Finite Group Databasebeta

← C2×#13078744 #15621974

Subgroups — C2×#13078744 #15621974

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic
3#13078744C2116yesmaximal, direct product factor
4C2×#10622475C211yesmaximal, characteristic
5C2×#10622418C211yesmaximal, characteristic
6C2×#10622467C211yesmaximal, characteristic, complemented
7C2×#10622404C211yesmaximal, characteristic, complemented
8C2×#10622406C211yesmaximal, characteristic, complemented
9C2×#10622795C211yesmaximal, characteristic, complemented
10C2×#10622421C211yesmaximal, characteristic
11C2×#10622799C211yesmaximal, characteristic
12C2×#10622329C211yesmaximal, characteristic, complemented
13C2×#10622643C211yesmaximal, characteristic, complemented
14C2×#10622643C211yesmaximal, characteristic, complemented
15C2×#10622318C211yesmaximal, characteristic
16C2×C11×#441C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×#66997C2211yescharacteristic
24C22×#4326C2211yescharacteristic
25C22×#4326C2211yescharacteristic
26C22×Dic44C2211yescharacteristic
27#10623109—24no—
28#10623109C2218yes—
29C4×Q8×D11—24no—
30C4×Q8×D11C2218yes—
31C2×#66950C2211yescharacteristic
32C2×#66949—21no—
33C2×C4⋊C4×D11—21no—
34C2×C4⋊C4×D11C2211yescharacteristic
35C2×#66942—21no—
36C2×#66941C2211yescharacteristic
37C2×#66940—21no—
38C2×#66940C2211yescharacteristic
39C2×#66925—21no—
40C2×C42×D11—21no—
41C2×C42×D11C2211yescharacteristic
42C2×C4×Dic22—21no—
43C2×C4×Dic22—21no—
44C2×C4×Dic22C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic
46C11×#441C2218yescomplemented
47C2×C11×#106C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#97C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53#10622799C2218yes—
54#10622795C2218yescomplemented
55C2×(C2×D11)⋊C8C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×#66881C2211yescharacteristic
58C2×#66880C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×Dic11⋊C8C2211yescharacteristic
62#10622643C2218yescomplemented
63#10622643C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66874C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66867C2211yescharacteristic
69#10622475C2218yes—
70#10622467C2218yescomplemented
71#10622421C2218yes—
72#10622418C2218yes—
73#10622406C2218yescomplemented
74#10622404C2218yescomplemented
75#10622329C2218yescomplemented
76#10622318C2218yes—
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C2×Q8×D11—24no—
80C2×Q8×D11—22no—
81C2×Q8×D11—24no—
82C2×Q8×D11C2314yes—
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11D411yescharacteristic
86C22×C4×D11D411yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×Dic22—21no—
89C22×Dic22—21no—
90C22×Dic22C2311yescharacteristic
91C22×Dic22C2311yescharacteristic
92C2×C11×Q16—24no—
93C2×C11×Q16C2314yes—
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C4×Q8×C11—22no—
97C4×Q8×C11—22no—
98C4×Q8×C11C2314yes—
99C4×Q8×C11C2314yes—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C42×C11—21no—
105C2×C42×C11—21no—
106C2×C42×C11C2311yescharacteristic
107#66999—22no—
108#66999C2314yes—
109Q8×Dic11—22no—
110Q8×Dic11C2314yes—
111#66997—22no—
112#66997C2314yes—
113C2×#4326—24no—
114C2×#4326—24no—
115C2×#4326C2314yes—
116C2×#4326C2314yes—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×C4×Dic11—21no—
132C2×C4×Dic11—21no—
133C2×C4×Dic11—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11D411yescharacteristic
136C2×C4×Dic11D411yescharacteristic
137C2×C4×Dic11C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C2×Dic44—24no—
141C2×Dic44C2314yes—
142#66950—22no—
143#66950C2314yes—
144#66949—28no—
145C4⋊C4×D11—28no—
146C4⋊C4×D11—22no—
147C4⋊C4×D11C2314yes—
148#66942—28no—
149#66941—22no—
150#66941C2314yes—
151#66940—28no—
152#66940—22no—
153#66940C2314yes—
154#66925—28no—
155C42×D11—28no—
156C42×D11D414yes—
157C42×D11C2314yes—
158C4×Dic22—22no—
159C4×Dic22—22no—
160C4×Dic22—28no—
161C4×Dic22—28no—
162C4×Dic22C2314yes—
163C4×Dic22C2314yes—
164C11×#106C2314yes—
165C11×#103C2314yes—
166C11×#103C2314yes—
167C11×#97C2314yes—
168#66899C2314yes—
169#66899C2314yes—
170(C2×D11)⋊C8C2314yes—
171(C2×D11)⋊C8C2314yes—
172#66881C2314yes—
173#66880C2314yes—
174#66880C2314yes—
175Dic11⋊C8C2314yes—
176Dic11⋊C8C2314yes—
177#66874C2314yes—
178#66874C2314yes—
179#66872C2314yes—
180#66872C2314yes—
181#66867C2314yes—
182C2×#3113—111nomaximal, Sylow
183C23×D11C2×D411yescharacteristic
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—22no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11#4114yes—
190C2×Q8×C11C2412yes—
191C2×Q8×C11C2412yes—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11C2×D411yescharacteristic
204C22×Dic11C2×D411yescharacteristic
205C22×Dic11C2×D411yescharacteristic
206Q8×D11—216no—
207Q8×D11—28no—
208Q8×D11—28no—
209C2×C4×D11—28no—
210C2×C4×D11—24no—
211C2×C4×D11—24no—
212C2×C4×D11—24no—
213C2×C4×D11—24no—
214C2×C4×D11—22no—
215C2×C4×D11—22no—
216C2×C4×D11—44no—
217C2×C4×D11C2×D414yes—
218C2×C4×D11C2×D412yes—
219C2×C4×D11C2×D414yes—
220C2×C4×D11C2412yes—
221C2×Dic22—28no—
222C2×Dic22—24no—
223C2×Dic22—24no—
224C2×Dic22—21no—
225C2×Dic22—21no—
226C2×Dic22—22no—
227C2×Dic22—22no—
228C2×Dic22—22no—
229C2×Dic22—44no—
230C2×Dic22#4114yes—
231C2×Dic22C2412yes—
232C2×Dic22C2412yes—
233C11×Q16—28no—
234C2×C8×C11—22no—
235C2×C8×C11—22no—
236C2×C8×C11C2412yes—
237C2×C8×C11C2412yes—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4C2412yes—
243C11×C4⋊C4C2412yes—
244C42×C11—24no—
245C42×C11—24no—
246C42×C11C2×D412yes—
247C42×C11C2412yes—
248#4326—28no—
249#4326—28no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11C2412yes—
257C4⋊Dic11C2412yes—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266C4×Dic11—24no—
267C4×Dic11—24no—
268C4×Dic11—24no—
269C4×Dic11—24no—
270C4×Dic11C2×D414yes—
271C4×Dic11C2×D414yes—
272C4×Dic11C2×D412yes—
273C4×Dic11C2412yes—
274C2×C11⋊C8—22no—
275C2×C11⋊C8—22no—
276C2×C11⋊C8C2412yes—
277C2×C11⋊C8C2412yes—
278Dic44—28no—
279C2×#533—111no—
280C22×C4×Q8—111no—
281#3113—1116no—
282C2×#483—111no—
283C2×#483—111no—
284C2×#475—111no—
285C2×#475—111no—
286C2×#462—111no—
287C2×#462—111no—
288C2×#451—111no—
289C2×#451—111no—
290C2×#441—111no—
291C2×#441—111no—
292C2×#441—111no—
293C2×#441D1111yescharacteristic, complemented
294C2×#432—111no—
295C23×C11C22×D411yescharacteristic
296C22×D11—22no—
297C22×D11—22no—
298C22×D11#13714yes—
299C22×D11C22×D412yes—
300Q8×C11—24no—
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11—42no—
305Q8×C11C2×#4114yes—
306C2×C4×C11—24no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11C22×D412yes—
317C2×C4×C11C22×D412yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C2×#4112yes—
320C2×C4×C11C2×#4112yes—
321C2×C4×C11C2511yescharacteristic
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11#13714yes—
333C2×Dic11C22×D412yes—
334C2×Dic11C22×D412yes—
335C2×Dic11C22×D412yes—
336C4×D11—216no—
337C4×D11—28no—
338C4×D11—24no—
339C4×D11—22no—
340C4×D11—22no—
341C4×D11—28no—
342C4×D11—48no—
343Dic22—216no—
344Dic22—24no—
345Dic22—22no—
346Dic22—22no—
347Dic22—22no—
348Dic22—42no—
349Dic22—48no—
350Dic22C2×#4114yes—
351C8×C11—22no—
352C8×C11—22no—
353C11⋊C8—22no—
354C11⋊C8—22no—
355C23×Q8—111no—
356C22×Q16—111no—
357C22×Q16—111no—
358C22×Q16—111no—
359C22×Q16C2×D1111yescharacteristic
360#533—118no—
361#533—224no—
362C2×C4⋊Q8—111no—
363C2×C4⋊Q8—111no—
364C2×#125—221no—
365C2×C22⋊Q8—111no—
366C2×C22⋊Q8—111no—
367C2×C22⋊Q8—221no—
368C2×C4×Q8—111no—
369C2×C4×Q8—118no—
370C2×C4×Q8—111no—
371C2×C4×Q8—111no—
372C2×C4×Q8—111no—
373C2×C4×Q8—221no—
374C2×C4×Q8—221no—
375C2×C4×Q8—221no—
376C2×C4×Q8—224no—
377C2×C4×Q8C2×D1111yescharacteristic
378C2×C4×Q8C2×D1111yescharacteristic
379C2×#117—221no—
380C22×C4⋊C4—111no—
381C22×C4⋊C4—221no—
382C22×C42—111no—
383C22×C42—221no—
384#483—118no—
385#483—118no—
386#475—118no—
387#475—118no—
388#462—118no—
389#462—118no—
390#451—118no—
391#451—118no—
392#441—118no—
393#441—118no—
394#441—118no—
395#441C2×D1118yescomplemented
396#432—118no—
397C2×#106—111no—
398C2×#106—111no—
399C2×#106—111no—
400C2×#106C2×D1111yescharacteristic
401C2×C4⋊C8—111no—
402C2×C4⋊C8—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—111no—
409C2×#103C2×D1111yescharacteristic
410C2×#103C2×D1111yescharacteristic
411C2×C22⋊C8—111no—
412C2×C22⋊C8—111no—
413C2×#97—111no—
414C2×#97C2×D1111yescharacteristic
415C22×C11#52512yes—
416C22×C11C2×#13712yes—
417C22×C11C2×#13712yes—
418C22×C11C23×D411yescharacteristic
419C2×D11—28no—
420C2×D11—22no—
421C2×D11—22no—
422C2×D11C2×#13714yes—
423C4×C11—24no—
424C4×C11—22no—
425C4×C11—22no—
426C4×C11—42no—
427C4×C11—42no—
428C4×C11—42no—
429C4×C11#52512yes—
430C4×C11C22×#4111yescharacteristic
431C4×C11C22×#4111yescharacteristic
432Dic11—22no—
433Dic11—24no—
434Dic11—22no—
435Dic11—42no—
436Dic11—42no—
437Dic11—42no—
438Dic11C2×#13714yes—
439C22×Q8—114no—
440C22×Q8—111no—
441C22×Q8—111no—
442C22×Q8—221no—
443C22×Q8—221no—
444C22×Q8—222no—
445C22×Q8—224no—
446C22×Q8—224no—
447C22×Q8C22×D1111yescharacteristic
448C22×Q8C22×D1111yescharacteristic
449C23×C4—111no—
450C23×C4—111no—
451C23×C4—111no—
452C23×C4—221no—
453C23×C4—221no—
454C2×Q16—24no—
455C2×Q16—114no—
456C2×Q16—114no—
457C2×Q16—114no—
458C2×Q16—224no—
459C2×Q16—224no—
460C2×Q16—224no—
461C2×Q16C22×D1114yes—
462C22×C8—111no—
463C22×C8—111no—
464C22×C8C22×D1111yescharacteristic
465C22×C8C22×D1111yescharacteristic
466C4⋊Q8—114no—
467C4⋊Q8—114no—
468C4⋊Q8—222no—
469C4⋊Q8—222no—
470#125—228no—
471C22⋊Q8—114no—
472C22⋊Q8—114no—
473C22⋊Q8—222no—
474C22⋊Q8—228no—
475C22⋊Q8—222no—
476C4×Q8—22no—
477C4×Q8—22no—
478C4×Q8—114no—
479C4×Q8—114no—
480C4×Q8—114no—
481C4×Q8—114no—
482C4×Q8—228no—
483C4×Q8—228no—
484C4×Q8—228no—
485C4×Q8—222no—
486C4×Q8—222no—
487C4×Q8—222no—
488C4×Q8—222no—
489C4×Q8C22×D1114yes—
490C4×Q8C22×D1114yes—
491#117—228no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—222no—
498C2×C4⋊C4—228no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4C22×D1111yescharacteristic
510C2×C4⋊C4C22×D1111yescharacteristic
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—111no—
516C2×C42—111no—
517C2×C42—111no—
518C2×C42—114no—
519C2×C42—114no—
520C2×C42—228no—
521C2×C42—221no—
522C2×C42—221no—
523C2×C42—221no—
524C2×C42—221no—
525C2×C42C22×D1111yescharacteristic
526#106—114no—
527#106—114no—
528#106—114no—
529#106C22×D1114yes—
530C4⋊C8—114no—
531C4⋊C8—114no—
532#103—114no—
533#103—114no—
534#103—114no—
535#103—114no—
536#103—114no—
537#103—114no—
538#103C22×D1114yes—
539#103C22×D1114yes—
540C22⋊C8—114no—
541C22⋊C8—114no—
542#97—114no—
543#97C22×D1114yes—
544C2×C11#311314yescomplemented
545C2×C11C2×#52511yescharacteristic
546C2×C11C22×#13711yescharacteristic
547C2×C11C22×#13711yescharacteristic
548D11—24no—
549C24—111no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—114no—
556C2×Q8—112no—
557C2×Q8—112no—
558C2×Q8—224no—
559C2×Q8—224no—
560C2×Q8—228no—
561C2×Q8—228no—
562C2×Q8—2216no—
563C2×Q8—228no—
564C2×Q8—222no—
565C2×Q8—221no—
566C2×Q8—221no—
567C2×Q8—222no—
568C2×Q8—222no—
569C2×Q8—444no—
570C2×Q8#433914yes—
571C2×Q8C23×D1112yes—
572C2×Q8C23×D1112yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—111no—
578C22×C4—111no—
579C22×C4—111no—
580C22×C4—114no—
581C22×C4—114no—
582C22×C4—112no—
583C22×C4—112no—
584C22×C4—224no—
585C22×C4—224no—
586C22×C4—224no—
587C22×C4—228no—
588C22×C4—224no—
589C22×C4—221no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—444no—
596C22×C4D4×D1111yescharacteristic
597C22×C4D4×D1111yescharacteristic
598C22×C4C23×D1111yescharacteristic
599Q16—28no—
600Q16—228no—
601Q16—228no—
602Q16—228no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—112no—
606C2×C8—112no—
607C2×C8—222no—
608C2×C8—222no—
609C2×C8C23×D1112yes—
610C2×C8C23×D1112yes—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—112no—
616C4⋊C4—112no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—221no—
626C4⋊C4—221no—
627C4⋊C4—224no—
628C4⋊C4—224no—
629C4⋊C4C23×D1112yes—
630C4⋊C4C23×D1112yes—
631C22⋊C4—224no—
632C22⋊C4—224no—
633C42—24no—
634C42—24no—
635C42—114no—
636C42—114no—
637C42—112no—
638C42—112no—
639C42—224no—
640C42—224no—
641C42—224no—
642C42—224no—
643C42D4×D1112yes—
644C42C23×D1112yes—
645C11C2×#311311yescharacteristic, complemented, Sylow
646C23—114no—
647C23—112no—
648C23—222no—
649C23—222no—
650C23C2×D4×D1111yescharacteristic
651Q8—24no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—42no—
656Q8—114no—
657Q8—2216no—
658Q8—224no—
659Q8—222no—
660Q8—222no—
661Q8—222no—
662Q8—448no—
663Q8—442no—
664Q8C2×#433914yes—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—114no—
676C2×C4—112no—
677C2×C4—112no—
678C2×C4—112no—
679C2×C4—228no—
680C2×C4—228no—
681C2×C4—2216no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—224no—
685C2×C4—222no—
686C2×C4—224no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—448no—
693C2×C4—442no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4C2×#433912yes—
697C2×C4C2×D4×D1112yes—
698C2×C4C2×D4×D1112yes—
699C2×C4C2×D4×D1111yescharacteristic
700C2×C4#41×D1112yes—
701C2×C4C24×D1111yescharacteristic
702C8—22no—
703C8—22no—
704C8—222no—
705C8—222no—
706C22—114no—
707C22—222no—
708C22—228no—
709C22—222no—
710C22#1062307812yes—
711C22D11×#13712yes—
712C22D11×#13712yes—
713C22C22×D4×D1111yescharacteristic
714C4—24no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—114no—
721C4—222no—
722C4—224no—
723C4—222no—
724C4—442no—
725C4—442no—
726C4—442no—
727C4#1062307812yes—
728C4C22×#433911yescharacteristic
729C4C2×#41×D1111yescharacteristic
730C2—224no—
731C2#1307874414yesdirect product factor
732C2C2×#1062307811yescharacteristic
733C2C2×D11×#13711yescharacteristic
734C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#441C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#441D11
hypocenterC11C2×#3113
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. #13078744C2direct (N × H)
6. C2×#10622467C2semidirect
7. C2×#10622404C2semidirect
8. C2×#10622406C2semidirect
9. C2×#10622795C2semidirect
12. C2×#10622329C2semidirect
13. C2×#10622643C2semidirect
14. C2×#10622643C2semidirect
16. C2×C11×#441C2semidirect
46. C11×#441C22semidirect
54. #10622795C22semidirect
62. #10622643C22semidirect
63. #10622643C22semidirect
70. #10622467C22semidirect
73. #10622406C22semidirect
74. #10622404C22semidirect
75. #10622329C22semidirect
293. C2×#441D11semidirect
395. #441C2×D11semidirect
544. C2×C11#3113semidirect
645. C11C2×#3113semidirect
731. C2#13078744direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×C4×Q8×D112
#130787442
C2×#106224752
C2×#106224182
C2×#106224672
C2×#106224042
C2×#106224062
C2×#106227952
C2×#106224212
C2×#106227992
C2×#106223292
C2×#106226432
C2×#106223182
C2×C11×#4412
C2×#311311