Finite Group Databasebeta

← C2×#23764297 #34292242

Subgroups — C2×#23764297 #34292242

Order 20224.

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×#14579181C211yesmaximal, characteristic
2C2×#19098599C211yesmaximal, characteristic, complemented
3C2×#19098579C211yesmaximal, characteristic, complemented
4C2×#19098537C211yesmaximal, characteristic, complemented
5C2×#19098536C211yesmaximal, characteristic, complemented
6C2×#19098521C211yesmaximal, characteristic, complemented
7#23764297C218yesmaximal, direct product factor
8C2×#421×C79C211yesmaximal, characteristic, complemented
9C22×#11929624C2211yescharacteristic
10C2×#14579181—21no—
11C2×#14579181—21no—
12C2×#14579181—22no—
13C2×#14579181—21no—
14C2×#14579181—21no—
15C2×#14579181—22no—
16C2×#14579181C414yescomplemented
17C2×#14579181C2214yes—
18C22×#11929614C411yescharacteristic, complemented
19C22×#11929612C411yescharacteristic, complemented
20C22×#11929611C411yescharacteristic, complemented
21C22×#11929609C411yescharacteristic, complemented
22C23×C79⋊C8C2211yescharacteristic
23C2×#14579120C2211yescharacteristic
24C2×#14579120C2211yescharacteristic
25#19098599—22no—
26#19098599C2214yescomplemented
27C2×#14579094—21no—
28C2×#14579092—21no—
29#19098579—22no—
30#19098579C2214yescomplemented
31C2×#14579087—22no—
32#19098537—22no—
33#19098537C2214yescomplemented
34#19098536—22no—
35#19098536C2214yescomplemented
36C2×#14579076—22no—
37C2×#14579075—22no—
38#19098521—22no—
39#19098521C2214yescomplemented
40C2×#14579071—21no—
41C2×C8×Dic79—21no—
42C22×#41×C79C2211yescharacteristic
43C22×M16×C79C2211yescharacteristic
44C2×#117×C79C2211yescharacteristic
45#421×C79—22no—
46#421×C79C2214yescomplemented
47C2×#104×C79—22no—
48C2×#11929624—21no—
49C2×#11929624—21no—
50C2×#11929624—21no—
51C2×#11929624—21no—
52C2×#11929624—21no—
53C2×#11929624—21no—
54C2×#11929624—21no—
55C2×#11929624—21no—
56C2×#11929624—21no—
57C2×#11929624—21no—
58C2×#11929624C2×C412yes—
59C2×#11929624C2312yes—
60C22×Dic158C2×C411yescharacteristic
61C22×D316C2×C411yescharacteristic
62C22×C22⋊D79—21no—
63C22×C4×D79—21no—
64#14579181—24no—
65#14579181—24no—
66#14579181—24no—
67#14579181—24no—
68#14579181—24no—
69#14579181—24no—
70#14579181—24no—
71#14579181—24no—
72C2×#11929614—21no—
73C2×#11929614—21no—
74C2×#11929614—22no—
75C2×#11929614C2×C414yescomplemented
76C2×#11929612—21no—
77C2×#11929612—21no—
78C2×#11929612—22no—
79C2×#11929612C2×C414yescomplemented
80C2×#11929611—21no—
81C2×#11929611—21no—
82C2×#11929611—22no—
83C2×#11929611C2×C414yescomplemented
84C2×#11929609—21no—
85C2×#11929609—21no—
86C2×#11929609—22no—
87C2×#11929609C2×C414yescomplemented
88C22×C79⋊C8C2×C411yescharacteristic
89C22×C79⋊C8C2×C411yescharacteristic
90C22×C79⋊C8C2×C412yes—
91C22×C79⋊C8D411yescharacteristic
92C22×C79⋊C8D411yescharacteristic
93C22×C79⋊C8D412yes—
94C22×C79⋊C8D411yescharacteristic
95C22×C79⋊C8D411yescharacteristic
96C22×C79⋊C8D412yes—
97C22×C79⋊C8C2312yes—
98#14579120—21no—
99#14579120—21no—
100#14579120—21no—
101#14579120—21no—
102#14579120—21no—
103#14579120D412yes—
104#14579120C2312yes—
105#14579120C2312yes—
106C2×C4⋊Dic79—21no—
107C2×C4⋊Dic79—21no—
108C2×C22⋊Dic79—21no—
109C2×C22⋊Dic79D412yes—
110C2×C4×Dic79—21no—
111C2×C4×Dic79—21no—
112#14579094—24no—
113#14579092—24no—
114#14579087—28no—
115#14579076—28no—
116#14579075—28no—
117#14579071—24no—
118C8×Dic79—24no—
119C2×#41×C79—21no—
120C2×#41×C79—21no—
121C2×#41×C79—21no—
122C2×#41×C79—21no—
123C2×#41×C79—21no—
124C2×#41×C79—21no—
125C2×#41×C79—21no—
126C2×#41×C79—21no—
127C2×#41×C79—21no—
128C2×#41×C79—21no—
129C2×#41×C79C2×C412yes—
130C2×#41×C79C2312yes—
131C22×Q8×C79C2×C411yescharacteristic
132C22×D4×C79—21no—
133C22×D4×C79C2×C411yescharacteristic
134C23×C4×C79—21no—
135C23×C4×C79C2311yescharacteristic
136C2×M16×C79—21no—
137C2×M16×C79—21no—
138C2×M16×C79—21no—
139C2×M16×C79D412yes—
140C2×M16×C79D412yes—
141C2×M16×C79C2312yes—
142C22×C8×C79—21no—
143#117×C79—21no—
144#117×C79—21no—
145#117×C79—21no—
146#117×C79C2312yes—
147C2×C4⋊C4×C79—21no—
148C2×C22⋊C4×C79—21no—
149C2×C42×C79—21no—
150#104×C79—28no—
151C23×D79—21no—
152#11929624—22no—
153#11929624—22no—
154#11929624—22no—
155#11929624—22no—
156#11929624—22no—
157#11929624—22no—
158#11929624—22no—
159#11929624—22no—
160#11929624—41no—
161#11929624—41no—
162#11929624—41no—
163#11929624—41no—
164#11929624—41no—
165#11929624—41no—
166#11929624—41no—
167#11929624—41no—
168C2×Dic158—21no—
169C2×Dic158—21no—
170C2×Dic158—21no—
171C2×Dic158—21no—
172C2×Dic158—21no—
173C2×Dic158C22×C412yes—
174C2×D316—21no—
175C2×D316—21no—
176C2×D316—21no—
177C2×D316—21no—
178C2×D316—21no—
179C2×D316C22×C412yes—
180C2×C22⋊D79—22no—
181C2×C22⋊D79—22no—
182C2×C22⋊D79—41no—
183C2×C22⋊D79—41no—
184C2×C22⋊D79—41no—
185C2×C22⋊D79—41no—
186C22×Dic79—21no—
187C22×Dic79—22no—
188C22×Dic79—41no—
189C2×C4×D79—22no—
190C2×C4×D79—22no—
191C2×C4×D79—41no—
192C2×C4×D79—41no—
193C2×C4×D79—41no—
194C2×C4×D79—41no—
195#11929614—24no—
196#11929614—24no—
197#11929612—24no—
198#11929612—24no—
199#11929611—24no—
200#11929611—24no—
201#11929609—24no—
202#11929609—24no—
203C2×C79⋊C8C22⋊C411yescharacteristic
204C2×C79⋊C8C22⋊C411yescharacteristic
205C2×C79⋊C8C22⋊C412yes—
206C2×C79⋊C8C22⋊C411yescharacteristic
207C2×C79⋊C8C22⋊C411yescharacteristic
208C2×C79⋊C8C22⋊C412yes—
209C2×C79⋊C8C22⋊C412yes—
210C2×C79⋊C8C22⋊C412yes—
211C2×C79⋊C8C22⋊C412yes—
212C2×C79⋊C8C22⋊C412yes—
213C2×C79⋊C8C22×C412yes—
214C2×C79⋊C8C22×C412yes—
215C2×C79⋊C8C2×D412yes—
216C2×C79⋊C8C2×D412yes—
217C2×C79⋊C8C2×D412yes—
218C2×C79⋊C8C2×D412yes—
219C4⋊Dic79—22no—
220C4⋊Dic79—22no—
221C4⋊Dic79—22no—
222C4⋊Dic79—41no—
223C22⋊Dic79—22no—
224C22⋊Dic79—22no—
225C22⋊Dic79—41no—
226C22⋊Dic79C2×D414yes—
227C4×Dic79—22no—
228C4×Dic79—22no—
229C4×Dic79—22no—
230C4×Dic79—41no—
231C24×C79—21no—
232C24×C79C2×D411yescharacteristic
233#41×C79—22no—
234#41×C79—22no—
235#41×C79—22no—
236#41×C79—22no—
237#41×C79—22no—
238#41×C79—22no—
239#41×C79—22no—
240#41×C79—22no—
241#41×C79—41no—
242#41×C79—41no—
243#41×C79—41no—
244#41×C79—41no—
245#41×C79—41no—
246#41×C79—41no—
247#41×C79—41no—
248#41×C79—41no—
249C2×Q8×C79—21no—
250C2×Q8×C79—21no—
251C2×Q8×C79—21no—
252C2×Q8×C79—21no—
253C2×Q8×C79—21no—
254C2×Q8×C79C22×C412yes—
255C2×D4×C79—22no—
256C2×D4×C79—22no—
257C2×D4×C79—21no—
258C2×D4×C79—21no—
259C2×D4×C79—21no—
260C2×D4×C79—21no—
261C2×D4×C79—21no—
262C2×D4×C79—41no—
263C2×D4×C79—41no—
264C2×D4×C79—41no—
265C2×D4×C79—41no—
266C2×D4×C79C22×C412yes—
267C22×C4×C79—21no—
268C22×C4×C79—22no—
269C22×C4×C79—22no—
270C22×C4×C79—41no—
271C22×C4×C79—41no—
272C22×C4×C79—41no—
273C22×C4×C79—41no—
274C22×C4×C79—41no—
275C22×C4×C79C22×C411yescharacteristic
276C22×C4×C79C22×C411yescharacteristic
277C22×C4×C79C2×D411yescharacteristic
278C22×C4×C79C2×D411yescharacteristic
279C22×C4×C79C2×D411yescharacteristic
280C22×C4×C79C2×D411yescharacteristic
281C22×C4×C79C2×D411yescharacteristic
282C22×C4×C79C2×D411yescharacteristic
283C22×C4×C79C2×D411yescharacteristic
284C22×C4×C79#4111yescharacteristic
285C22×C4×C79#4111yescharacteristic
286C22×C4×C79#4111yescharacteristic
287C22×C4×C79#4111yescharacteristic
288C22×C4×C79C2411yescharacteristic
289M16×C79—22no—
290M16×C79—22no—
291M16×C79—22no—
292M16×C79C2×D414yes—
293C2×C8×C79—22no—
294C2×C8×C79—22no—
295C2×C8×C79—22no—
296C4⋊C4×C79—22no—
297C4⋊C4×C79—41no—
298C22⋊C4×C79—22no—
299C22⋊C4×C79—41no—
300C42×C79—22no—
301C42×C79—41no—
302C23×C79—22no—
303C23×C79—42no—
304C23×C79—41no—
305C23×C79—41no—
306C23×C79—82no—
307C23×C79C4×D411yescharacteristic
308C23×C79C4×D411yescharacteristic
309C23×C79#12111yescharacteristic
310C23×C79#12111yescharacteristic
311C23×C79#12711yescharacteristic
312C23×C79#12711yescharacteristic
313C23×C79C22×D411yescharacteristic
314C22×D79—22no—
315C22×D79—41no—
316C22×D79—41no—
317C22×D79—82no—
318Q8×C79—22no—
319Q8×C79—22no—
320Q8×C79—41no—
321Q8×C79—41no—
322D4×C79—22no—
323D4×C79—22no—
324D4×C79—42no—
325D4×C79—42no—
326D4×C79—42no—
327D4×C79—42no—
328D4×C79—41no—
329D4×C79—41no—
330C2×C4×C79—22no—
331C2×C4×C79—41no—
332C2×C4×C79—41no—
333C2×C4×C79—42no—
334C2×C4×C79—42no—
335C2×C4×C79—42no—
336C2×C4×C79—42no—
337C2×C4×C79—42no—
338C2×C4×C79—82no—
339C2×C4×C79C2×C22⋊C411yescharacteristic
340C2×C4×C79C2×C22⋊C411yescharacteristic
341C2×C4×C79C2×C22⋊C411yescharacteristic
342C2×C4×C79C2×C22⋊C411yescharacteristic
343C2×C4×C79C4×D411yescharacteristic
344C2×C4×C79C4×D411yescharacteristic
345C2×C4×C79C4×D411yescharacteristic
346C2×C4×C79C4×D411yescharacteristic
347C2×C4×C79C4×D411yescharacteristic
348C2×C4×C79C4×D411yescharacteristic
349C2×C4×C79#12111yescharacteristic
350C2×C4×C79#12111yescharacteristic
351C2×C4×C79#12111yescharacteristic
352C2×C4×C79#12111yescharacteristic
353C2×C4×C79#12111yescharacteristic
354C2×C4×C79#12111yescharacteristic
355C2×C4×C79#12411yescharacteristic
356C2×C4×C79#12411yescharacteristic
357C2×C4×C79#12411yescharacteristic
358C2×C4×C79#12411yescharacteristic
359C2×C4×C79#12711yescharacteristic
360C2×C4×C79#12711yescharacteristic
361C2×C4×C79C23×C411yescharacteristic
362C2×C4×C79C22×D411yescharacteristic
363C2×C4×C79C22×D411yescharacteristic
364C2×C4×C79C22×D411yescharacteristic
365C2×C4×C79C2×#4111yescharacteristic
366C2×C4×C79C2×#4111yescharacteristic
367C22⋊D79—42no—
368C22⋊D79—42no—
369C22⋊D79—42no—
370C22⋊D79—42no—
371C2×Dic79—22no—
372C2×Dic79—24no—
373C2×Dic79—44no—
374C2×Dic79—41no—
375C2×Dic79—41no—
376C2×Dic79—42no—
377C2×Dic79—82no—
378D316—22no—
379D316—22no—
380D316—41no—
381D316—41no—
382C4×D79—42no—
383C4×D79—42no—
384C4×D79—42no—
385C4×D79—42no—
386Dic158—22no—
387Dic158—22no—
388Dic158—41no—
389Dic158—41no—
390C8×C79—24no—
391C79⋊C8C2×C22⋊C412yes—
392C79⋊C8C2×C22⋊C412yes—
393C79⋊C8C2×C22⋊C412yes—
394C79⋊C8C2×C22⋊C412yes—
395C22×C79—22no—
396C22×C79—22no—
397C22×C79—22no—
398C22×C79—41no—
399C22×C79—41no—
400C22×C79—41no—
401C22×C79—41no—
402C22×C79—42no—
403C22×C79—82no—
404C22×C79—82no—
405C22×C79—82no—
406C22×C79#39011yescharacteristic
407C22×C79#39011yescharacteristic
408C22×C79#39011yescharacteristic
409C22×C79#39011yescharacteristic
410C22×C79C2×C4×D411yescharacteristic
411C22×C79C2×#12111yescharacteristic
412C22×C79C2×#12711yescharacteristic
413C2×D79—42no—
414C2×D79—82no—
415C2×D79—82no—
416C2×D79—82no—
417C4×C79—42no—
418C4×C79—82no—
419C4×C79#39011yescharacteristic
420C4×C79#39011yescharacteristic
421C4×C79#39011yescharacteristic
422C4×C79#39011yescharacteristic
423C4×C79C22×C22⋊C411yescharacteristic
424C4×C79C2×C4×D411yescharacteristic
425C4×C79C2×#12111yescharacteristic
426C4×C79C2×#12411yescharacteristic
427Dic79—44no—
428Dic79—42no—
429Dic79—82no—
430C2×#1976—791nomaximal, Sylow
431C2×C79—21no—
432C2×C79—21no—
433C2×C79—21no—
434C2×C79—21no—
435C2×C79—21no—
436C2×C79—21no—
437C2×C79—82no—
438C2×C79#197612yescomplemented
439C2×C79C2×#39011yescharacteristic
440D79—82no—
441C22×#135—791no—
442C2×#427—791no—
443C2×#421—791no—
444C2×#421D7911yescharacteristic, complemented
445C2×#410—791no—
446C2×#410—791no—
447C2×#405—791no—
448#1976—798no—
449C79C2×#197611yescharacteristic, complemented, Sylow
450C22×#41—791no—
451C22×#41C2×D7911yescharacteristic
452C2×#135—794no—
453C2×#135—794no—
454C2×#135—1581no—
455C2×#135—1581no—
456C2×#135—1582no—
457C2×#135—1581no—
458C2×#135—1581no—
459C2×#135—1582no—
460C22×Q16—791no—
461C22×SD16—791no—
462C22×SD16—791no—
463C22×D8—791no—
464C22×M16C2×D7911yescharacteristic
465C23×C8—791no—
466C2×#117—791no—
467C2×#117—791no—
468C2×#117C2×D7911yescharacteristic
469#427—794no—
470#427—1582no—
471C2×#107—1581no—
472C2×#106—1581no—
473#421—22no—
474#421—794no—
475#421—1582no—
476#421C2×D7914yescomplemented
477C2×#104—22no—
478C2×#104—1582no—
479#410—794no—
480#410—794no—
481#410—1582no—
482#410—1582no—
483C2×#99—1582no—
484C2×#99—1582no—
485#405—794no—
486#405—1582no—
487C2×#97—1581no—
488C2×C4×C8—1581no—
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—792no—
500C2×#41—792no—
501C2×#41—1581no—
502C2×#41—1581no—
503C2×#41—1581no—
504C2×#41—1581no—
505C2×#41—1581no—
506C2×#41—1581no—
507C2×#41—1581no—
508C2×#41—1581no—
509C2×#41—1581no—
510C2×#41—1581no—
511C2×#41C4×D7912yes—
512C2×#41C22×D7912yes—
513C22×Q8—791no—
514C22×Q8C4×D7911yescharacteristic
515C22×D4—21no—
516C22×D4—791no—
517C22×D4—1581no—
518C22×D4C4×D7911yescharacteristic
519C23×C4—21no—
520C23×C4—1581no—
521C23×C4C22×D7911yescharacteristic
522#135—1584no—
523#135—1584no—
524#135—1584no—
525#135—1584no—
526#135—1584no—
527#135—1584no—
528#135—1584no—
529#135—1584no—
530C2×Q16—794no—
531C2×Q16—1581no—
532C2×Q16—1581no—
533C2×Q16—1582no—
534C2×SD16—794no—
535C2×SD16—794no—
536C2×SD16—1581no—
537C2×SD16—1581no—
538C2×SD16—1582no—
539C2×SD16—1581no—
540C2×SD16—1581no—
541C2×SD16—1582no—
542C2×D8—794no—
543C2×D8—1581no—
544C2×D8—1581no—
545C2×D8—1582no—
546C2×M16—21no—
547C2×M16—21no—
548C2×M16—21no—
549C2×M16C22⋊D7912yes—
550C2×M16C22⋊D7912yes—
551C2×M16C22×D7912yes—
552C22×C8—21no—
553C22×C8—791no—
554C22×C8—791no—
555C22×C8—792no—
556C22×C8—791no—
557C22×C8—791no—
558C22×C8—792no—
559C22×C8—791no—
560C22×C8—791no—
561C22×C8—792no—
562C22×C8—792no—
563#117—21no—
564#117—21no—
565#117—21no—
566#117—792no—
567#117—792no—
568#117—792no—
569#117—1581no—
570#117—1581no—
571#117—1581no—
572#117—1581no—
573#117—1581no—
574#117C22×D7912yes—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—1581no—
577C2×C4⋊C4—1581no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—792no—
580C2×C22⋊C4—1581no—
581C2×C42—21no—
582C2×C42—1581no—
583C2×C42—1581no—
584#107—1584no—
585#106—1584no—
586#104—28no—
587#104—1588no—
588#99—1588no—
589#99—1588no—
590#97—1584no—
591C4×C8—1584no—
592C24—21no—
593C24—1581no—
594C24D4×D7911yescharacteristic
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—3161no—
612#41—3161no—
613#41—3161no—
614#41—3161no—
615#41—3161no—
616#41—3161no—
617#41—3161no—
618#41—3161no—
619#41—1582no—
620#41—1582no—
621#41—1582no—
622#41—1582no—
623#41—1582no—
624#41—1582no—
625#41—1582no—
626#41—1582no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—792no—
633C2×Q8—1581no—
634C2×Q8—1581no—
635C2×Q8—1581no—
636C2×Q8—1581no—
637C2×Q8—1581no—
638C2×Q8C2×C4×D7912yes—
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—3161no—
651C2×D4—3161no—
652C2×D4—3161no—
653C2×D4—3161no—
654C2×D4—792no—
655C2×D4—1582no—
656C2×D4—1582no—
657C2×D4—1581no—
658C2×D4—1581no—
659C2×D4—1581no—
660C2×D4—1581no—
661C2×D4—1581no—
662C2×D4C2×C4×D7912yes—
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—3161no—
672C22×C4—3161no—
673C22×C4—3161no—
674C22×C4—3161no—
675C22×C4—3161no—
676C22×C4—1581no—
677C22×C4—1582no—
678C22×C4—1582no—
679C22×C4—1582no—
680C22×C4C2×C4×D7911yescharacteristic
681C22×C4C2×C4×D7911yescharacteristic
682C22×C4D4×D7911yescharacteristic
683C22×C4D4×D7911yescharacteristic
684C22×C4D4×D7911yescharacteristic
685C22×C4D4×D7911yescharacteristic
686C22×C4D4×D7911yescharacteristic
687C22×C4C2×C22⋊D7911yescharacteristic
688C22×C4C2×C22⋊D7911yescharacteristic
689C22×C4#1192962311yescharacteristic
690C22×C4#1192962311yescharacteristic
691C22×C4#1192962411yescharacteristic
692C22×C4#1192962411yescharacteristic
693C22×C4C23×D7911yescharacteristic
694Q16—1584no—
695Q16—1584no—
696SD16—1584no—
697SD16—1584no—
698SD16—1584no—
699SD16—1584no—
700D8—1584no—
701D8—1584no—
702M16—22no—
703M16—22no—
704M16—22no—
705M16C2×C22⋊D7914yes—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—22no—
709C2×C8—791no—
710C2×C8—791no—
711C2×C8—792no—
712C2×C8—791no—
713C2×C8—791no—
714C2×C8—792no—
715C2×C8—792no—
716C2×C8—792no—
717C2×C8—792no—
718C2×C8—792no—
719C2×C8—792no—
720C2×C8—792no—
721C2×C8—792no—
722C2×C8—792no—
723C2×C8—792no—
724C2×C8—792no—
725C4⋊C4—22no—
726C4⋊C4—41no—
727C4⋊C4—3161no—
728C4⋊C4—1582no—
729C4⋊C4—1582no—
730C4⋊C4—1582no—
731C22⋊C4—22no—
732C22⋊C4—41no—
733C22⋊C4—3161no—
734C22⋊C4—794no—
735C22⋊C4—1582no—
736C22⋊C4—1582no—
737C42—22no—
738C42—41no—
739C42—3161no—
740C42—1582no—
741C42—1582no—
742C42—1582no—
743C23—22no—
744C23—42no—
745C23—41no—
746C23—41no—
747C23—82no—
748C23—3161no—
749C23—3161no—
750C23—6322no—
751C23—1582no—
752C23(C22⋊D79)⋊C411yescharacteristic
753C23(C22⋊D79)⋊C411yescharacteristic
754C23#1457913411yescharacteristic
755C23#1457913411yescharacteristic
756C23#1457915711yescharacteristic
757C23#1457915711yescharacteristic
758C23C2×D4×D7911yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763Q8—3161no—
764Q8—3161no—
765Q8—1582no—
766Q8—1582no—
767D4—22no—
768D4—22no—
769D4—42no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—41no—
774D4—41no—
775D4—3162no—
776D4—3162no—
777D4—3162no—
778D4—3162no—
779D4—3161no—
780D4—3161no—
781D4—1582no—
782D4—1582no—
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—3164no—
793C2×C4—3161no—
794C2×C4—3161no—
795C2×C4—3162no—
796C2×C4—3162no—
797C2×C4—3162no—
798C2×C4—3162no—
799C2×C4—3162no—
800C2×C4—6322no—
801C2×C4—1582no—
802C2×C4—1584no—
803C2×C4C22⋊C4×D7911yescharacteristic
804C2×C4C22⋊C4×D7911yescharacteristic
805C2×C4C22⋊C4×D7911yescharacteristic
806C2×C4C22⋊C4×D7911yescharacteristic
807C2×C4(C22⋊D79)⋊C411yescharacteristic
808C2×C4(C22⋊D79)⋊C411yescharacteristic
809C2×C4C4×C22⋊D7911yescharacteristic
810C2×C4C4×C22⋊D7911yescharacteristic
811C2×C4C4×C22⋊D7911yescharacteristic
812C2×C4C4×C22⋊D7911yescharacteristic
813C2×C4#1457913311yescharacteristic
814C2×C4#1457913311yescharacteristic
815C2×C4#1457913311yescharacteristic
816C2×C4#1457913311yescharacteristic
817C2×C4#1457913411yescharacteristic
818C2×C4#1457913411yescharacteristic
819C2×C4#1457914711yescharacteristic
820C2×C4#1457914711yescharacteristic
821C2×C4#1457914711yescharacteristic
822C2×C4#1457914711yescharacteristic
823C2×C4#1457915711yescharacteristic
824C2×C4#1457915711yescharacteristic
825C2×C4C22×C4×D7911yescharacteristic
826C2×C4C2×D4×D7911yescharacteristic
827C2×C4C2×D4×D7911yescharacteristic
828C2×C4C22×C22⋊D7911yescharacteristic
829C2×C4C2×#1192962311yescharacteristic
830C2×C4C2×#1192962411yescharacteristic
831C8—24no—
832C8—792no—
833C8—792no—
834C8—792no—
835C8—792no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—42no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—3162no—
848C22—6322no—
849C22—6322no—
850C22—6322no—
851C22#1909846311yescharacteristic
852C22#1909846311yescharacteristic
853C22#1909846311yescharacteristic
854C22#1909846311yescharacteristic
855C22C2×(C22⋊D79)⋊C411yescharacteristic
856C22C2×#1457913411yescharacteristic
857C22C2×#1457915711yescharacteristic
858C4—42no—
859C4—82no—
860C4—3164no—
861C4—3162no—
862C4—6322no—
863C4#1909846311yescharacteristic
864C4#1909846311yescharacteristic
865C4#1909846311yescharacteristic
866C4#1909846311yescharacteristic
867C4C2×C22⋊C4×D7911yescharacteristic
868C4C2×C4×C22⋊D7911yescharacteristic
869C4C2×#1457913311yescharacteristic
870C4C2×#1457914711yescharacteristic
871C2—21no—
872C2—21no—
873C2—21no—
874C2—21no—
875C2—21no—
876C2—21no—
877C2—82no—
878C2—6322no—
879C2#2376429712yesdirect product factor
880C2C2×#1909846311yescharacteristic
subgroupG/H
centerC2×C4#14579133
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC2×#421×C79C2
socleC22×C79#390
prime radicalC22×#14579181C2
cosocleC22×C4×C79C24
hypercenterC2×#421D79
hypocenterC79C2×#1976
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#19098599C2semidirect
3. C2×#19098579C2semidirect
4. C2×#19098537C2semidirect
5. C2×#19098536C2semidirect
6. C2×#19098521C2semidirect
7. #23764297C2direct (N × H)
8. C2×#421×C79C2semidirect
16. C2×#14579181C4semidirect
18. C22×#11929614C4semidirect
19. C22×#11929612C4semidirect
20. C22×#11929611C4semidirect
21. C22×#11929609C4semidirect
26. #19098599C22semidirect
30. #19098579C22semidirect
33. #19098537C22semidirect
35. #19098536C22semidirect
39. #19098521C22semidirect
46. #421×C79C22semidirect
75. C2×#11929614C2×C4semidirect
79. C2×#11929612C2×C4semidirect
83. C2×#11929611C2×C4semidirect
87. C2×#11929609C2×C4semidirect
438. C2×C79#1976semidirect
444. C2×#421D79semidirect
449. C79C2×#1976semidirect
476. #421C2×D79semidirect
879. C2#23764297direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791812
C2×#190985992
C2×#190985792
C2×#190985372
C2×#190985362
C2×#190985212
#237642972
C2×#421×C792
C2×#197679