Finite Group Databasebeta

← C2×#21446716 #29683986

Subgroups — C2×#21446716 #29683986

Order 15616.

1474 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519797C211yesmaximal, characteristic
2C2×#16839798C211yesmaximal, characteristic, complemented
3C2×#16839778C211yesmaximal, characteristic, complemented
4C2×#16839736C211yesmaximal, characteristic, complemented
5C2×#16839735C211yesmaximal, characteristic, complemented
6C2×#16839720C211yesmaximal, characteristic, complemented
7#21446716C218yesmaximal, direct product factor
8C2×C61×#421C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C2×#14519797—21no—
11C2×#14519797—21no—
12C2×#14519797—22no—
13C2×#14519797—21no—
14C2×#14519797—21no—
15C2×#14519797—22no—
16C2×#14519797C414yescomplemented
17C2×#14519797C2214yes—
18C22×#11758202C411yescharacteristic, complemented
19C22×#11758200C411yescharacteristic, complemented
20C22×#11758201C411yescharacteristic, complemented
21C22×#11758199C411yescharacteristic, complemented
22C23×#92418C2211yescharacteristic
23C2×#14519736C2211yescharacteristic
24C2×#14519736C2211yescharacteristic
25#16839798—22no—
26#16839798C2214yescomplemented
27C2×#14519710—21no—
28C2×#14519708—21no—
29#16839778—22no—
30#16839778C2214yescomplemented
31C2×#14519703—22no—
32#16839736—22no—
33#16839736C2214yescomplemented
34#16839735—22no—
35#16839735C2214yescomplemented
36C2×#14519692—22no—
37C2×#14519691—22no—
38#16839720—22no—
39#16839720C2214yescomplemented
40C2×#14519687—21no—
41C2×C8×Dic61—21no—
42C22×#41×C61C2211yescharacteristic
43C22×M16×C61C2211yescharacteristic
44C2×#117×C61C2211yescharacteristic
45C61×#421—22no—
46C61×#421C2214yescomplemented
47C2×#104×C61—22no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222—21no—
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—21no—
56C2×#11758222—21no—
57C2×#11758222—21no—
58C2×#11758222C2×C412yes—
59C2×#11758222C2312yes—
60C22×Dic122C2×C411yescharacteristic
61C22×D244C2×C411yescharacteristic
62C22×C22⋊D61—21no—
63C22×C4×D61—21no—
64#14519797—24no—
65#14519797—24no—
66#14519797—24no—
67#14519797—24no—
68#14519797—24no—
69#14519797—24no—
70#14519797—24no—
71#14519797—24no—
72C2×#11758202—21no—
73C2×#11758202—21no—
74C2×#11758202—22no—
75C2×#11758202C2×C414yescomplemented
76C2×#11758200—21no—
77C2×#11758200—21no—
78C2×#11758200—22no—
79C2×#11758200C2×C414yescomplemented
80C2×#11758201—21no—
81C2×#11758201—21no—
82C2×#11758201—22no—
83C2×#11758201C2×C414yescomplemented
84C2×#11758199—21no—
85C2×#11758199—21no—
86C2×#11758199—22no—
87C2×#11758199C2×C414yescomplemented
88C22×#92418C2×C411yescharacteristic
89C22×#92418C2×C411yescharacteristic
90C22×#92418C2×C412yes—
91C22×#92418D411yescharacteristic
92C22×#92418D411yescharacteristic
93C22×#92418D412yes—
94C22×#92418D411yescharacteristic
95C22×#92418D411yescharacteristic
96C22×#92418D412yes—
97C22×#92418C2312yes—
98#14519736—21no—
99#14519736—21no—
100#14519736—21no—
101#14519736—21no—
102#14519736—21no—
103#14519736D412yes—
104#14519736C2312yes—
105#14519736C2312yes—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61D412yes—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112#14519710—24no—
113#14519708—24no—
114#14519703—28no—
115#14519692—28no—
116#14519691—28no—
117#14519687—24no—
118C8×Dic61—24no—
119C2×#41×C61—21no—
120C2×#41×C61—21no—
121C2×#41×C61—21no—
122C2×#41×C61—21no—
123C2×#41×C61—21no—
124C2×#41×C61—21no—
125C2×#41×C61—21no—
126C2×#41×C61—21no—
127C2×#41×C61—21no—
128C2×#41×C61—21no—
129C2×#41×C61C2×C412yes—
130C2×#41×C61C2312yes—
131C22×Q8×C61C2×C411yescharacteristic
132C22×D4×C61—21no—
133C22×D4×C61C2×C411yescharacteristic
134C23×C4×C61—21no—
135C23×C4×C61C2311yescharacteristic
136C2×M16×C61—21no—
137C2×M16×C61—21no—
138C2×M16×C61—21no—
139C2×M16×C61D412yes—
140C2×M16×C61D412yes—
141C2×M16×C61C2312yes—
142C22×C8×C61—21no—
143#117×C61—21no—
144#117×C61—21no—
145#117×C61—21no—
146#117×C61C2312yes—
147C2×C4⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C42×C61—21no—
150#104×C61—28no—
151C24×C61—21no—
152C24×C61C2×D411yescharacteristic
153C23×D61—21no—
154#41×C61—22no—
155#41×C61—22no—
156#41×C61—22no—
157#41×C61—22no—
158#41×C61—22no—
159#41×C61—22no—
160#41×C61—22no—
161#41×C61—22no—
162#41×C61—41no—
163#41×C61—41no—
164#41×C61—41no—
165#41×C61—41no—
166#41×C61—41no—
167#41×C61—41no—
168#41×C61—41no—
169#41×C61—41no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61C22×C412yes—
176C2×D4×C61—22no—
177C2×D4×C61—22no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—41no—
184C2×D4×C61—41no—
185C2×D4×C61—41no—
186C2×D4×C61—41no—
187C2×D4×C61C22×C412yes—
188C22×C4×C61—21no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—41no—
192C22×C4×C61—41no—
193C22×C4×C61—41no—
194C22×C4×C61—41no—
195C22×C4×C61—41no—
196C22×C4×C61C22×C411yescharacteristic
197C22×C4×C61C22×C411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61#4111yescharacteristic
206C22×C4×C61#4111yescharacteristic
207C22×C4×C61#4111yescharacteristic
208C22×C4×C61#4111yescharacteristic
209C22×C4×C61C2411yescharacteristic
210C2×C22⋊D61—22no—
211C2×C22⋊D61—22no—
212C2×C22⋊D61—41no—
213C2×C22⋊D61—41no—
214C2×C22⋊D61—41no—
215C2×C22⋊D61—41no—
216C22×Dic61—21no—
217C22×Dic61—22no—
218C22×Dic61—41no—
219#11758222—22no—
220#11758222—22no—
221#11758222—22no—
222#11758222—22no—
223#11758222—22no—
224#11758222—22no—
225#11758222—22no—
226#11758222—22no—
227#11758222—41no—
228#11758222—41no—
229#11758222—41no—
230#11758222—41no—
231#11758222—41no—
232#11758222—41no—
233#11758222—41no—
234#11758222—41no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244C22×C412yes—
241C2×C4×D61—22no—
242C2×C4×D61—22no—
243C2×C4×D61—41no—
244C2×C4×D61—41no—
245C2×C4×D61—41no—
246C2×C4×D61—41no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122—21no—
252C2×Dic122C22×C412yes—
253M16×C61—22no—
254M16×C61—22no—
255M16×C61—22no—
256M16×C61C2×D414yes—
257C2×C8×C61—22no—
258C2×C8×C61—22no—
259C2×C8×C61—22no—
260C4⋊C4×C61—22no—
261C4⋊C4×C61—41no—
262C22⋊C4×C61—22no—
263C22⋊C4×C61—41no—
264C42×C61—22no—
265C42×C61—41no—
266C22⋊Dic61—22no—
267C22⋊Dic61—22no—
268C22⋊Dic61—41no—
269C22⋊Dic61C2×D414yes—
270#11758202—24no—
271#11758202—24no—
272#11758201—24no—
273#11758201—24no—
274#11758200—24no—
275#11758200—24no—
276#11758199—24no—
277#11758199—24no—
278C4⋊Dic61—22no—
279C4⋊Dic61—22no—
280C4⋊Dic61—22no—
281C4⋊Dic61—41no—
282C4×Dic61—22no—
283C4×Dic61—22no—
284C4×Dic61—22no—
285C4×Dic61—41no—
286C2×#92418C22⋊C411yescharacteristic
287C2×#92418C22⋊C411yescharacteristic
288C2×#92418C22⋊C412yes—
289C2×#92418C22⋊C411yescharacteristic
290C2×#92418C22⋊C411yescharacteristic
291C2×#92418C22⋊C412yes—
292C2×#92418C22⋊C412yes—
293C2×#92418C22⋊C412yes—
294C2×#92418C22⋊C412yes—
295C2×#92418C22⋊C412yes—
296C2×#92418C22×C412yes—
297C2×#92418C22×C412yes—
298C2×#92418C2×D412yes—
299C2×#92418C2×D412yes—
300C2×#92418C2×D412yes—
301C2×#92418C2×D412yes—
302C23×C61—22no—
303C23×C61—42no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—82no—
307C23×C61C4×D411yescharacteristic
308C23×C61C4×D411yescharacteristic
309C23×C61#12111yescharacteristic
310C23×C61#12111yescharacteristic
311C23×C61#12711yescharacteristic
312C23×C61#12711yescharacteristic
313C23×C61C22×D411yescharacteristic
314C22×D61—22no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—82no—
318Q8×C61—22no—
319Q8×C61—22no—
320Q8×C61—41no—
321Q8×C61—41no—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—42no—
325D4×C61—42no—
326D4×C61—42no—
327D4×C61—42no—
328D4×C61—41no—
329D4×C61—41no—
330C2×C4×C61—22no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—42no—
334C2×C4×C61—42no—
335C2×C4×C61—42no—
336C2×C4×C61—42no—
337C2×C4×C61—42no—
338C2×C4×C61—82no—
339C2×C4×C61C2×C22⋊C411yescharacteristic
340C2×C4×C61C2×C22⋊C411yescharacteristic
341C2×C4×C61C2×C22⋊C411yescharacteristic
342C2×C4×C61C2×C22⋊C411yescharacteristic
343C2×C4×C61C4×D411yescharacteristic
344C2×C4×C61C4×D411yescharacteristic
345C2×C4×C61C4×D411yescharacteristic
346C2×C4×C61C4×D411yescharacteristic
347C2×C4×C61C4×D411yescharacteristic
348C2×C4×C61C4×D411yescharacteristic
349C2×C4×C61#12111yescharacteristic
350C2×C4×C61#12111yescharacteristic
351C2×C4×C61#12111yescharacteristic
352C2×C4×C61#12111yescharacteristic
353C2×C4×C61#12111yescharacteristic
354C2×C4×C61#12111yescharacteristic
355C2×C4×C61#12411yescharacteristic
356C2×C4×C61#12411yescharacteristic
357C2×C4×C61#12411yescharacteristic
358C2×C4×C61#12411yescharacteristic
359C2×C4×C61#12711yescharacteristic
360C2×C4×C61#12711yescharacteristic
361C2×C4×C61C23×C411yescharacteristic
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C2×#4111yescharacteristic
366C2×C4×C61C2×#4111yescharacteristic
367C22⋊D61—42no—
368C22⋊D61—42no—
369C22⋊D61—42no—
370C22⋊D61—42no—
371C2×Dic61—22no—
372C2×Dic61—24no—
373C2×Dic61—44no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—42no—
377C2×Dic61—82no—
378D244—22no—
379D244—22no—
380D244—41no—
381D244—41no—
382C4×D61—42no—
383C4×D61—42no—
384C4×D61—42no—
385C4×D61—42no—
386Dic122—22no—
387Dic122—22no—
388Dic122—41no—
389Dic122—41no—
390C8×C61—24no—
391#92418C2×C22⋊C412yes—
392#92418C2×C22⋊C412yes—
393#92418C2×C22⋊C412yes—
394#92418C2×C22⋊C412yes—
395C2×#1976—611nomaximal, Sylow
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—42no—
404C22×C61—82no—
405C22×C61—82no—
406C22×C61—82no—
407C22×C61#39011yescharacteristic
408C22×C61#39011yescharacteristic
409C22×C61#39011yescharacteristic
410C22×C61#39011yescharacteristic
411C22×C61C2×C4×D411yescharacteristic
412C22×C61C2×#12111yescharacteristic
413C22×C61C2×#12711yescharacteristic
414C2×D61—42no—
415C2×D61—82no—
416C2×D61—82no—
417C2×D61—82no—
418C4×C61—42no—
419C4×C61—82no—
420C4×C61#39011yescharacteristic
421C4×C61#39011yescharacteristic
422C4×C61#39011yescharacteristic
423C4×C61#39011yescharacteristic
424C4×C61C22×C22⋊C411yescharacteristic
425C4×C61C2×C4×D411yescharacteristic
426C4×C61C2×#12111yescharacteristic
427C4×C61C2×#12411yescharacteristic
428Dic61—44no—
429Dic61—42no—
430Dic61—82no—
431C22×#135—611no—
432C2×#427—611no—
433C2×#421—611no—
434C2×#421D6111yescharacteristic, complemented
435C2×#410—611no—
436C2×#410—611no—
437C2×#405—611no—
438#1976—618no—
439C2×C61—21no—
440C2×C61—21no—
441C2×C61—21no—
442C2×C61—21no—
443C2×C61—21no—
444C2×C61—21no—
445C2×C61—82no—
446C2×C61#197612yescomplemented
447C2×C61C2×#39011yescharacteristic
448D61—82no—
449C22×#41—611no—
450C22×#41C2×D6111yescharacteristic
451C2×#135—614no—
452C2×#135—614no—
453C2×#135—1221no—
454C2×#135—1221no—
455C2×#135—1222no—
456C2×#135—1221no—
457C2×#135—1221no—
458C2×#135—1222no—
459C22×Q16—611no—
460C22×SD16—611no—
461C22×SD16—611no—
462C22×D8—611no—
463C22×M16C2×D6111yescharacteristic
464C23×C8—611no—
465C2×#117—611no—
466C2×#117—611no—
467C2×#117C2×D6111yescharacteristic
468#427—614no—
469#427—1222no—
470C2×#107—1221no—
471C2×#106—1221no—
472#421—22no—
473#421—614no—
474#421—1222no—
475#421C2×D6114yescomplemented
476C2×#104—22no—
477C2×#104—1222no—
478#410—614no—
479#410—614no—
480#410—1222no—
481#410—1222no—
482C2×#99—1222no—
483C2×#99—1222no—
484#405—614no—
485#405—1222no—
486C2×#97—1221no—
487C2×C4×C8—1221no—
488C61C2×#197611yescharacteristic, complemented, Sylow
489C2×#41—21no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—612no—
500C2×#41—612no—
501C2×#41—1221no—
502C2×#41—1221no—
503C2×#41—1221no—
504C2×#41—1221no—
505C2×#41—1221no—
506C2×#41—1221no—
507C2×#41—1221no—
508C2×#41—1221no—
509C2×#41—1221no—
510C2×#41—1221no—
511C2×#41C4×D6112yes—
512C2×#41C22×D6112yes—
513C22×Q8—611no—
514C22×Q8C4×D6111yescharacteristic
515C22×D4—21no—
516C22×D4—611no—
517C22×D4—1221no—
518C22×D4C4×D6111yescharacteristic
519C23×C4—21no—
520C23×C4—1221no—
521C23×C4C22×D6111yescharacteristic
522#135—1224no—
523#135—1224no—
524#135—1224no—
525#135—1224no—
526#135—1224no—
527#135—1224no—
528#135—1224no—
529#135—1224no—
530C2×Q16—614no—
531C2×Q16—1221no—
532C2×Q16—1221no—
533C2×Q16—1222no—
534C2×SD16—614no—
535C2×SD16—614no—
536C2×SD16—1221no—
537C2×SD16—1221no—
538C2×SD16—1222no—
539C2×SD16—1221no—
540C2×SD16—1221no—
541C2×SD16—1222no—
542C2×D8—614no—
543C2×D8—1221no—
544C2×D8—1221no—
545C2×D8—1222no—
546C2×M16—21no—
547C2×M16—21no—
548C2×M16—21no—
549C2×M16C22⋊D6112yes—
550C2×M16C22⋊D6112yes—
551C2×M16C22×D6112yes—
552C22×C8—21no—
553C22×C8—611no—
554C22×C8—611no—
555C22×C8—612no—
556C22×C8—611no—
557C22×C8—611no—
558C22×C8—612no—
559C22×C8—611no—
560C22×C8—611no—
561C22×C8—612no—
562C22×C8—612no—
563#117—21no—
564#117—21no—
565#117—21no—
566#117—612no—
567#117—612no—
568#117—612no—
569#117—1221no—
570#117—1221no—
571#117—1221no—
572#117—1221no—
573#117—1221no—
574#117C22×D6112yes—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—1221no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—612no—
580C2×C22⋊C4—1221no—
581C2×C42—21no—
582C2×C42—1221no—
583C2×C42—1221no—
584#107—1224no—
585#106—1224no—
586#104—28no—
587#104—1228no—
588#99—1228no—
589#99—1228no—
590#97—1224no—
591C4×C8—1224no—
592C24—21no—
593C24—1221no—
594C24D4×D6111yescharacteristic
595#41—22no—
596#41—22no—
597#41—22no—
598#41—22no—
599#41—22no—
600#41—22no—
601#41—22no—
602#41—22no—
603#41—41no—
604#41—41no—
605#41—41no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—41no—
611#41—1222no—
612#41—1222no—
613#41—1222no—
614#41—1222no—
615#41—1222no—
616#41—1222no—
617#41—1222no—
618#41—1222no—
619#41—2441no—
620#41—2441no—
621#41—2441no—
622#41—2441no—
623#41—2441no—
624#41—2441no—
625#41—2441no—
626#41—2441no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—612no—
633C2×Q8—1221no—
634C2×Q8—1221no—
635C2×Q8—1221no—
636C2×Q8—1221no—
637C2×Q8—1221no—
638C2×Q8C2×C4×D6112yes—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4—41no—
649C2×D4—41no—
650C2×D4—612no—
651C2×D4—1222no—
652C2×D4—1222no—
653C2×D4—1221no—
654C2×D4—1221no—
655C2×D4—1221no—
656C2×D4—1221no—
657C2×D4—1221no—
658C2×D4—2441no—
659C2×D4—2441no—
660C2×D4—2441no—
661C2×D4—2441no—
662C2×D4C2×C4×D6112yes—
663C22×C4—21no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—1221no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—2441no—
676C22×C4—2441no—
677C22×C4—2441no—
678C22×C4—2441no—
679C22×C4—2441no—
680C22×C4C2×C4×D6111yescharacteristic
681C22×C4C2×C4×D6111yescharacteristic
682C22×C4#1175822211yescharacteristic
683C22×C4#1175822211yescharacteristic
684C22×C4D4×D6111yescharacteristic
685C22×C4D4×D6111yescharacteristic
686C22×C4D4×D6111yescharacteristic
687C22×C4D4×D6111yescharacteristic
688C22×C4D4×D6111yescharacteristic
689C22×C4#1175822411yescharacteristic
690C22×C4#1175822411yescharacteristic
691C22×C4C2×C22⋊D6111yescharacteristic
692C22×C4C2×C22⋊D6111yescharacteristic
693C22×C4C23×D6111yescharacteristic
694Q16—1224no—
695Q16—1224no—
696SD16—1224no—
697SD16—1224no—
698SD16—1224no—
699SD16—1224no—
700D8—1224no—
701D8—1224no—
702M16—22no—
703M16—22no—
704M16—22no—
705M16C2×C22⋊D6114yes—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—22no—
709C2×C8—612no—
710C2×C8—612no—
711C2×C8—612no—
712C2×C8—612no—
713C2×C8—612no—
714C2×C8—612no—
715C2×C8—611no—
716C2×C8—611no—
717C2×C8—612no—
718C2×C8—611no—
719C2×C8—611no—
720C2×C8—612no—
721C2×C8—612no—
722C2×C8—612no—
723C2×C8—612no—
724C2×C8—612no—
725C4⋊C4—22no—
726C4⋊C4—41no—
727C4⋊C4—1222no—
728C4⋊C4—1222no—
729C4⋊C4—1222no—
730C4⋊C4—2441no—
731C22⋊C4—22no—
732C22⋊C4—41no—
733C22⋊C4—614no—
734C22⋊C4—1222no—
735C22⋊C4—1222no—
736C22⋊C4—2441no—
737C42—22no—
738C42—41no—
739C42—1222no—
740C42—1222no—
741C42—1222no—
742C42—2441no—
743C23—22no—
744C23—42no—
745C23—41no—
746C23—41no—
747C23—82no—
748C23—1222no—
749C23—4882no—
750C23—2441no—
751C23—2441no—
752C23#1451973711yescharacteristic
753C23#1451973711yescharacteristic
754C23#1451975011yescharacteristic
755C23#1451975011yescharacteristic
756C23#1451977311yescharacteristic
757C23#1451977311yescharacteristic
758C23C2×D4×D6111yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763Q8—1222no—
764Q8—1222no—
765Q8—2441no—
766Q8—2441no—
767D4—22no—
768D4—22no—
769D4—42no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—41no—
774D4—41no—
775D4—1222no—
776D4—1222no—
777D4—2442no—
778D4—2442no—
779D4—2442no—
780D4—2442no—
781D4—2441no—
782D4—2441no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—82no—
792C2×C4—1222no—
793C2×C4—1224no—
794C2×C4—4882no—
795C2×C4—2442no—
796C2×C4—2444no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2442no—
800C2×C4—2442no—
801C2×C4—2442no—
802C2×C4—2442no—
803C2×C4C22⋊C4×D6111yescharacteristic
804C2×C4C22⋊C4×D6111yescharacteristic
805C2×C4C22⋊C4×D6111yescharacteristic
806C2×C4C22⋊C4×D6111yescharacteristic
807C2×C4#1451973711yescharacteristic
808C2×C4#1451973711yescharacteristic
809C2×C4C4×C22⋊D6111yescharacteristic
810C2×C4C4×C22⋊D6111yescharacteristic
811C2×C4C4×C22⋊D6111yescharacteristic
812C2×C4C4×C22⋊D6111yescharacteristic
813C2×C4#1451974911yescharacteristic
814C2×C4#1451974911yescharacteristic
815C2×C4#1451974911yescharacteristic
816C2×C4#1451974911yescharacteristic
817C2×C4#1451975011yescharacteristic
818C2×C4#1451975011yescharacteristic
819C2×C4#1451976311yescharacteristic
820C2×C4#1451976311yescharacteristic
821C2×C4#1451976311yescharacteristic
822C2×C4#1451976311yescharacteristic
823C2×C4#1451977311yescharacteristic
824C2×C4#1451977311yescharacteristic
825C2×C4C22×C4×D6111yescharacteristic
826C2×C4C2×D4×D6111yescharacteristic
827C2×C4C2×D4×D6111yescharacteristic
828C2×C4C22×C22⋊D6111yescharacteristic
829C2×C4C2×#1175822411yescharacteristic
830C2×C4C2×#1175822211yescharacteristic
831C8—24no—
832C8—612no—
833C8—612no—
834C8—612no—
835C8—612no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—42no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—4882no—
848C22—4882no—
849C22—4882no—
850C22—2442no—
851C22#1683966211yescharacteristic
852C22#1683966211yescharacteristic
853C22#1683966211yescharacteristic
854C22#1683966211yescharacteristic
855C22C2×#1451973711yescharacteristic
856C22C2×#1451975011yescharacteristic
857C22C2×#1451977311yescharacteristic
858C4—42no—
859C4—82no—
860C4—4882no—
861C4—2444no—
862C4—2442no—
863C4#1683966211yescharacteristic
864C4#1683966211yescharacteristic
865C4#1683966211yescharacteristic
866C4#1683966211yescharacteristic
867C4C2×C22⋊C4×D6111yescharacteristic
868C4C2×C4×C22⋊D6111yescharacteristic
869C4C2×#1451974911yescharacteristic
870C4C2×#1451976311yescharacteristic
871C2—21no—
872C2—21no—
873C2—21no—
874C2—21no—
875C2—21no—
876C2—21no—
877C2—82no—
878C2—4882no—
879C2#2144671612yesdirect product factor
880C2C2×#1683966211yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#421C2
socleC22×C61#390
prime radicalC22×#14519797C2
cosocleC22×C4×C61C24
hypercenterC2×#421D61
hypocenterC61C2×#1976
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#16839798C2semidirect
3. C2×#16839778C2semidirect
4. C2×#16839736C2semidirect
5. C2×#16839735C2semidirect
6. C2×#16839720C2semidirect
7. #21446716C2direct (N × H)
8. C2×C61×#421C2semidirect
16. C2×#14519797C4semidirect
18. C22×#11758202C4semidirect
19. C22×#11758200C4semidirect
20. C22×#11758201C4semidirect
21. C22×#11758199C4semidirect
26. #16839798C22semidirect
30. #16839778C22semidirect
33. #16839736C22semidirect
35. #16839735C22semidirect
39. #16839720C22semidirect
46. C61×#421C22semidirect
75. C2×#11758202C2×C4semidirect
79. C2×#11758200C2×C4semidirect
83. C2×#11758201C2×C4semidirect
87. C2×#11758199C2×C4semidirect
434. C2×#421D61semidirect
446. C2×C61#1976semidirect
475. #421C2×D61semidirect
488. C61C2×#1976semidirect
879. C2#21446716direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197972
C2×#168397982
C2×#168397782
C2×#168397362
C2×#168397352
C2×#168397202
#214467162
C2×C61×#4212
C2×#197661