Finite Group Databasebeta

← #34345323

Subgroups — #34345323

Order 20224.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098840C211yesmaximal, characteristic, complemented
2C22×#14579081C211yesmaximal, characteristic
3C22⋊C4×D316C211yesmaximal, characteristic
4#23764929C211yesmaximal, characteristic, complemented
5#23764785C211yesmaximal, characteristic, complemented
6#23764785C211yesmaximal, characteristic, complemented
7#23764533C211yesmaximal, characteristic, complemented
8#23763646C211yesmaximal, characteristic, complemented
9#23763646C211yesmaximal, characteristic, complemented
10#23763588C211yesmaximal, characteristic, complemented
11#23763580C211yesmaximal, characteristic, complemented
12#23763427C211yesmaximal, characteristic, complemented
13#23763397C211yesmaximal, characteristic, complemented
14#23763330C211yesmaximal, characteristic
15C79×#2440C211yesmaximal, characteristic, complemented
16C23×D316C2211yescharacteristic
17C23×C79⋊C8C2211yescharacteristic
18C2×C4×D316C2211yescharacteristic
19C2×C4×D316C2211yescharacteristic
20C2×C22⋊C4×D79—21no—
21#19098840—24no—
22C2×#14579094C2211yescharacteristic, complemented
23C2×#14579094C2211yescharacteristic, complemented
24C2×#14579094C2211yescharacteristic, complemented
25C2×#14579094C2211yescharacteristic, complemented
26C2×C4⋊(C79⋊C8)C2211yescharacteristic, complemented
27C2×C4⋊(C79⋊C8)C2211yescharacteristic, complemented
28C2×#14579081—24no—
29C2×#14579081C2211yescharacteristic
30C2×#14579081C2211yescharacteristic
31C2×#14579081C2211yescharacteristic
32C2×#14579081C2211yescharacteristic
33C2×#14579081C2211yescharacteristic
34C2×#14579081C2211yescharacteristic
35C2×#14579081C2211yescharacteristic
36C2×#14579081C2211yescharacteristic
37C2×C22⋊(C79⋊C8)C2211yescharacteristic
38#19098465C2211yescharacteristic
39#19098465C2211yescharacteristic
40#19098441—21no—
41#19098441—21no—
42#19098423C2211yescharacteristic
43#19098418—21no—
44#19098325C2211yescharacteristic, complemented
45#19098325C2211yescharacteristic, complemented
46#19098325C2211yescharacteristic, complemented
47#19098325C2211yescharacteristic, complemented
48#19098318C2211yescharacteristic, complemented
49#19098318C2211yescharacteristic, complemented
50C2×C4⋊Q8×C79C2211yescharacteristic, complemented
51C2×C22⋊Q8×C79—21no—
52C22×C4⋊C4×C79C2211yescharacteristic
53#398×C79—21no—
54#395×C79—21no—
55#389×C79C2211yescharacteristic, complemented
56#389×C79C2211yescharacteristic, complemented
57#385×C79—21no—
58#384×C79C2211yescharacteristic, complemented
59#380×C79C2211yescharacteristic
60C4×C22⋊C4×C79C2211yescharacteristic
61C24×D79—21no—
62C22×D316—22no—
63C22×D316—22no—
64C22×D316—21no—
65C22×D316—22no—
66C22×D316—41no—
67C22×D316—41no—
68C22×D316Q814yescomplemented
69C22×D316C2311yescharacteristic
70C22×D316C2311yescharacteristic
71C22×C4×D79—21no—
72C22×C4×D79—21no—
73C22×C79⋊C8—22no—
74C22×C79⋊C8—22no—
75C22×C79⋊C8—41no—
76C22×C79⋊C8C2311yescharacteristic
77C22×C79⋊C8C2311yescharacteristic
78C22×C79⋊C8C2311yescharacteristic
79C22×C79⋊C8C2311yescharacteristic
80C4×D316—22no—
81C4×D316—22no—
82C4×D316—41no—
83C4×D316—41no—
84C2×C4⋊Dic79C2311yescharacteristic
85C2×C4⋊Dic79C2311yescharacteristic
86C2×C22⋊Dic79—21no—
87C2×(C2×D79)⋊C4—21no—
88C2×(C2×D79)⋊C4—21no—
89C2×(C2×D79)⋊C4—21no—
90C2×(C2×D79)⋊C4—21no—
91C2×(C2×D79)⋊C4—21no—
92C2×(C2×D79)⋊C4—21no—
93C22⋊C4×D79—44no—
94#14579094—22no—
95#14579094—22no—
96#14579094—41no—
97#14579094—41no—
98C4⋊(C79⋊C8)—22no—
99C4⋊(C79⋊C8)—41no—
100#14579081—22no—
101#14579081—22no—
102#14579081—22no—
103#14579081—22no—
104#14579081—22no—
105#14579081—41no—
106#14579081—41no—
107#14579081D414yes—
108C22⋊(C79⋊C8)—22no—
109C79⋊#95—21no—
110C22×Q8×C79—21no—
111C23×C4×C79—21no—
112C23×C4×C79C2311yescharacteristic
113C4⋊Q8×C79—22no—
114C4⋊Q8×C79—41no—
115C22⋊Q8×C79—44no—
116C2×C4⋊C4×C79—22no—
117C2×C4⋊C4×C79—21no—
118C2×C4⋊C4×C79—21no—
119C2×C4⋊C4×C79—21no—
120C2×C4⋊C4×C79—21no—
121C2×C4⋊C4×C79—21no—
122C2×C4⋊C4×C79—21no—
123C2×C4⋊C4×C79—41no—
124C2×C4⋊C4×C79C2311yescharacteristic
125C2×C4⋊C4×C79C2311yescharacteristic
126C2×C4⋊C4×C79C2311yescharacteristic
127C2×C4⋊C4×C79C2311yescharacteristic
128C2×C22⋊C4×C79—21no—
129C2×C22⋊C4×C79D411yescharacteristic
130C2×C22⋊C4×C79D411yescharacteristic
131C2×C42×C79C2311yescharacteristic
132C2×C42×C79C2311yescharacteristic
133#95×C79—21no—
134#95×C79—21no—
135#95×C79—21no—
136#95×C79D411yescharacteristic
137#95×C79D411yescharacteristic
138C23×D79—21no—
139C23×D79—21no—
140C23×D79—24no—
141C23×D79—42no—
142C23×D79—42no—
143C23×D79—42no—
144C23×D79—42no—
145C23×D79—81no—
146C23×D79—81no—
147C2×D316—28no—
148C2×D316—24no—
149C2×D316—21no—
150C2×D316—21no—
151C2×D316—21no—
152C2×D316—21no—
153C2×D316—21no—
154C2×D316—21no—
155C2×D316—21no—
156C2×D316—21no—
157C2×D316—42no—
158C2×D316—42no—
159C2×D316—44no—
160C2×D316—44no—
161C2×D316—44no—
162C2×D316C2×D412yes—
163C2×D316C2×Q812yes—
164C2×D316C2×Q812yes—
165C2×D316#4112yes—
166C22×Dic79—21no—
167C22×Dic79—21no—
168C2×C4×D79—42no—
169C2×C4×D79—42no—
170C2×C4×D79—42no—
171C2×C4×D79—42no—
172C2×C4×D79—81no—
173C2×C4×D79—81no—
174C2×C79⋊C8—21no—
175C2×C79⋊C8—21no—
176C2×C79⋊C8—21no—
177C2×C79⋊C8—21no—
178C2×C79⋊C8—21no—
179C2×C79⋊C8—21no—
180C2×C79⋊C8—21no—
181C2×C79⋊C8—21no—
182C2×C79⋊C8—21no—
183C2×C79⋊C8—21no—
184C2×C79⋊C8—21no—
185C2×C79⋊C8—44no—
186C2×C79⋊C8C2×D412yes—
187C4⋊Dic79—21no—
188C4⋊Dic79—21no—
189C4⋊Dic79—21no—
190C4⋊Dic79—21no—
191C22⋊Dic79—42no—
192(C2×D79)⋊C4—42no—
193(C2×D79)⋊C4—42no—
194(C2×D79)⋊C4—42no—
195(C2×D79)⋊C4—42no—
196(C2×D79)⋊C4—81no—
197(C2×D79)⋊C4—81no—
198C24×C79C2×D411yescharacteristic
199C2×Q8×C79—42no—
200C2×Q8×C79—42no—
201C2×Q8×C79—81no—
202C22×C4×C79—21no—
203C22×C4×C79—21no—
204C22×C4×C79—21no—
205C22×C4×C79—21no—
206C22×C4×C79—21no—
207C22×C4×C79—21no—
208C22×C4×C79—21no—
209C22×C4×C79—21no—
210C22×C4×C79—42no—
211C22×C4×C79—42no—
212C22×C4×C79—81no—
213C22×C4×C79C2×D411yescharacteristic
214C22×C4×C79C2×D411yescharacteristic
215C22×C4×C79C2×D411yescharacteristic
216C22×C4×C79C2×D411yescharacteristic
217C22×C4×C79C2×D411yescharacteristic
218C22×C4×C79C2×Q812yes—
219C22×C4×C79#4112yes—
220C22×C4×C79C2411yescharacteristic
221C4⋊C4×C79—21no—
222C4⋊C4×C79—21no—
223C4⋊C4×C79—21no—
224C4⋊C4×C79—21no—
225C4⋊C4×C79—21no—
226C4⋊C4×C79—21no—
227C4⋊C4×C79—21no—
228C4⋊C4×C79—42no—
229C4⋊C4×C79—42no—
230C4⋊C4×C79—42no—
231C4⋊C4×C79—42no—
232C4⋊C4×C79—42no—
233C4⋊C4×C79—81no—
234C4⋊C4×C79C2×D412yes—
235C22⋊C4×C79—22no—
236C22⋊C4×C79—42no—
237C22⋊C4×C79D814yes—
238C42×C79—21no—
239C42×C79—21no—
240C42×C79—21no—
241C42×C79—21no—
242C23×C79—21no—
243C23×C79—21no—
244C23×C79—21no—
245C23×C79—21no—
246C23×C79C22⋊Q812yes—
247C23×C79C2×D812yes—
248C23×C79#13712yes—
249C23×C79C22×D411yescharacteristic
250C22×D79—22no—
251C22×D79—22no—
252C22×D79—22no—
253C22×D79—22no—
254C22×D79—48no—
255C22×D79—41no—
256C22×D79—41no—
257C22×D79—41no—
258C22×D79—41no—
259C22×D79—41no—
260C22×D79—41no—
261C22×D79—41no—
262C22×D79—41no—
263C22×D79—41no—
264C22×D79—41no—
265C22×D79—48no—
266C22×D79—84no—
267C22×D79—84no—
268C22×D79—84no—
269C22×D79—84no—
270C22×D79—84no—
271Q8×C79—84no—
272C2×C4×C79—21no—
273C2×C4×C79—21no—
274C2×C4×C79—21no—
275C2×C4×C79—21no—
276C2×C4×C79—21no—
277C2×C4×C79—21no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—21no—
283C2×C4×C79—22no—
284C2×C4×C79—21no—
285C2×C4×C79—21no—
286C2×C4×C79—21no—
287C2×C4×C79—21no—
288C2×C4×C79—21no—
289C2×C4×C79—41no—
290C2×C4×C79—41no—
291C2×C4×C79—41no—
292C2×C4×C79—41no—
293C2×C4×C79—41no—
294C2×C4×C79—41no—
295C2×C4×C79—41no—
296C2×C4×C79—41no—
297C2×C4×C79—41no—
298C2×C4×C79—41no—
299C2×C4×C79—41no—
300C2×C4×C79—84no—
301C2×C4×C79C22⋊Q812yes—
302C2×C4×C79C2×D812yes—
303C2×C4×C79C2×D812yes—
304C2×C4×C79C22×D411yescharacteristic
305C2×C4×C79C22×Q811yescharacteristic
306C2×C4×C79C2×#4111yescharacteristic
307C2×C4×C79C2×#4111yescharacteristic
308C2×C4×C79H(5,𝔽2)11yescharacteristic
309C2×C4×C79H(5,𝔽2)11yescharacteristic
310C2×Dic79—41no—
311C2×Dic79—41no—
312C2×Dic79—41no—
313C2×Dic79—41no—
314C2×Dic79—41no—
315C2×Dic79—41no—
316D316—22no—
317D316—22no—
318D316—22no—
319D316—22no—
320D316—22no—
321D316—48no—
322D316—41no—
323D316—41no—
324D316C22⋊Q814yescomplemented
325C4×D79—84no—
326C4×D79—84no—
327C79⋊C8—22no—
328C79⋊C8—41no—
329C79⋊C8—41no—
330C79⋊C8—41no—
331C22×C79—22no—
332C22×C79—22no—
333C22×C79—22no—
334C22×C79—22no—
335C22×C79—22no—
336C22×C79—22no—
337C22×C79#47414yescomplemented
338C22×C79C2×C22⋊Q811yescharacteristic
339C22×C79D4211yescharacteristic
340C22×C79#54611yescharacteristic
341C22×C79C22×D811yescharacteristic
342C22×C79C2×#13711yescharacteristic
343C22×C79#57611yescharacteristic
344C22×C79#57711yescharacteristic
345C2×D79—24no—
346C2×D79—42no—
347C2×D79—42no—
348C2×D79—42no—
349C2×D79—42no—
350C2×D79—42no—
351C2×D79—42no—
352C2×D79—42no—
353C2×D79—42no—
354C2×D79—42no—
355C2×D79—816no—
356C2×D79—81no—
357C2×D79—81no—
358C2×D79—81no—
359C2×D79—81no—
360C4×C79—22no—
361C4×C79—22no—
362C4×C79—22no—
363C4×C79—41no—
364C4×C79—42no—
365C4×C79—41no—
366C4×C79—81no—
367C4×C79—81no—
368C4×C79—81no—
369C4×C79C2×C22⋊Q811yescharacteristic
370C4×C79#54311yescharacteristic
371C4×C79#54611yescharacteristic
372C4×C79#55111yescharacteristic
373Dic79—81no—
374Dic79—81no—
375#25950—791nomaximal, Sylow
376C2×C79—24no—
377C2×C79#243711yescharacteristic
378C2×C79C2×#47411yescharacteristic
379C2×C79#308111yescharacteristic
380C2×C79#326611yescharacteristic
381C2×C79D4×D811yescharacteristic
382C2×C79#329411yescharacteristic
383C2×C79#331411yescharacteristic
384D79—44no—
385D79—82no—
386C2×#474—791no—
387C22×#102—791no—
388#2440D7911yescharacteristic, complemented
389D4×C22⋊C4—791no—
390#2093—791no—
391#2067—791no—
392#2067—791no—
393#2023—791no—
394#1862—791no—
395#1862—791no—
396#1852—791no—
397#1850—791no—
398#1808—791no—
399#1802—791no—
400#1786—791no—
401C79#2595011yescharacteristic, complemented, Sylow
402C23×D4—791no—
403C23×C8—791no—
404C2×C4⋊Q8C2×D7911yescharacteristic, complemented
405C2×C22⋊Q8—21no—
406C2×C4×D4—791no—
407C2×C4×D4—791no—
408C22×C4⋊C4C2×D7911yescharacteristic
409C22×C22⋊C4—1581no—
410#474—1584no—
411C2×#107—791no—
412C2×#107—791no—
413C2×#107—791no—
414C2×#107—791no—
415C2×C4⋊C8—791no—
416C2×C4⋊C8—791no—
417C2×#102—791no—
418C2×#102—791no—
419C2×#102—791no—
420C2×#102—791no—
421C2×#102—791no—
422C2×#102—791no—
423C2×#102—791no—
424C2×#102—791no—
425C2×#102—1584no—
426C2×C22⋊C8—791no—
427#398—21no—
428#395—21no—
429#390—791no—
430#390—791no—
431#389C2×D7911yescharacteristic, complemented
432#389C2×D7911yescharacteristic, complemented
433#386—1581no—
434#386—1581no—
435#385—21no—
436#384C2×D7911yescharacteristic, complemented
437#380—791no—
438#380C2×D7911yescharacteristic
439#379—1581no—
440C4×C22⋊C4C2×D7911yescharacteristic
441#340—791no—
442#340—791no—
443#340—791no—
444#340—791no—
445#336—791no—
446#336—791no—
447C25—1581no—
448C22×Q8—21no—
449C22×D4—3161no—
450C22×D4—3161no—
451C22×D4—794no—
452C22×D4—791no—
453C22×D4—791no—
454C22×D4—1582no—
455C22×D4—1582no—
456C22×D4—1581no—
457C22×D4—1582no—
458C23×C4—21no—
459C23×C4—1581no—
460C23×C4—1581no—
461C23×C4C22×D7911yescharacteristic
462C22×C8—3161no—
463C22×C8—791no—
464C22×C8—791no—
465C22×C8—791no—
466C22×C8—791no—
467C22×C8—1582no—
468C22×C8—1582no—
469C4⋊Q8—22no—
470C4⋊Q8—41no—
471C22⋊Q8—44no—
472C4×D4—3161no—
473C4×D4—3161no—
474C4×D4—1582no—
475C4×D4—1582no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4—791no—
485C2×C4⋊C4—791no—
486C2×C4⋊C4C22×D7911yescharacteristic
487C2×C4⋊C4C22×D7911yescharacteristic
488C2×C4⋊C4C22×D7911yescharacteristic
489C2×C4⋊C4C22×D7911yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—3164no—
492C2×C22⋊C4—1581no—
493C2×C22⋊C4—1581no—
494C2×C22⋊C4—1581no—
495C2×C22⋊C4—1581no—
496C2×C22⋊C4—1581no—
497C2×C22⋊C4—1581no—
498C2×C22⋊C4—1581no—
499C2×C22⋊C4C22⋊D7911yescharacteristic
500C2×C22⋊C4C22⋊D7911yescharacteristic
501C2×C42C22×D7911yescharacteristic
502C2×C42C22×D7911yescharacteristic
503#107—3161no—
504#107—3161no—
505#107—1582no—
506#107—1582no—
507C4⋊C8—3161no—
508C4⋊C8—1582no—
509#102—3161no—
510#102—3161no—
511#102—794no—
512#102—1582no—
513#102—1582no—
514#102—1582no—
515#102—1582no—
516#102—1582no—
517C22⋊C8—1582no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—1581no—
522#95C22⋊D7911yescharacteristic
523#95C22⋊D7911yescharacteristic
524C24—3162no—
525C24—3162no—
526C24—3162no—
527C24—3162no—
528C24—6321no—
529C24—6321no—
530C24—1581no—
531C24—1584no—
532C24—1581no—
533C24C2×C22⋊D7911yescharacteristic
534C2×Q8—42no—
535C2×Q8—42no—
536C2×Q8—81no—
537C2×D4—3162no—
538C2×D4—3162no—
539C2×D4—3164no—
540C2×D4—3164no—
541C2×D4—3164no—
542C2×D4—792no—
543C2×D4—792no—
544C2×D4—792no—
545C2×D4—792no—
546C2×D4—1588no—
547C2×D4—1581no—
548C2×D4—1581no—
549C2×D4—1581no—
550C2×D4—1581no—
551C2×D4—1581no—
552C2×D4—1581no—
553C2×D4—1581no—
554C2×D4—1584no—
555C2×D4—1581no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—3162no—
568C22×C4—3162no—
569C22×C4—3162no—
570C22×C4—3162no—
571C22×C4—6321no—
572C22×C4—6321no—
573C22×C4—1581no—
574C22×C4—1581no—
575C22×C4C2×C22⋊D7911yescharacteristic
576C22×C4C2×C22⋊D7911yescharacteristic
577C22×C4C2×C22⋊D7911yescharacteristic
578C22×C4C2×C22⋊D7911yescharacteristic
579C22×C4C2×C22⋊D7911yescharacteristic
580C22×C4Q8×D7912yes—
581C22×C4#1192962512yes—
582C22×C4C23×D7911yescharacteristic
583C2×C8—3164no—
584C2×C8—792no—
585C2×C8—1581no—
586C2×C8—1581no—
587C2×C8—1581no—
588C2×C8—1581no—
589C2×C8—1581no—
590C2×C8—1581no—
591C2×C8—1581no—
592C2×C8—1581no—
593C2×C8—1581no—
594C2×C8—1581no—
595C2×C8—1581no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—81no—
609C4⋊C4—1581no—
610C4⋊C4—1581no—
611C4⋊C4—1581no—
612C4⋊C4—1581no—
613C4⋊C4D4×D7912yes—
614C22⋊C4—22no—
615C22⋊C4—42no—
616C22⋊C4—3162no—
617C22⋊C4—3162no—
618C22⋊C4—3162no—
619C22⋊C4—3162no—
620C22⋊C4—3162no—
621C22⋊C4—6321no—
622C22⋊C4—6321no—
623C22⋊C4#1192960914yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—3168no—
633C23—3161no—
634C23—3161no—
635C23—3161no—
636C23—3161no—
637C23—3161no—
638C23—3161no—
639C23—3161no—
640C23—3168no—
641C23—3161no—
642C23—3161no—
643C23—3161no—
644C23—6324no—
645C23—6324no—
646C23—6324no—
647C23—6324no—
648C23—6324no—
649C23—1582no—
650C23—1582no—
651C23—1582no—
652C23—1582no—
653C23#1457913712yes—
654C23C2×#1192960912yes—
655C23#1457919212yes—
656C23C22×C22⋊D7911yescharacteristic
657Q8—84no—
658D4—3168no—
659D4—3161no—
660D4—3161no—
661D4—794no—
662D4—1582no—
663D4—1582no—
664D4—1582no—
665D4—1582no—
666D4—1582no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—84no—
696C2×C4—3161no—
697C2×C4—3161no—
698C2×C4—3161no—
699C2×C4—3161no—
700C2×C4—3161no—
701C2×C4—3161no—
702C2×C4—6324no—
703C2×C4—6324no—
704C2×C4#1457913712yes—
705C2×C4C2×#1192960912yes—
706C2×C4C2×#1192960912yes—
707C2×C4C2×D4×D7911yescharacteristic
708C2×C4C2×Q8×D7911yescharacteristic
709C2×C4#41×D7911yescharacteristic
710C2×C4C2×#1192962511yescharacteristic
711C2×C4#1457920611yescharacteristic
712C2×C4#1457920711yescharacteristic
713C8—3161no—
714C8—3161no—
715C8—3161no—
716C8—1582no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—3162no—
724C22—3162no—
725C22—3162no—
726C22—3162no—
727C22—3162no—
728C22—3162no—
729C22—3162no—
730C22—3162no—
731C22—3162no—
732C22—63216no—
733C22—6321no—
734C22—6321no—
735C22—6321no—
736C22—6321no—
737C22—1584no—
738C22#1909884014yescomplemented
739C22C2×#1457913711yescharacteristic
740C22D4×C22⋊D7911yescharacteristic
741C22#1909920111yescharacteristic
742C22C22×#1192960911yescharacteristic
743C22C2×#1457919211yescharacteristic
744C22#1909936611yescharacteristic
745C22#1909937111yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—42no—
750C4—41no—
751C4—41no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—6321no—
756C4—6321no—
757C4C22⋊Q8×D7911yescharacteristic
758C4#1909918811yescharacteristic
759C4#1909920411yescharacteristic
760C4#1909924011yescharacteristic
761C2—24no—
762C2—3164no—
763C2—6322no—
764C2#2376706311yescharacteristic
765C2C2×#1909884011yescharacteristic
766C2#2377322511yescharacteristic
767C2#2377491111yescharacteristic
768C2D4×#1192960911yescharacteristic
769C2#2377520711yescharacteristic
770C2#2377547511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC79×#2440C2
socleC23×C79C22×D4
prime radicalC23×D316C22
hypercenter#2440D79
hypocenterC79#25950
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C2×#19098840C2semidirect
4. #23764929C2semidirect
5. #23764785C2semidirect
6. #23764785C2semidirect
7. #23764533C2semidirect
8. #23763646C2semidirect
9. #23763646C2semidirect
10. #23763588C2semidirect
11. #23763580C2semidirect
12. #23763427C2semidirect
13. #23763397C2semidirect
15. C79×#2440C2semidirect
22. C2×#14579094C22semidirect
23. C2×#14579094C22semidirect
24. C2×#14579094C22semidirect
25. C2×#14579094C22semidirect
26. C2×C4⋊(C79⋊C8)C22semidirect
27. C2×C4⋊(C79⋊C8)C22semidirect
44. #19098325C22semidirect
45. #19098325C22semidirect
46. #19098325C22semidirect
47. #19098325C22semidirect
48. #19098318C22semidirect
49. #19098318C22semidirect
50. C2×C4⋊Q8×C79C22semidirect
55. #389×C79C22semidirect
56. #389×C79C22semidirect
58. #384×C79C22semidirect
68. C22×D316Q8semidirect
324. D316C22⋊Q8semidirect
337. C22×C79#474semidirect
388. #2440D79semidirect
401. C79#25950semidirect
404. C2×C4⋊Q8C2×D79semidirect
431. #389C2×D79semidirect
432. #389C2×D79semidirect
436. #384C2×D79semidirect
738. C22#19098840semidirect

Maximal subgroups

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

subgroupindex
C2×#190988402
C22×#145790812
C22⋊C4×D3162
#237649292
#237647852
#237645332
#237636462
#237635882
#237635802
#237634272
#237633972
#237633302
C79×#24402
#2595079