Finite Group Databasebeta

← C2×#23773317 #35156040

Subgroups — C2×#23773317 #35156040

Order 20224.

2378 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099075C211yesmaximal, characteristic
2C2×#117×D79C211yesmaximal, characteristic, complemented
3#23773317C2116yesmaximal, direct product factor
4C2×#19098900C211yesmaximal, characteristic, complemented
5C2×#19098883C211yesmaximal, characteristic, complemented
6C2×#19098907C211yesmaximal, characteristic, complemented
7C2×#19098906C211yesmaximal, characteristic, complemented
8C2×#19098890C211yesmaximal, characteristic, complemented
9C2×#19098889C211yesmaximal, characteristic, complemented
10C2×#19098895C211yesmaximal, characteristic, complemented
11C2×#19098878C211yesmaximal, characteristic, complemented
12C2×#19098599C211yesmaximal, characteristic, complemented
13C2×#19098560C211yesmaximal, characteristic, complemented
14C2×#19098557C211yesmaximal, characteristic, complemented
15C22×(C2×D79)⋊C8C211yesmaximal, characteristic, complemented
16C2×#427×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C23×C79⋊C8C2211yescharacteristic
20#19099075—24no—
21#19099075C2218yes—
22C2×#14579145—21no—
23C2×#14579141C2211yescharacteristic
24C2×#14579141C2211yescharacteristic
25C2×#14579136C2211yescharacteristic
26C2×#14579136C2211yescharacteristic
27C2×#14579131—21no—
28C2×C4×D316—21no—
29C2×C4×D316—21no—
30C2×#14579120C2211yescharacteristic
31C2×#14579119C2211yescharacteristic
32C2×#14579119C2211yescharacteristic
33C2×#14579118—21no—
34C2×#14579117—21no—
35#117×D79—24no—
36#117×D79C2218yescomplemented
37C2×C4⋊C4×D79C2211yescharacteristic
38C2×C4⋊C4×D79C2211yescharacteristic
39C2×C22⋊C4×D79—21no—
40C2×C42×D79—21no—
41#19098907C2218yescomplemented
42#19098906C2218yescomplemented
43#19098900C2218yescomplemented
44#19098895C2218yescomplemented
45#19098890C2218yescomplemented
46#19098889C2218yescomplemented
47#19098883C2218yescomplemented
48#19098878C2218yescomplemented
49#19098599C2218yescomplemented
50C2×#14579094C2211yescharacteristic, complemented
51C2×#14579094C2211yescharacteristic, complemented
52C2×#14579092C2211yescharacteristic, complemented
53C2×#14579092C2211yescharacteristic, complemented
54#19098560C2218yescomplemented
55#19098557C2218yescomplemented
56C2×#14579086C2211yescharacteristic, complemented
57C2×#14579086C2211yescharacteristic, complemented
58C2×#14579084C2211yescharacteristic, complemented
59C2×#14579084C2211yescharacteristic, complemented
60C2×#14579083C2211yescharacteristic, complemented
61C2×#14579083C2211yescharacteristic, complemented
62C2×#14579081C2211yescharacteristic, complemented
63C2×#14579081C2211yescharacteristic, complemented
64C2×(C2×D79)⋊C8C2211yescharacteristic
65C2×(C2×D79)⋊C8C2211yescharacteristic
66C2×(C2×D79)⋊C8C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×(C2×D79)⋊C8C2218yescomplemented
69C23×C8×C79C2211yescharacteristic
70C2×#117×C79C2211yescharacteristic
71C2×#117×C79C2211yescharacteristic
72#427×C79C2218yescomplemented
73C2×#107×C79C2211yescharacteristic, complemented
74C2×#107×C79C2211yescharacteristic, complemented
75C2×#106×C79C2211yescharacteristic, complemented
76C2×#106×C79C2211yescharacteristic, complemented
77C24×D79D411yescharacteristic
78C2×#11929624—22no—
79C2×#11929624—24no—
80C2×#11929624—24no—
81C2×#11929624C2314yes—
82C22×Dic158C2311yescharacteristic
83C22×D316—21no—
84C22×D316—21no—
85C22×D316C2311yescharacteristic
86C22×C22⋊D79—21no—
87C23×Dic79D411yescharacteristic
88C22×C4×D79—24no—
89C22×C4×D79—24no—
90C22×C4×D79—21no—
91C22×C4×D79—21no—
92C22×C4×D79—21no—
93C22×C4×D79D411yescharacteristic
94C22×C4×D79D414yes—
95C22×C4×D79D411yescharacteristic
96C22×C4×D79C2311yescharacteristic
97C22×C4×D79C2314yes—
98C22×C4×D79C2311yescharacteristic
99C22×C79⋊C8—24no—
100C22×C79⋊C8C2311yescharacteristic
101C22×C79⋊C8C2311yescharacteristic
102C22×C79⋊C8C2314yes—
103#14579145—28no—
104#14579141—22no—
105#14579141—22no—
106#14579141C2314yes—
107#14579141C2314yes—
108#14579136—22no—
109#14579136—22no—
110#14579136C2314yes—
111#14579136C2314yes—
112#14579131—28no—
113C4×D316—28no—
114C4×D316—28no—
115#14579120—22no—
116#14579120C2314yes—
117#14579119—22no—
118#14579119—22no—
119#14579119C2314yes—
120#14579119C2314yes—
121#14579118—28no—
122#14579117—28no—
123C2×C4⋊Dic79—21no—
124C2×C4⋊Dic79—21no—
125C2×C4⋊Dic79C2311yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C4⋊C4×D79—22no—
130C4⋊C4×D79—22no—
131C4⋊C4×D79C2314yes—
132C4⋊C4×D79C2314yes—
133C2×C22⋊Dic79—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C22⋊C4×D79—28no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79—21no—
143C2×C4×Dic79—21no—
144C42×D79—28no—
145#14579094C2314yescomplemented
146#14579094C2314yescomplemented
147#14579092C2314yescomplemented
148#14579092C2314yescomplemented
149#14579086C2314yescomplemented
150#14579086C2314yescomplemented
151#14579084C2314yescomplemented
152#14579084C2314yescomplemented
153#14579083C2314yescomplemented
154#14579083C2314yescomplemented
155#14579081C2314yescomplemented
156#14579081C2314yescomplemented
157(C2×D79)⋊C8C2314yes—
158(C2×D79)⋊C8C2314yes—
159(C2×D79)⋊C8C2314yes—
160(C2×D79)⋊C8C2314yes—
161C23×C4×C79C2311yescharacteristic
162C22×C8×C79—24no—
163C22×C8×C79C2311yescharacteristic
164C22×C8×C79C2311yescharacteristic
165C22×C8×C79C2314yes—
166#117×C79—22no—
167#117×C79—22no—
168#117×C79C2314yes—
169#117×C79C2314yes—
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176C2×C42×C79—21no—
177C2×C42×C79—21no—
178#107×C79C2314yescomplemented
179#107×C79C2314yescomplemented
180#106×C79C2314yescomplemented
181#106×C79C2314yescomplemented
182C23×D79—24no—
183C23×D79—24no—
184C23×D79—21no—
185C23×D79—42no—
186C23×D79C2×D411yescharacteristic
187C23×D79C2×D414yes—
188C23×D79C2×D411yescharacteristic
189#11929624—28no—
190#11929624—28no—
191#11929624—48no—
192C2×Dic158—21no—
193C2×Dic158—22no—
194C2×Dic158—22no—
195C2×Dic158C2412yes—
196C2×D316—24no—
197C2×D316—24no—
198C2×D316—21no—
199C2×D316—22no—
200C2×D316—22no—
201C2×D316—44no—
202C2×D316—44no—
203C2×D316C2412yes—
204C2×C22⋊D79—24no—
205C2×C22⋊D79—44no—
206C22×Dic79—24no—
207C22×Dic79—21no—
208C22×Dic79—21no—
209C22×Dic79—21no—
210C22×Dic79C2×D411yescharacteristic
211C22×Dic79C2×D411yescharacteristic
212C22×Dic79C2×D414yes—
213C2×C4×D79—24no—
214C2×C4×D79—24no—
215C2×C4×D79—24no—
216C2×C4×D79—24no—
217C2×C4×D79—216no—
218C2×C4×D79—24no—
219C2×C4×D79—22no—
220C2×C4×D79—22no—
221C2×C4×D79—28no—
222C2×C4×D79—22no—
223C2×C4×D79—22no—
224C2×C4×D79—28no—
225C2×C4×D79—44no—
226C2×C4×D79—44no—
227C2×C4×D79—44no—
228C2×C4×D79C2×D414yes—
229C2×C4×D79C2×D412yes—
230C2×C4×D79C2×D414yes—
231C2×C4×D79C2×D412yes—
232C2×C4×D79C2412yes—
233C2×C4×D79C2412yes—
234C2×C79⋊C8—22no—
235C2×C79⋊C8—22no—
236C2×C79⋊C8—28no—
237C2×C79⋊C8C2412yes—
238C2×C79⋊C8C2412yes—
239C4⋊Dic79—24no—
240C4⋊Dic79—24no—
241C4⋊Dic79—21no—
242C4⋊Dic79—21no—
243C4⋊Dic79C2412yes—
244C4⋊Dic79C2412yes—
245Dic79⋊C4—24no—
246Dic79⋊C4—24no—
247C22⋊Dic79—24no—
248(C2×D79)⋊C4—24no—
249(C2×D79)⋊C4—24no—
250(C2×D79)⋊C4—24no—
251(C2×D79)⋊C4—24no—
252(C2×D79)⋊C4—24no—
253(C2×D79)⋊C4—24no—
254C4×Dic79—24no—
255C4×Dic79—24no—
256C4×Dic79—24no—
257C24×C79C2×D411yescharacteristic
258C22×C4×C79—21no—
259C22×C4×C79—21no—
260C22×C4×C79—21no—
261C22×C4×C79—21no—
262C22×C4×C79C2×D412yes—
263C22×C4×C79C2×D411yescharacteristic
264C22×C4×C79#4114yes—
265C22×C4×C79#4114yes—
266C22×C4×C79C2411yescharacteristic
267C22×C4×C79C2412yes—
268C2×C8×C79—22no—
269C2×C8×C79—22no—
270C2×C8×C79—28no—
271C2×C8×C79C2412yes—
272C2×C8×C79C2412yes—
273C4⋊C4×C79—21no—
274C4⋊C4×C79—21no—
275C4⋊C4×C79—21no—
276C4⋊C4×C79—21no—
277C4⋊C4×C79C2412yes—
278C4⋊C4×C79C2412yes—
279C4⋊C4×C79C2412yes—
280C4⋊C4×C79C2412yes—
281C22⋊C4×C79—24no—
282C22⋊C4×C79—24no—
283C42×C79—24no—
284C42×C79—24no—
285C23×C79—22no—
286C23×C79—22no—
287C23×C79#12314yes—
288C23×C79C22×D412yes—
289C23×C79C22×D411yescharacteristic
290C22×D79—22no—
291C22×D79—22no—
292C22×D79—28no—
293C22×D79—22no—
294C22×D79—22no—
295C22×D79—22no—
296C22×D79—28no—
297C22×D79—22no—
298C22×D79—44no—
299C22×D79—416no—
300C22×D79—42no—
301C22×D79—42no—
302C22×D79—42no—
303C22×D79#13514yes—
304C22×D79C22×D412yes—
305C22×D79C22×D412yes—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—42no—
311C2×C4×C79—42no—
312C2×C4×C79—42no—
313C2×C4×C79—42no—
314C2×C4×C79#12314yes—
315C2×C4×C79#12318yes—
316C2×C4×C79C22×D412yes—
317C2×C4×C79C22×D411yescharacteristic
318C2×C4×C79C2×#4112yes—
319C2×C4×C79C2×#4114yes—
320C2×C4×C79C2×#4112yes—
321C2×C4×C79C2×#4114yes—
322C2×C4×C79C2511yescharacteristic
323C22⋊D79—48no—
324C2×Dic79—28no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—22no—
330C2×Dic79—42no—
331C2×Dic79—42no—
332C2×Dic79—42no—
333C2×Dic79C22×D412yes—
334C2×Dic79C22×D412yes—
335D316—22no—
336D316—22no—
337D316—48no—
338D316—48no—
339D316—42no—
340C4×D79—24no—
341C4×D79—24no—
342C4×D79—28no—
343C4×D79—28no—
344C4×D79—22no—
345C4×D79—22no—
346C4×D79—22no—
347C4×D79—22no—
348C4×D79—48no—
349C4×D79—48no—
350C4×D79—48no—
351Dic158—22no—
352Dic158—22no—
353Dic158—42no—
354C8×C79—22no—
355C8×C79—22no—
356C79⋊C8—22no—
357C79⋊C8—22no—
358C22×C79—28no—
359C22×C79—22no—
360C22×C79—22no—
361C22×C79C2×#12314yes—
362C22×C79C2×#12312yes—
363C22×C79C2×#13512yes—
364C22×C79#57512yes—
365C22×C79C23×D411yescharacteristic
366C2×D79—28no—
367C2×D79—22no—
368C2×D79—22no—
369C2×D79—22no—
370C2×D79—22no—
371C2×D79—22no—
372C2×D79—416no—
373C2×D79—44no—
374C2×D79—42no—
375C2×D79—42no—
376C2×D79—42no—
377C2×D79—84no—
378C2×D79C2×#13514yes—
379C4×C79—42no—
380C4×C79—42no—
381C4×C79—42no—
382C4×C79—42no—
383C4×C79C2×#12312yes—
384C4×C79C2×#12314yes—
385C4×C79C22×#4111yescharacteristic
386C4×C79C22×#4111yescharacteristic
387Dic79—22no—
388Dic79—22no—
389Dic79—42no—
390Dic79—42no—
391Dic79—42no—
392C2×#3091—791nomaximal, Sylow
393C2×C79—24no—
394C2×C79#309114yescomplemented
395C2×C79C22×#12311yescharacteristic
396C2×C79C22×#13511yescharacteristic
397C2×C79C2×#57511yescharacteristic
398D79—24no—
399D79—42no—
400D79—82no—
401C2×#525—791no—
402C22×#117—791no—
403#3091—7916no—
404C2×#484—791no—
405C2×#481—791no—
406C2×#485—791no—
407C2×#485—791no—
408C2×#482—791no—
409C2×#482—791no—
410C2×#483—791no—
411C2×#480—791no—
412C2×#427—791no—
413C2×#427D7911yescharacteristic, complemented
414C2×#416—791no—
415C2×#416—791no—
416C22×C22⋊C8—791no—
417C79C2×#309111yescharacteristic, complemented, Sylow
418C22×#41—791no—
419C24×C4—791no—
420C23×C8—791no—
421C23×C8C2×D7911yescharacteristic
422#525—798no—
423#525—1584no—
424C2×#123—1581no—
425C2×C22⋊Q8—791no—
426C2×C22⋊Q8—791no—
427C2×#121—791no—
428C2×#121—791no—
429C2×#120—1581no—
430C2×C4×D4—1581no—
431C2×C4×D4—1581no—
432C2×#117—791no—
433C2×#117—798no—
434C2×#117—791no—
435C2×#117—791no—
436C2×#117—1581no—
437C2×#117—1581no—
438C2×#117—1584no—
439C2×#117C2×D7911yescharacteristic
440C2×#117C2×D7911yescharacteristic
441C22×C4⋊C4—791no—
442C22×C4⋊C4—791no—
443C22×C22⋊C4—1581no—
444C22×C42—1581no—
445#485—798no—
446#485—798no—
447#484—798no—
448#483—798no—
449#482—798no—
450#482—798no—
451#481—798no—
452#480—798no—
453#427—798no—
454#427C2×D7918yescomplemented
455C2×#107—791no—
456C2×#107—791no—
457C2×#107C2×D7911yescharacteristic, complemented
458C2×#107C2×D7911yescharacteristic, complemented
459C2×#106—791no—
460C2×#106—791no—
461C2×#106C2×D7911yescharacteristic, complemented
462C2×#106C2×D7911yescharacteristic, complemented
463#416—798no—
464#416—798no—
465C2×#103—791no—
466C2×#103—791no—
467C2×#103—791no—
468C2×#103—791no—
469C2×#102—791no—
470C2×#102—791no—
471C2×#102—791no—
472C2×#102—791no—
473C2×C22⋊C8—791no—
474C2×C22⋊C8—791no—
475C2×C22⋊C8—791no—
476C2×C22⋊C8—791no—
477C2×C22⋊C8—798no—
478C25—791no—
479C2×#41—794no—
480C2×#41—1584no—
481C2×#41—1584no—
482C2×#41—1582no—
483C22×Q8—791no—
484C22×D4—791no—
485C22×D4—1581no—
486C22×D4—1581no—
487C22×D4—1581no—
488C23×C4—791no—
489C23×C4—794no—
490C23×C4—791no—
491C23×C4—791no—
492C23×C4—791no—
493C23×C4—791no—
494C23×C4—794no—
495C23×C4—1581no—
496C23×C4—1581no—
497C23×C4—1581no—
498C23×C4—1584no—
499C23×C4—1584no—
500C23×C4C22×D7911yescharacteristic
501C22×C8—24no—
502C22×C8—791no—
503C22×C8—791no—
504C22×C8—794no—
505C22×C8—1584no—
506C22×C8C22×D7911yescharacteristic
507C22×C8C22×D7911yescharacteristic
508C22×C8C22×D7914yes—
509#123—1588no—
510C22⋊Q8—794no—
511C22⋊Q8—794no—
512C22⋊Q8—1582no—
513C22⋊Q8—1582no—
514#121—794no—
515#121—794no—
516#121—1582no—
517#121—1582no—
518#120—1588no—
519C4×D4—1588no—
520C4×D4—1588no—
521#117—22no—
522#117—22no—
523#117—794no—
524#117—794no—
525#117—794no—
526#117—1588no—
527#117—1588no—
528#117—1582no—
529#117—1582no—
530#117—1582no—
531#117C22×D7914yes—
532#117C22×D7914yes—
533C2×C4⋊C4—791no—
534C2×C4⋊C4—791no—
535C2×C4⋊C4—794no—
536C2×C4⋊C4—794no—
537C2×C4⋊C4—1582no—
538C2×C4⋊C4—1582no—
539C2×C4⋊C4—1581no—
540C2×C4⋊C4—1581no—
541C2×C4⋊C4—1581no—
542C2×C4⋊C4—1581no—
543C2×C4⋊C4C22×D7911yescharacteristic
544C2×C4⋊C4C22×D7911yescharacteristic
545C2×C4⋊C4C22×D7911yescharacteristic
546C2×C4⋊C4C22×D7911yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1588no—
550C2×C22⋊C4—1581no—
551C2×C22⋊C4—1581no—
552C2×C22⋊C4—1581no—
553C2×C22⋊C4—1581no—
554C2×C22⋊C4—1581no—
555C2×C22⋊C4—1581no—
556C2×C22⋊C4—1581no—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—1588no—
560C2×C42—1581no—
561C2×C42—1581no—
562C2×C42—1581no—
563#107—794no—
564#107—794no—
565#107C22×D7914yescomplemented
566#107C22×D7914yescomplemented
567#106—794no—
568#106—794no—
569#106C22×D7914yescomplemented
570#106C22×D7914yescomplemented
571#103—794no—
572#103—794no—
573#103—794no—
574#103—794no—
575#102—794no—
576#102—794no—
577#102—794no—
578#102—794no—
579C22⋊C8—794no—
580C22⋊C8—794no—
581C22⋊C8—794no—
582C22⋊C8—794no—
583C24—3162no—
584C24—794no—
585C24—791no—
586C24—791no—
587C24—1584no—
588C24—1581no—
589C24—1584no—
590C24D4×D7911yescharacteristic
591#41—3168no—
592#41—1588no—
593#41—1588no—
594C2×Q8—792no—
595C2×Q8—1582no—
596C2×Q8—1582no—
597C2×Q8—1581no—
598C2×D4—3164no—
599C2×D4—3164no—
600C2×D4—3164no—
601C2×D4—792no—
602C2×D4—1584no—
603C2×D4—1584no—
604C2×D4—1584no—
605C2×D4—1582no—
606C2×D4—1582no—
607C2×D4—1581no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—3164no—
613C22×C4—3164no—
614C22×C4—3164no—
615C22×C4—791no—
616C22×C4—791no—
617C22×C4—794no—
618C22×C4—792no—
619C22×C4—792no—
620C22×C4—794no—
621C22×C4—792no—
622C22×C4—794no—
623C22×C4—792no—
624C22×C4—1584no—
625C22×C4—1584no—
626C22×C4—1581no—
627C22×C4—1581no—
628C22×C4—1581no—
629C22×C4—1584no—
630C22×C4—1584no—
631C22×C4—1582no—
632C22×C4—1582no—
633C22×C4—1588no—
634C22×C4—1582no—
635C22×C4—1582no—
636C22×C4—1588no—
637C22×C4—1584no—
638C22×C4—1584no—
639C22×C4—15816no—
640C22×C4D4×D7912yes—
641C22×C4D4×D7911yescharacteristic
642C22×C4#1192962414yes—
643C22×C4#1192962514yes—
644C22×C4C23×D7911yescharacteristic
645C22×C4C23×D7912yes—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—28no—
649C2×C8—792no—
650C2×C8—792no—
651C2×C8—1582no—
652C2×C8—1582no—
653C2×C8—1588no—
654C2×C8C23×D7912yes—
655C2×C8C23×D7912yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—792no—
661C4⋊C4—792no—
662C4⋊C4—1584no—
663C4⋊C4—1584no—
664C4⋊C4—1584no—
665C4⋊C4—1584no—
666C4⋊C4—1581no—
667C4⋊C4—1581no—
668C4⋊C4C23×D7912yes—
669C4⋊C4C23×D7912yes—
670C4⋊C4C23×D7912yes—
671C4⋊C4C23×D7912yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—1584no—
675C22⋊C4—1584no—
676C22⋊C4—1584no—
677C22⋊C4—1584no—
678C22⋊C4—1584no—
679C22⋊C4—1584no—
680C22⋊C4—1584no—
681C42—24no—
682C42—24no—
683C42—1584no—
684C42—1584no—
685C42—1584no—
686C23—22no—
687C23—22no—
688C23—31616no—
689C23—3164no—
690C23—3162no—
691C23—3162no—
692C23—3162no—
693C23—794no—
694C23—792no—
695C23—792no—
696C23—1588no—
697C23—1582no—
698C23—1588no—
699C23—1582no—
700C23—1582no—
701C23—1582no—
702C23—1582no—
703C23—1582no—
704C23#1457914614yes—
705C23C2×D4×D7912yes—
706C23C2×D4×D7911yescharacteristic
707Q8—3162no—
708Q8—1582no—
709Q8—1582no—
710D4—3168no—
711D4—3168no—
712D4—3168no—
713D4—3162no—
714D4—1582no—
715D4—1582no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—3168no—
725C2×C4—3168no—
726C2×C4—3162no—
727C2×C4—3162no—
728C2×C4—3162no—
729C2×C4—3168no—
730C2×C4—792no—
731C2×C4—792no—
732C2×C4—1582no—
733C2×C4—1582no—
734C2×C4—1582no—
735C2×C4—1588no—
736C2×C4—1582no—
737C2×C4—1582no—
738C2×C4—1588no—
739C2×C4—1588no—
740C2×C4—1584no—
741C2×C4—1584no—
742C2×C4—1582no—
743C2×C4—1582no—
744C2×C4—1582no—
745C2×C4—1582no—
746C2×C4#1457914614yes—
747C2×C4#1457914618yes—
748C2×C4C2×D4×D7912yes—
749C2×C4C2×D4×D7911yescharacteristic
750C2×C4C2×#1192962412yes—
751C2×C4C2×#1192962414yes—
752C2×C4C2×#1192962512yes—
753C2×C4C2×#1192962514yes—
754C2×C4C24×D7911yescharacteristic
755C8—22no—
756C8—22no—
757C8—1582no—
758C8—1582no—
759C22—22no—
760C22—22no—
761C22—28no—
762C22—31616no—
763C22—3164no—
764C22—3162no—
765C22—3162no—
766C22—3162no—
767C22—794no—
768C22—6324no—
769C22—1582no—
770C22—1582no—
771C22—1582no—
772C22—1582no—
773C22—1582no—
774C22—1588no—
775C22C2×#1457914614yes—
776C22C2×#1457914612yes—
777C22#135×D7912yes—
778C22#1909936012yes—
779C22C22×D4×D7911yescharacteristic
780C4—42no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—3162no—
785C4—3162no—
786C4—3162no—
787C4—1582no—
788C4—1582no—
789C4C2×#1457914614yes—
790C4C2×#1457914612yes—
791C4C22×#1192962411yescharacteristic
792C4C22×#1192962511yescharacteristic
793C2—24no—
794C2—3162no—
795C2—6322no—
796C2—1584no—
797C2#2377331714yesdirect product factor
798C2C22×#1457914611yescharacteristic
799C2C2×#135×D7911yescharacteristic
800C2C2×#1909936011yescharacteristic
subgroupG/H
centerC22×C4D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#427×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099075C2
hypercenterC2×#427D79
hypocenterC79C2×#3091
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×#117×D79C2semidirect
3. #23773317C2direct (N × H)
4. C2×#19098900C2semidirect
5. C2×#19098883C2semidirect
6. C2×#19098907C2semidirect
7. C2×#19098906C2semidirect
8. C2×#19098890C2semidirect
9. C2×#19098889C2semidirect
10. C2×#19098895C2semidirect
11. C2×#19098878C2semidirect
12. C2×#19098599C2semidirect
13. C2×#19098560C2semidirect
14. C2×#19098557C2semidirect
15. C22×(C2×D79)⋊C8C2semidirect
16. C2×#427×C79C2semidirect
36. #117×D79C22semidirect
41. #19098907C22semidirect
42. #19098906C22semidirect
43. #19098900C22semidirect
44. #19098895C22semidirect
45. #19098890C22semidirect
46. #19098889C22semidirect
47. #19098883C22semidirect
48. #19098878C22semidirect
49. #19098599C22semidirect
50. C2×#14579094C22semidirect
51. C2×#14579094C22semidirect
52. C2×#14579092C22semidirect
53. C2×#14579092C22semidirect
54. #19098560C22semidirect
55. #19098557C22semidirect
56. C2×#14579086C22semidirect
57. C2×#14579086C22semidirect
58. C2×#14579084C22semidirect
59. C2×#14579084C22semidirect
60. C2×#14579083C22semidirect
61. C2×#14579083C22semidirect
62. C2×#14579081C22semidirect
63. C2×#14579081C22semidirect
68. C2×(C2×D79)⋊C8C22semidirect
72. #427×C79C22semidirect
73. C2×#107×C79C22semidirect
74. C2×#107×C79C22semidirect
75. C2×#106×C79C22semidirect
76. C2×#106×C79C22semidirect
145. #14579094C23semidirect
146. #14579094C23semidirect
147. #14579092C23semidirect
148. #14579092C23semidirect
149. #14579086C23semidirect
150. #14579086C23semidirect
151. #14579084C23semidirect
152. #14579084C23semidirect
153. #14579083C23semidirect
154. #14579083C23semidirect
155. #14579081C23semidirect
156. #14579081C23semidirect
178. #107×C79C23semidirect
179. #107×C79C23semidirect
180. #106×C79C23semidirect
181. #106×C79C23semidirect
394. C2×C79#3091semidirect
413. C2×#427D79semidirect
417. C79C2×#3091semidirect
454. #427C2×D79semidirect
457. C2×#107C2×D79semidirect
458. C2×#107C2×D79semidirect
461. C2×#106C2×D79semidirect
462. C2×#106C2×D79semidirect
565. #107C22×D79semidirect
566. #107C22×D79semidirect
569. #106C22×D79semidirect
570. #106C22×D79semidirect
797. C2#23773317direct (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×#117×D792
#237733172
C2×#190989002
C2×#190988832
C2×#190989072
C2×#190989062
C2×#190988902
C2×#190988892
C2×#190988952
C2×#190988782
C2×#190985992
C2×#190985602
C2×#190985572
C22×(C2×D79)⋊C82
C2×#427×C792
C2×#309179