Finite Group Databasebeta

← C2×#23774234 #35158891

Subgroups — C2×#23774234 #35158891

Order 20224.

2342 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099075C211yesmaximal, characteristic
2C2×C22⋊Q8×D79C211yesmaximal, characteristic, complemented
3#23774234C2116yesmaximal, direct product factor
4C2×#19098900C211yesmaximal, characteristic, complemented
5C2×#19098883C211yesmaximal, characteristic, complemented
6C2×#19098904C211yesmaximal, characteristic, complemented
7C2×#19098822C211yesmaximal, characteristic, complemented
8C2×#19098820C211yesmaximal, characteristic, complemented
9C2×#19098812C211yesmaximal, characteristic, complemented
10C2×#19098810C211yesmaximal, characteristic, complemented
11C2×#19098727C211yesmaximal, characteristic, complemented
12C2×#19098723C211yesmaximal, characteristic, complemented
13C2×#19098720C211yesmaximal, characteristic, complemented
14C2×#19098703C211yesmaximal, characteristic, complemented
15C2×#19098525C211yesmaximal, characteristic, complemented
16C2×#485×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C22×Q8×D79C2211yescharacteristic
19C23×C4×D79C2211yescharacteristic
20C22×Dic316C2211yescharacteristic, complemented
21C22×#11929614C2211yescharacteristic, complemented
22C22×#11929613C2211yescharacteristic, complemented
23C22×#11929611C2211yescharacteristic, complemented
24C22×#11929607C2211yescharacteristic
25C22×#11929607C2211yescharacteristic
26#19099075—24no—
27#19099075C2218yes—
28C2×#14579145—21no—
29C2×#14579141C2211yescharacteristic
30C2×#14579141C2211yescharacteristic
31C2×#14579141C2211yescharacteristic
32C2×#14579140C2211yescharacteristic
33C2×#14579139—21no—
34C2×#14579138—21no—
35C2×#14579137C2211yescharacteristic
36C22⋊Q8×D79—24no—
37C22⋊Q8×D79C2218yescomplemented
38C2×#14579136C2211yescharacteristic
39C2×#14579136C2211yescharacteristic
40C2×#14579131—21no—
41C2×C4×D316—21no—
42C2×C4×D316—21no—
43C2×C4⋊C4×D79—21no—
44C2×C4⋊C4×D79C2211yescharacteristic
45C2×C22⋊C4×D79—21no—
46#19098904C2218yescomplemented
47#19098900C2218yescomplemented
48#19098883C2218yescomplemented
49#19098822C2218yescomplemented
50#19098820C2218yescomplemented
51#19098812C2218yescomplemented
52#19098810C2218yescomplemented
53#19098727C2218yescomplemented
54#19098723C2218yescomplemented
55#19098720C2218yescomplemented
56#19098703C2218yescomplemented
57C2×#14579094C2211yescharacteristic, complemented
58C2×#14579092C2211yescharacteristic, complemented
59C2×#14579086C2211yescharacteristic, complemented
60C2×#14579084C2211yescharacteristic, complemented
61C2×#14579084C2211yescharacteristic, complemented
62C2×#14579084C2211yescharacteristic, complemented
63C2×#14579083C2211yescharacteristic, complemented
64C2×#14579081C2211yescharacteristic, complemented
65#19098525C2218yescomplemented
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×(C2×D79)⋊C8C2211yescharacteristic
69C2×C22⋊Q8×C79C2211yescharacteristic
70C2×#117×C79C2211yescharacteristic
71#485×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic, complemented
73C2×#106×C79C2211yescharacteristic, complemented
74C2×#103×C79C2211yescharacteristic, complemented
75C2×#103×C79C2211yescharacteristic, complemented
76C2×C22⋊C8×C79C2211yescharacteristic
77C24×D79D411yescharacteristic
78C2×#11929624—22no—
79C2×#11929624—42no—
80C2×#11929624—42no—
81C2×#11929624C2314yes—
82C22×Dic158—21no—
83C22×Dic158C2311yescharacteristic
84C22×Dic158C2311yescharacteristic
85C2×Q8×D79—22no—
86C2×Q8×D79—42no—
87C2×Q8×D79—42no—
88C2×Q8×D79C2314yes—
89C22×D316—21no—
90C22×D316—21no—
91C22×D316C2311yescharacteristic
92C22×C22⋊D79—21no—
93C23×Dic79D411yescharacteristic
94C22×C4×D79—21no—
95C22×C4×D79—21no—
96C22×C4×D79—21no—
97C22×C4×D79—42no—
98C22×C4×D79—42no—
99C22×C4×D79D411yescharacteristic
100C22×C4×D79D411yescharacteristic
101C22×C4×D79D414yes—
102C22×C4×D79C2311yescharacteristic
103C22×C4×D79C2311yescharacteristic
104C22×C4×D79C2314yes—
105C2×Dic316—42no—
106C2×Dic316C2314yescomplemented
107C2×#11929614—42no—
108C2×#11929614C2314yescomplemented
109C2×#11929613—42no—
110C2×#11929613C2314yescomplemented
111C2×#11929611—42no—
112C2×#11929611C2314yescomplemented
113C2×#11929607—42no—
114C2×#11929607—42no—
115C2×#11929607C2314yes—
116C2×#11929607C2314yes—
117C22×C79⋊C8C2311yescharacteristic
118C22×C79⋊C8C2311yescharacteristic
119#14579145—28no—
120#14579141—22no—
121#14579141—22no—
122#14579141—22no—
123#14579141C2314yes—
124#14579141C2314yes—
125#14579141C2314yes—
126#14579140—22no—
127#14579140C2314yes—
128#14579139—28no—
129#14579138—28no—
130#14579137—22no—
131#14579137C2314yes—
132#14579136—22no—
133#14579136—22no—
134#14579136C2314yes—
135#14579136C2314yes—
136#14579131—28no—
137C4×D316—28no—
138C4×D316—28no—
139C2×C4⋊Dic79—21no—
140C2×C4⋊Dic79—21no—
141C2×C4⋊Dic79—21no—
142C2×C4⋊Dic79C2311yescharacteristic
143C2×Dic79⋊C4—21no—
144C2×Dic79⋊C4—21no—
145C2×Dic79⋊C4—21no—
146C4⋊C4×D79—28no—
147C4⋊C4×D79—22no—
148C4⋊C4×D79C2314yes—
149C2×C22⋊Dic79—21no—
150C2×(C2×D79)⋊C4—21no—
151C2×(C2×D79)⋊C4—21no—
152C2×(C2×D79)⋊C4—21no—
153C2×(C2×D79)⋊C4—21no—
154C2×(C2×D79)⋊C4—21no—
155C2×(C2×D79)⋊C4—21no—
156C22⋊C4×D79—28no—
157#14579094C2314yescomplemented
158#14579092C2314yescomplemented
159#14579086C2314yescomplemented
160#14579084C2314yescomplemented
161#14579084C2314yescomplemented
162#14579084C2314yescomplemented
163#14579083C2314yescomplemented
164#14579081C2314yescomplemented
165C22⋊(C79⋊C8)C2314yes—
166(C2×D79)⋊C8C2314yes—
167(C2×D79)⋊C8C2314yes—
168C22×Q8×C79C2311yescharacteristic
169C23×C4×C79C2311yescharacteristic
170C22×C8×C79C2311yescharacteristic
171C22×C8×C79C2311yescharacteristic
172C22⋊Q8×C79—22no—
173C22⋊Q8×C79C2314yes—
174#117×C79—22no—
175#117×C79C2314yes—
176C2×C4⋊C4×C79—21no—
177C2×C4⋊C4×C79C2311yescharacteristic
178C2×C4⋊C4×C79C2311yescharacteristic
179C2×C4⋊C4×C79C2311yescharacteristic
180C2×C22⋊C4×C79—21no—
181C2×C22⋊C4×C79—21no—
182C2×C42×C79—21no—
183#107×C79C2314yescomplemented
184#106×C79C2314yescomplemented
185#103×C79C2314yescomplemented
186#103×C79C2314yescomplemented
187C22⋊C8×C79C2314yes—
188C23×D79—24no—
189C23×D79—21no—
190C23×D79—42no—
191C23×D79—42no—
192C23×D79C2×D411yescharacteristic
193C23×D79C2×D411yescharacteristic
194C23×D79C2×D414yes—
195#11929624—44no—
196#11929624—44no—
197#11929624—48no—
198C2×Dic158—24no—
199C2×Dic158—21no—
200C2×Dic158—21no—
201C2×Dic158—22no—
202C2×Dic158—22no—
203C2×Dic158—22no—
204C2×Dic158—22no—
205C2×Dic158—44no—
206C2×Dic158C2412yes—
207C2×Dic158C2412yes—
208Q8×D79—44no—
209Q8×D79—44no—
210Q8×D79—48no—
211C2×D316—24no—
212C2×D316—24no—
213C2×D316—21no—
214C2×D316—22no—
215C2×D316—22no—
216C2×D316—44no—
217C2×D316—44no—
218C2×D316C2412yes—
219C2×C22⋊D79—24no—
220C2×C22⋊D79—44no—
221C22×Dic79—21no—
222C22×Dic79—21no—
223C22×Dic79—21no—
224C22×Dic79—42no—
225C22×Dic79C2×D411yescharacteristic
226C22×Dic79C2×D411yescharacteristic
227C22×Dic79C2×D414yes—
228C2×C4×D79—24no—
229C2×C4×D79—24no—
230C2×C4×D79—24no—
231C2×C4×D79—22no—
232C2×C4×D79—22no—
233C2×C4×D79—22no—
234C2×C4×D79—22no—
235C2×C4×D79—42no—
236C2×C4×D79—42no—
237C2×C4×D79—48no—
238C2×C4×D79—44no—
239C2×C4×D79—44no—
240C2×C4×D79—44no—
241C2×C4×D79—44no—
242C2×C4×D79—44no—
243C2×C4×D79C2×D412yes—
244C2×C4×D79C2×D412yes—
245C2×C4×D79C2×D414yes—
246C2×C4×D79C2×D414yes—
247C2×C4×D79C2412yes—
248C2×C4×D79C2412yes—
249Dic316—44no—
250#11929614—44no—
251#11929613—44no—
252#11929611—44no—
253#11929607—44no—
254#11929607—44no—
255C2×C79⋊C8—22no—
256C2×C79⋊C8—22no—
257C2×C79⋊C8C2412yes—
258C2×C79⋊C8C2412yes—
259C4⋊Dic79—24no—
260C4⋊Dic79—24no—
261C4⋊Dic79—24no—
262C4⋊Dic79—21no—
263C4⋊Dic79C2412yes—
264Dic79⋊C4—24no—
265Dic79⋊C4—24no—
266Dic79⋊C4—24no—
267C22⋊Dic79—24no—
268(C2×D79)⋊C4—24no—
269(C2×D79)⋊C4—24no—
270(C2×D79)⋊C4—24no—
271(C2×D79)⋊C4—24no—
272(C2×D79)⋊C4—24no—
273(C2×D79)⋊C4—24no—
274C24×C79C2×D411yescharacteristic
275C2×Q8×C79—21no—
276C2×Q8×C79—22no—
277C2×Q8×C79—22no—
278C2×Q8×C79C2412yes—
279C22×C4×C79—22no—
280C22×C4×C79—22no—
281C22×C4×C79—21no—
282C22×C4×C79—21no—
283C22×C4×C79—21no—
284C22×C4×C79—21no—
285C22×C4×C79C2×D412yes—
286C22×C4×C79C2×D411yescharacteristic
287C22×C4×C79C2412yes—
288C22×C4×C79C2411yescharacteristic
289C2×C8×C79—22no—
290C2×C8×C79—22no—
291C2×C8×C79C2412yes—
292C2×C8×C79C2412yes—
293C4⋊C4×C79—24no—
294C4⋊C4×C79—21no—
295C4⋊C4×C79—21no—
296C4⋊C4×C79—21no—
297C4⋊C4×C79C2412yes—
298C4⋊C4×C79C2412yes—
299C4⋊C4×C79C2412yes—
300C22⋊C4×C79—24no—
301C22⋊C4×C79—24no—
302C42×C79—24no—
303C23×C79—22no—
304C23×C79—22no—
305C23×C79—22no—
306C23×C79C22×D412yes—
307C23×C79C22×D411yescharacteristic
308C22×D79—22no—
309C22×D79—22no—
310C22×D79—22no—
311C22×D79—22no—
312C22×D79—22no—
313C22×D79—28no—
314C22×D79—22no—
315C22×D79—44no—
316C22×D79—44no—
317C22×D79—416no—
318C22×D79—42no—
319C22×D79—42no—
320C22×D79—42no—
321C22×D79#13714yes—
322C22×D79C22×D412yes—
323C22×D79C22×D412yes—
324Q8×C79—22no—
325Q8×C79—22no—
326Q8×C79—42no—
327C2×C4×C79—22no—
328C2×C4×C79—24no—
329C2×C4×C79—22no—
330C2×C4×C79—22no—
331C2×C4×C79—22no—
332C2×C4×C79—22no—
333C2×C4×C79—22no—
334C2×C4×C79—22no—
335C2×C4×C79—42no—
336C2×C4×C79—42no—
337C2×C4×C79—42no—
338C2×C4×C79—42no—
339C2×C4×C79C22×D412yes—
340C2×C4×C79C22×D411yescharacteristic
341C2×C4×C79H(5,𝔽2)12yes—
342C2×C4×C79H(5,𝔽2)12yes—
343C2×C4×C79C2511yescharacteristic
344C22⋊D79—48no—
345C2×Dic79—22no—
346C2×Dic79—22no—
347C2×Dic79—22no—
348C2×Dic79—22no—
349C2×Dic79—22no—
350C2×Dic79—44no—
351C2×Dic79—42no—
352C2×Dic79—42no—
353C2×Dic79—42no—
354C2×Dic79C22×D412yes—
355C2×Dic79C22×D412yes—
356D316—22no—
357D316—22no—
358D316—48no—
359D316—48no—
360D316—42no—
361C4×D79—24no—
362C4×D79—24no—
363C4×D79—22no—
364C4×D79—22no—
365C4×D79—22no—
366C4×D79—22no—
367C4×D79—44no—
368C4×D79—44no—
369C4×D79—48no—
370C4×D79—48no—
371C4×D79—48no—
372Dic158—22no—
373Dic158—22no—
374Dic158—22no—
375Dic158—22no—
376Dic158—48no—
377Dic158—42no—
378Dic158—42no—
379C8×C79—22no—
380C8×C79—22no—
381C79⋊C8—22no—
382C79⋊C8—22no—
383C22×C79—22no—
384C22×C79—22no—
385C22×C79—22no—
386C22×C79—44no—
387C22×C79#53412yes—
388C22×C79C2×#13712yes—
389C22×C79#57512yes—
390C22×C79C23×D411yescharacteristic
391C2×D79—22no—
392C2×D79—28no—
393C2×D79—22no—
394C2×D79—22no—
395C2×D79—22no—
396C2×D79—22no—
397C2×D79—416no—
398C2×D79—44no—
399C2×D79—42no—
400C2×D79—42no—
401C2×D79—42no—
402C2×D79—84no—
403C2×D79C2×#13714yes—
404C4×C79—22no—
405C4×C79—42no—
406C4×C79—42no—
407C4×C79—42no—
408C4×C79—42no—
409C4×C79#53412yes—
410C4×C79C2×H(5,𝔽2)11yescharacteristic
411C4×C79C2×H(5,𝔽2)11yescharacteristic
412Dic79—22no—
413Dic79—22no—
414Dic79—42no—
415Dic79—42no—
416Dic79—42no—
417C2×#3196—791nomaximal, Sylow
418C2×C79—42no—
419C2×C79#319614yescomplemented
420C2×C79C2×#53411yescharacteristic
421C2×C79C22×#13711yescharacteristic
422C2×C79C2×#57511yescharacteristic
423D79—24no—
424D79—42no—
425D79—82no—
426C2×#525—791no—
427C22×C22⋊Q8—791no—
428#3196—7916no—
429C2×#484—791no—
430C2×#481—791no—
431C2×#485—791no—
432C2×#485D7911yescharacteristic, complemented
433C2×#470—791no—
434C2×#470—791no—
435C2×#468—791no—
436C2×#468—791no—
437C2×#452—791no—
438C2×#452—791no—
439C2×#451—791no—
440C2×#448—791no—
441C2×#407—791no—
442C79C2×#319611yescharacteristic, complemented, Sylow
443C22×#41—791no—
444C23×Q8—791no—
445C24×C4—791no—
446C22×Q16—791no—
447C22×Q16—791no—
448C22×SD16—791no—
449C22×SD16—791no—
450C22×M16—791no—
451C22×M16—791no—
452#525—798no—
453#525—1584no—
454C2×#123—1581no—
455C2×C22⋊Q8—791no—
456C2×C22⋊Q8—791no—
457C2×C22⋊Q8—798no—
458C2×C22⋊Q8—791no—
459C2×C22⋊Q8—791no—
460C2×C22⋊Q8—791no—
461C2×C22⋊Q8—1581no—
462C2×C22⋊Q8—1581no—
463C2×C22⋊Q8—1584no—
464C2×C22⋊Q8C2×D7911yescharacteristic
465C2×#121—791no—
466C2×#121—791no—
467C2×#120—1581no—
468C2×C4×D4—1581no—
469C2×C4×D4—1581no—
470C2×#117C2×D7911yescharacteristic
471C22×C4⋊C4—791no—
472C22×C4⋊C4—1581no—
473C22×C22⋊C4—1581no—
474#485—798no—
475#485C2×D7918yescomplemented
476#484—798no—
477#481—798no—
478#470—798no—
479#470—798no—
480#468—798no—
481#468—798no—
482#452—798no—
483#452—798no—
484#451—798no—
485#448—798no—
486C2×#107—791no—
487C2×#107C2×D7911yescharacteristic, complemented
488C2×#106—791no—
489C2×#106C2×D7911yescharacteristic, complemented
490C2×#103—791no—
491C2×#103—791no—
492C2×#103—791no—
493C2×#103—791no—
494C2×#103C2×D7911yescharacteristic, complemented
495C2×#103C2×D7911yescharacteristic, complemented
496C2×#102—791no—
497C2×#102—791no—
498#407—798no—
499C2×C22⋊C8—791no—
500C2×C22⋊C8—791no—
501C2×C22⋊C8—791no—
502C2×C22⋊C8C2×D7911yescharacteristic
503C25—791no—
504C2×#41—3162no—
505C2×#41—3162no—
506C2×#41—794no—
507C2×#41—1582no—
508C22×Q8—3162no—
509C22×Q8—3162no—
510C22×Q8—794no—
511C22×Q8—791no—
512C22×Q8—791no—
513C22×Q8—1581no—
514C22×Q8—1582no—
515C22×Q8C22×D7911yescharacteristic
516C22×D4—791no—
517C22×D4—1581no—
518C22×D4—1581no—
519C22×D4—1581no—
520C23×C4—3162no—
521C23×C4—3162no—
522C23×C4—791no—
523C23×C4—791no—
524C23×C4—791no—
525C23×C4—794no—
526C23×C4—794no—
527C23×C4—791no—
528C23×C4—791no—
529C23×C4—1581no—
530C23×C4—1581no—
531C23×C4—1581no—
532C23×C4C22×D7911yescharacteristic
533C2×Q16—3162no—
534C2×Q16—3162no—
535C2×Q16—794no—
536C2×Q16—794no—
537C2×SD16—3162no—
538C2×SD16—3162no—
539C2×SD16—794no—
540C2×SD16—794no—
541C2×M16—3162no—
542C2×M16—3162no—
543C2×M16—794no—
544C2×M16—794no—
545C22×C8—791no—
546C22×C8—791no—
547C22×C8C22×D7911yescharacteristic
548C22×C8C22×D7911yescharacteristic
549#123—1588no—
550C22⋊Q8—22no—
551C22⋊Q8—794no—
552C22⋊Q8—794no—
553C22⋊Q8—794no—
554C22⋊Q8—794no—
555C22⋊Q8—794no—
556C22⋊Q8—1588no—
557C22⋊Q8—1588no—
558C22⋊Q8—1582no—
559C22⋊Q8—1582no—
560C22⋊Q8—1582no—
561C22⋊Q8—1582no—
562C22⋊Q8—1582no—
563C22⋊Q8C22×D7914yes—
564#121—794no—
565#121—794no—
566#121—1582no—
567#121—1582no—
568#120—1588no—
569C4×D4—1588no—
570C4×D4—1588no—
571#117—22no—
572#117C22×D7914yes—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—791no—
575C2×C4⋊C4—794no—
576C2×C4⋊C4—1582no—
577C2×C4⋊C4—1588no—
578C2×C4⋊C4—1581no—
579C2×C4⋊C4—1581no—
580C2×C4⋊C4—1581no—
581C2×C4⋊C4—1581no—
582C2×C4⋊C4—1581no—
583C2×C4⋊C4—1581no—
584C2×C4⋊C4C22×D7911yescharacteristic
585C2×C4⋊C4C22×D7911yescharacteristic
586C2×C4⋊C4C22×D7911yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—1588no—
590C2×C22⋊C4—1581no—
591C2×C22⋊C4—1581no—
592C2×C22⋊C4—1581no—
593C2×C22⋊C4—1581no—
594C2×C22⋊C4—1581no—
595C2×C22⋊C4—1581no—
596C2×C22⋊C4—1581no—
597C2×C42—21no—
598#107—794no—
599#107C22×D7914yescomplemented
600#106—794no—
601#106C22×D7914yescomplemented
602#103—794no—
603#103—794no—
604#103—794no—
605#103—794no—
606#103C22×D7914yescomplemented
607#103C22×D7914yescomplemented
608#102—794no—
609#102—794no—
610C22⋊C8—794no—
611C22⋊C8—794no—
612C22⋊C8—794no—
613C22⋊C8C22×D7914yes—
614C24—3162no—
615C24—3162no—
616C24—794no—
617C24—791no—
618C24—791no—
619C24—1584no—
620C24—1581no—
621C24D4×D7911yescharacteristic
622#41—3168no—
623#41—3164no—
624#41—3164no—
625C2×Q8—21no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—3164no—
629C2×Q8—3164no—
630C2×Q8—3164no—
631C2×Q8—3168no—
632C2×Q8—792no—
633C2×Q8—792no—
634C2×Q8—1584no—
635C2×Q8—1582no—
636C2×Q8—1582no—
637C2×Q8—1582no—
638C2×Q8—1582no—
639C2×Q8—1581no—
640C2×Q8—1581no—
641C2×Q8C23×D7912yes—
642C2×D4—3164no—
643C2×D4—3164no—
644C2×D4—3164no—
645C2×D4—792no—
646C2×D4—1584no—
647C2×D4—1584no—
648C2×D4—1584no—
649C2×D4—1582no—
650C2×D4—1582no—
651C2×D4—1581no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—3164no—
659C22×C4—3162no—
660C22×C4—3162no—
661C22×C4—3164no—
662C22×C4—3164no—
663C22×C4—3168no—
664C22×C4—3164no—
665C22×C4—3164no—
666C22×C4—3162no—
667C22×C4—794no—
668C22×C4—794no—
669C22×C4—794no—
670C22×C4—791no—
671C22×C4—791no—
672C22×C4—792no—
673C22×C4—792no—
674C22×C4—792no—
675C22×C4—792no—
676C22×C4—1584no—
677C22×C4—1584no—
678C22×C4—1581no—
679C22×C4—1581no—
680C22×C4—1581no—
681C22×C4—1584no—
682C22×C4—1582no—
683C22×C4—1582no—
684C22×C4—1582no—
685C22×C4—1582no—
686C22×C4D4×D7912yes—
687C22×C4D4×D7911yescharacteristic
688C22×C4C23×D7912yes—
689C22×C4C23×D7911yescharacteristic
690Q16—3164no—
691Q16—3164no—
692SD16—3164no—
693SD16—3164no—
694M16—3164no—
695M16—3164no—
696C2×C8—22no—
697C2×C8—22no—
698C2×C8—792no—
699C2×C8—792no—
700C2×C8—1582no—
701C2×C8—1582no—
702C2×C8C23×D7912yes—
703C2×C8C23×D7912yes—
704C4⋊C4—24no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—792no—
709C4⋊C4—1584no—
710C4⋊C4—1584no—
711C4⋊C4—1584no—
712C4⋊C4—1584no—
713C4⋊C4—1584no—
714C4⋊C4—1584no—
715C4⋊C4—1581no—
716C4⋊C4C23×D7912yes—
717C4⋊C4C23×D7912yes—
718C4⋊C4C23×D7912yes—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—1584no—
722C22⋊C4—1584no—
723C22⋊C4—1584no—
724C22⋊C4—1584no—
725C22⋊C4—1584no—
726C22⋊C4—1584no—
727C22⋊C4—1584no—
728C42—24no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—3164no—
733C23—3164no—
734C23—31616no—
735C23—3162no—
736C23—3162no—
737C23—3162no—
738C23—794no—
739C23—792no—
740C23—792no—
741C23—1588no—
742C23—1582no—
743C23—1582no—
744C23—1582no—
745C23—1582no—
746C23—1582no—
747C23—1582no—
748C23C2×D4×D7912yes—
749C23C2×D4×D7911yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—42no—
753Q8—3168no—
754Q8—3162no—
755Q8—3162no—
756Q8—1582no—
757Q8—1582no—
758Q8—1582no—
759Q8—1582no—
760D4—3168no—
761D4—3168no—
762D4—3168no—
763D4—3162no—
764D4—1582no—
765D4—1582no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—3168no—
779C2×C4—3164no—
780C2×C4—3164no—
781C2×C4—3168no—
782C2×C4—3168no—
783C2×C4—3162no—
784C2×C4—3162no—
785C2×C4—3162no—
786C2×C4—3164no—
787C2×C4—792no—
788C2×C4—792no—
789C2×C4—1582no—
790C2×C4—1582no—
791C2×C4—1582no—
792C2×C4—1582no—
793C2×C4—1582no—
794C2×C4—1582no—
795C2×C4—1582no—
796C2×C4—1582no—
797C2×C4—1582no—
798C2×C4—1584no—
799C2×C4—1584no—
800C2×C4C2×D4×D7912yes—
801C2×C4C2×D4×D7911yescharacteristic
802C2×C4#1457920712yes—
803C2×C4#1457920712yes—
804C2×C4C24×D7911yescharacteristic
805C8—22no—
806C8—22no—
807C8—1582no—
808C8—1582no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—44no—
813C22—31616no—
814C22—3164no—
815C22—3162no—
816C22—3162no—
817C22—3162no—
818C22—794no—
819C22—6324no—
820C22—1582no—
821C22—1582no—
822C22—1582no—
823C22—1588no—
824C22—1582no—
825C22—1582no—
826C22#1909912412yes—
827C22#137×D7912yes—
828C22#1909936012yes—
829C22C22×D4×D7911yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—3162no—
836C4—3162no—
837C4—3162no—
838C4—1582no—
839C4—1582no—
840C4#1909912412yes—
841C4C2×#1457920711yescharacteristic
842C4C2×#1457920711yescharacteristic
843C2—42no—
844C2—3162no—
845C2—6322no—
846C2—1584no—
847C2#2377423414yesdirect product factor
848C2C2×#1909912411yescharacteristic
849C2C2×#137×D7911yescharacteristic
850C2C2×#1909936011yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#485×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099075C2
hypercenterC2×#485D79
hypocenterC79C2×#3196
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊Q8×D79C2semidirect
3. #23774234C2direct (N × H)
4. C2×#19098900C2semidirect
5. C2×#19098883C2semidirect
6. C2×#19098904C2semidirect
7. C2×#19098822C2semidirect
8. C2×#19098820C2semidirect
9. C2×#19098812C2semidirect
10. C2×#19098810C2semidirect
11. C2×#19098727C2semidirect
12. C2×#19098723C2semidirect
13. C2×#19098720C2semidirect
14. C2×#19098703C2semidirect
15. C2×#19098525C2semidirect
16. C2×#485×C79C2semidirect
20. C22×Dic316C22semidirect
21. C22×#11929614C22semidirect
22. C22×#11929613C22semidirect
23. C22×#11929611C22semidirect
37. C22⋊Q8×D79C22semidirect
46. #19098904C22semidirect
47. #19098900C22semidirect
48. #19098883C22semidirect
49. #19098822C22semidirect
50. #19098820C22semidirect
51. #19098812C22semidirect
52. #19098810C22semidirect
53. #19098727C22semidirect
54. #19098723C22semidirect
55. #19098720C22semidirect
56. #19098703C22semidirect
57. C2×#14579094C22semidirect
58. C2×#14579092C22semidirect
59. C2×#14579086C22semidirect
60. C2×#14579084C22semidirect
61. C2×#14579084C22semidirect
62. C2×#14579084C22semidirect
63. C2×#14579083C22semidirect
64. C2×#14579081C22semidirect
65. #19098525C22semidirect
71. #485×C79C22semidirect
72. C2×#107×C79C22semidirect
73. C2×#106×C79C22semidirect
74. C2×#103×C79C22semidirect
75. C2×#103×C79C22semidirect
106. C2×Dic316C23semidirect
108. C2×#11929614C23semidirect
110. C2×#11929613C23semidirect
112. C2×#11929611C23semidirect
157. #14579094C23semidirect
158. #14579092C23semidirect
159. #14579086C23semidirect
160. #14579084C23semidirect
161. #14579084C23semidirect
162. #14579084C23semidirect
163. #14579083C23semidirect
164. #14579081C23semidirect
183. #107×C79C23semidirect
184. #106×C79C23semidirect
185. #103×C79C23semidirect
186. #103×C79C23semidirect
419. C2×C79#3196semidirect
432. C2×#485D79semidirect
442. C79C2×#3196semidirect
475. #485C2×D79semidirect
487. C2×#107C2×D79semidirect
489. C2×#106C2×D79semidirect
494. C2×#103C2×D79semidirect
495. C2×#103C2×D79semidirect
599. #107C22×D79semidirect
601. #106C22×D79semidirect
606. #103C22×D79semidirect
607. #103C22×D79semidirect
847. C2#23774234direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190990752
C2×C22⋊Q8×D792
#237742342
C2×#190989002
C2×#190988832
C2×#190989042
C2×#190988222
C2×#190988202
C2×#190988122
C2×#190988102
C2×#190987272
C2×#190987232
C2×#190987202
C2×#190987032
C2×#190985252
C2×#485×C792
C2×#319679