
65. #10623086C22semidirect
66. #10623079C22semidirect
67. D4×Dic22C22semidirect
68. C4×#4341C22semidirect
72. #10623038C22semidirect
86. C2×#66941C22semidirect
128. C2×#4341D4semidirect
300. #4341C2×D4semidirect
378. C2×#547D11semidirect
415. C2×C4×C112−1+4semidirect
437. C2×Dic112−1+4semidirect
480. #547C2×D11semidirect
567. C4×C11C2×2−1+4semidirect
574. Dic11C2×2−1+4semidirect
719. C2×C11#3499semidirect
848. C11C2×#3499semidirect
915. C2×C4#67043semidirect
954. C4C2×#67043semidirect
959. C2#13082395direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670432
#130823952
C2×D4×Dic222
C2×#106232582
C2×#106231632
C2×#106230862
C2×#106230382
C2×#106231422
C2×#106233552
C2×#106231862
C2×#106231592
C2×#106231792
C2×#106230792
C2×#106231272
C22×#669412
C2×D11×C4⋊Q82
C2×C4×#43412
C2×C11×#5472
C2×#349911