Finite Group Databasebeta

← #34305640

Subgroups — #34305640

Order 20224.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772058C211yesmaximal, characteristic, complemented
2#23771849C211yesmaximal, characteristic
3#23764113C211yesmaximal, characteristic, complemented
4#23764106C211yesmaximal, characteristic, complemented
5#23764050C211yesmaximal, characteristic, complemented
6#23764050C211yesmaximal, characteristic, complemented
7#23763677C211yesmaximal, characteristic, complemented
8#23763677C211yesmaximal, characteristic, complemented
9#23763499C211yesmaximal, characteristic, complemented
10#23763442C211yesmaximal, characteristic, complemented
11#23763344C211yesmaximal, characteristic
12#23763247C211yesmaximal, characteristic, complemented
13#23763240C211yesmaximal, characteristic, complemented
14#23763181C211yesmaximal, characteristic, complemented
15C79×#2896C211yesmaximal, characteristic
16C2×#14579168C2211yescharacteristic
17C2×#14579168C2211yescharacteristic
18#19098624—21no—
19#19098624—21no—
20#19098620—21no—
21#19098616—21no—
22C2×#14579097C2211yescharacteristic, complemented
23C2×#14579097C2211yescharacteristic, complemented
24#19098590C2211yescharacteristic, complemented
25#19098590C2211yescharacteristic, complemented
26C2×#14579088C2211yescharacteristic
27C2×#14579088C2211yescharacteristic
28C2×#14579088C2211yescharacteristic
29C2×#14579088C2211yescharacteristic
30#19098530—21no—
31#19098530—21no—
32#19098530C2211yescharacteristic
33#19098530C2211yescharacteristic
34#19098527—21no—
35#19098527C2211yescharacteristic
36#19098527C2211yescharacteristic
37C2×C22⋊(C79⋊C8)—21no—
38C2×C22⋊(C79⋊C8)C2211yescharacteristic
39#19098519C2211yescharacteristic, complemented
40#19098519C2211yescharacteristic, complemented
41C2×#14579071C2211yescharacteristic, complemented
42C2×C8×Dic79C2211yescharacteristic, complemented
43C4×C22⋊Dic79C2211yescharacteristic
44#19098328C2211yescharacteristic, complemented
45#19098328C2211yescharacteristic, complemented
46#19098322C2211yescharacteristic, complemented
47#19098322C2211yescharacteristic, complemented
48#19098322C2211yescharacteristic, complemented
49#19098322C2211yescharacteristic, complemented
50#19098317C2211yescharacteristic, complemented
51#19098317C2211yescharacteristic, complemented
52C22×#41×C79C2211yescharacteristic
53C22×M16×C79C2211yescharacteristic
54C2×#117×C79C2211yescharacteristic
55#419×C79C411yescharacteristic, complemented
56#419×C79C411yescharacteristic, complemented
57#418×C79C411yescharacteristic, complemented
58#418×C79C411yescharacteristic, complemented
59#417×C79C411yescharacteristic, complemented
60#417×C79C411yescharacteristic, complemented
61#417×C79C411yescharacteristic, complemented
62#417×C79C411yescharacteristic, complemented
63#416×C79C2211yescharacteristic
64#416×C79C2211yescharacteristic
65#416×C79C2211yescharacteristic
66#416×C79C2211yescharacteristic
67#14579168—22no—
68#14579168—22no—
69#14579168—41no—
70#14579168—41no—
71C2×#11929608—21no—
72C2×#11929608—21no—
73C2×#11929608C2311yescharacteristic
74C2×#11929608C2311yescharacteristic
75C2×#11929608C2311yescharacteristic
76C2×#11929608C2311yescharacteristic
77C22×C79⋊C8—21no—
78C22×C79⋊C8—21no—
79C22×C79⋊C8C2311yescharacteristic
80C22×C79⋊C8C2311yescharacteristic
81C2×C22⋊Dic79—21no—
82C2×C4×Dic79C2311yescharacteristic
83C2×C4×Dic79C2311yescharacteristic
84#14579097—41no—
85#14579097—41no—
86C4⋊(C79⋊C8)—21no—
87C4⋊(C79⋊C8)—21no—
88C4⋊(C79⋊C8)—21no—
89C4⋊(C79⋊C8)—21no—
90#14579088—22no—
91#14579088—22no—
92#14579088—41no—
93#14579088—41no—
94C22⋊(C79⋊C8)—21no—
95C22⋊(C79⋊C8)—21no—
96C22⋊(C79⋊C8)—21no—
97C22⋊(C79⋊C8)—21no—
98C22⋊(C79⋊C8)—21no—
99C22⋊(C79⋊C8)—21no—
100C22⋊(C79⋊C8)—21no—
101C22⋊(C79⋊C8)—21no—
102C22⋊(C79⋊C8)D411yescharacteristic
103C22⋊(C79⋊C8)D411yescharacteristic
104C22⋊(C79⋊C8)D411yescharacteristic
105C22⋊(C79⋊C8)D411yescharacteristic
106#14579072—21no—
107#14579072—21no—
108#14579071—41no—
109C4×C79⋊C8—21no—
110C4×C79⋊C8—21no—
111C8×Dic79—41no—
112C79⋊#95—21no—
113C2×#41×C79—21no—
114C2×#41×C79—21no—
115C2×#41×C79—22no—
116C2×#41×C79—22no—
117C2×#41×C79—41no—
118C2×#41×C79—41no—
119C2×#41×C79C2×C411yescharacteristic
120C2×#41×C79C2×C411yescharacteristic
121C2×#41×C79C2311yescharacteristic
122C2×#41×C79C2311yescharacteristic
123C22×Q8×C79C2×C411yescharacteristic
124C22×D4×C79—21no—
125C22×D4×C79C2×C411yescharacteristic
126C23×C4×C79—21no—
127C23×C4×C79C2311yescharacteristic
128C2×M16×C79—41no—
129C2×M16×C79—41no—
130C2×M16×C79C2×C411yescharacteristic
131C2×M16×C79C2×C411yescharacteristic
132C2×M16×C79C2×C411yescharacteristic
133C2×M16×C79C2×C411yescharacteristic
134C22×C8×C79C2311yescharacteristic
135C22×C8×C79C2311yescharacteristic
136#117×C79—21no—
137#117×C79—21no—
138#117×C79C2×C411yescharacteristic
139#117×C79C2×C411yescharacteristic
140#117×C79C2311yescharacteristic
141#117×C79C2311yescharacteristic
142C2×C4⋊C4×C79C2×C411yescharacteristic
143C2×C4⋊C4×C79C2×C411yescharacteristic
144C2×C22⋊C4×C79—21no—
145C2×C42×C79—21no—
146#103×C79C2×C411yescharacteristic
147#103×C79C2×C411yescharacteristic
148#103×C79C2×C411yescharacteristic
149#103×C79C2×C411yescharacteristic
150#103×C79C2×C411yescharacteristic
151#103×C79C2×C411yescharacteristic
152#103×C79C2×C411yescharacteristic
153#103×C79C2×C411yescharacteristic
154#102×C79C2×C411yescharacteristic
155#102×C79C2×C411yescharacteristic
156#102×C79C2×C411yescharacteristic
157#102×C79C2×C411yescharacteristic
158#102×C79C2×C411yescharacteristic
159#102×C79C2×C411yescharacteristic
160#102×C79C2×C411yescharacteristic
161#102×C79C2×C411yescharacteristic
162C22×Dic79—21no—
163C22×Dic79—21no—
164#11929608—21no—
165#11929608—21no—
166#11929608—21no—
167#11929608—21no—
168#11929608—21no—
169#11929608—21no—
170#11929608—21no—
171#11929608—21no—
172#11929608—42no—
173#11929608—42no—
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—42no—
183C2×C79⋊C8—42no—
184C2×C79⋊C8C2×D411yescharacteristic
185C2×C79⋊C8C2×D411yescharacteristic
186C2×C79⋊C8C2×D411yescharacteristic
187C2×C79⋊C8C2×D411yescharacteristic
188C22⋊Dic79—42no—
189C4×Dic79—21no—
190C4×Dic79—21no—
191C4×Dic79—21no—
192C4×Dic79—21no—
193C24×C79—21no—
194C24×C79#4111yescharacteristic
195#41×C79—21no—
196#41×C79—21no—
197#41×C79—22no—
198#41×C79—22no—
199#41×C79—21no—
200#41×C79—21no—
201#41×C79—21no—
202#41×C79—21no—
203#41×C79—42no—
204#41×C79—42no—
205#41×C79—41no—
206#41×C79—41no—
207#41×C79—42no—
208#41×C79—42no—
209#41×C79#4112yes—
210#41×C79#4112yes—
211C2×Q8×C79—21no—
212C2×Q8×C79—22no—
213C2×Q8×C79—41no—
214C2×Q8×C79C22×C411yescharacteristic
215C2×Q8×C79C22×C411yescharacteristic
216C2×D4×C79—21no—
217C2×D4×C79—22no—
218C2×D4×C79—21no—
219C2×D4×C79—21no—
220C2×D4×C79—21no—
221C2×D4×C79—21no—
222C2×D4×C79—41no—
223C2×D4×C79—42no—
224C2×D4×C79—42no—
225C2×D4×C79C22×C411yescharacteristic
226C2×D4×C79C22×C411yescharacteristic
227C22×C4×C79—21no—
228C22×C4×C79—21no—
229C22×C4×C79—21no—
230C22×C4×C79—21no—
231C22×C4×C79—21no—
232C22×C4×C79—21no—
233C22×C4×C79—21no—
234C22×C4×C79—21no—
235C22×C4×C79—21no—
236C22×C4×C79—21no—
237C22×C4×C79—21no—
238C22×C4×C79—42no—
239C22×C4×C79—42no—
240C22×C4×C79C22×C411yescharacteristic
241C22×C4×C79C22×C411yescharacteristic
242C22×C4×C79C2×D411yescharacteristic
243C22×C4×C79C2×D411yescharacteristic
244C22×C4×C79#4111yescharacteristic
245C22×C4×C79C2411yescharacteristic
246M16×C79—41no—
247M16×C79—41no—
248M16×C79—41no—
249M16×C79—41no—
250C2×C8×C79—21no—
251C2×C8×C79—21no—
252C2×C8×C79—21no—
253C2×C8×C79—21no—
254C2×C8×C79C22×C411yescharacteristic
255C2×C8×C79C22×C411yescharacteristic
256C2×C8×C79C22×C411yescharacteristic
257C2×C8×C79C22×C411yescharacteristic
258C4⋊C4×C79—21no—
259C4⋊C4×C79—21no—
260C4⋊C4×C79C22×C411yescharacteristic
261C4⋊C4×C79C22×C411yescharacteristic
262C4⋊C4×C79C22×C411yescharacteristic
263C4⋊C4×C79C22×C411yescharacteristic
264C22⋊C4×C79—21no—
265C22⋊C4×C79—21no—
266C22⋊C4×C79—21no—
267C22⋊C4×C79—21no—
268C42×C79—21no—
269C42×C79—21no—
270C42×C79—21no—
271C42×C79—21no—
272C23×C79—21no—
273C23×C79—21no—
274C23×C79—21no—
275C23×C79—21no—
276C23×C79—41no—
277C23×C79—41no—
278C23×C79—42no—
279C23×C79—42no—
280C23×C79—81no—
281C23×C79C4×D411yescharacteristic
282C23×C79C4×D411yescharacteristic
283C23×C79C2×#4111yescharacteristic
284Q8×C79—21no—
285Q8×C79—21no—
286Q8×C79—21no—
287Q8×C79—42no—
288Q8×C79#11712yes—
289D4×C79—22no—
290D4×C79—22no—
291D4×C79—21no—
292D4×C79—21no—
293D4×C79—21no—
294D4×C79—42no—
295D4×C79—42no—
296D4×C79—42no—
297D4×C79—41no—
298D4×C79—41no—
299D4×C79#11712yes—
300C2×C4×C79—21no—
301C2×C4×C79—21no—
302C2×C4×C79—21no—
303C2×C4×C79—21no—
304C2×C4×C79—21no—
305C2×C4×C79—21no—
306C2×C4×C79—21no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—21no—
310C2×C4×C79—21no—
311C2×C4×C79—21no—
312C2×C4×C79—21no—
313C2×C4×C79—21no—
314C2×C4×C79—21no—
315C2×C4×C79—21no—
316C2×C4×C79—21no—
317C2×C4×C79—21no—
318C2×C4×C79—42no—
319C2×C4×C79—42no—
320C2×C4×C79—42no—
321C2×C4×C79—42no—
322C2×C4×C79—41no—
323C2×C4×C79—41no—
324C2×C4×C79—81no—
325C2×C4×C79C4×D411yescharacteristic
326C2×C4×C79C4×D411yescharacteristic
327C2×C4×C79C23×C411yescharacteristic
328C2×C4×C79C22×D411yescharacteristic
329C2×C4×C79C2×#4111yescharacteristic
330C2×C4×C79C2×#4111yescharacteristic
331C2×C4×C79H(5,𝔽2)11yescharacteristic
332C2×C4×C79H(5,𝔽2)11yescharacteristic
333C2×Dic79—22no—
334C2×Dic79—41no—
335C2×Dic79—41no—
336C2×Dic79—41no—
337C2×Dic79—41no—
338C2×Dic79—41no—
339C8×C79—21no—
340C8×C79—21no—
341C8×C79—21no—
342C8×C79—21no—
343C79⋊C8—21no—
344C79⋊C8—21no—
345C79⋊C8—21no—
346C79⋊C8—21no—
347C79⋊C8—41no—
348C79⋊C8—41no—
349C79⋊C8—41no—
350C79⋊C8—41no—
351C22×C79—21no—
352C22×C79—21no—
353C22×C79—21no—
354C22×C79—21no—
355C22×C79—22no—
356C22×C79—21no—
357C22×C79—21no—
358C22×C79—21no—
359C22×C79—21no—
360C22×C79—41no—
361C22×C79—41no—
362C22×C79—41no—
363C22×C79—41no—
364C22×C79—41no—
365C22×C79—81no—
366C22×C79—81no—
367C22×C79—84no—
368C22×C79C2×C4×D411yescharacteristic
369C22×C79#55111yescharacteristic
370C22×C79#55111yescharacteristic
371C4×C79—21no—
372C4×C79—21no—
373C4×C79—22no—
374C4×C79—41no—
375C4×C79—41no—
376C4×C79—41no—
377C4×C79—41no—
378C4×C79—41no—
379C4×C79C2×#11711yescharacteristic
380C4×C79#51811yescharacteristic
381C4×C79#54611yescharacteristic
382C4×C79#54611yescharacteristic
383Dic79—42no—
384Dic79—81no—
385#22588—791nomaximal, Sylow
386C2×C79—21no—
387C2×C79—21no—
388C2×C79—41no—
389C2×C79—41no—
390C2×C79—42no—
391C2×C79—81no—
392C2×C79#234211yescharacteristic
393C2×C79#295511yescharacteristic
394C2×C79#295611yescharacteristic
395#2924—791no—
396#2896D7911yescharacteristic
397#2880—791no—
398#1938—791no—
399#1937—791no—
400#1929—791no—
401#1929—791no—
402#1866—791no—
403#1866—791no—
404#1826—791no—
405#1811—791no—
406#1789—791no—
407#1765—791no—
408#1764—791no—
409#1753—791no—
410C79#2258811yescharacteristic, complemented, Sylow
411C22×#41C2×D7911yescharacteristic
412C2×#131—791no—
413C2×#131—791no—
414C22×M16C2×D7911yescharacteristic
415C2×#117C2×D7911yescharacteristic
416#433—1581no—
417#433—1581no—
418#432—1581no—
419#431—1581no—
420C2×#108—791no—
421C2×#108—791no—
422#424—791no—
423#424—791no—
424C2×#104—791no—
425C2×#104—791no—
426C2×#104—791no—
427C2×#104—791no—
428#419Dic7911yescharacteristic, complemented
429#419Dic7911yescharacteristic, complemented
430#418Dic7911yescharacteristic, complemented
431#418Dic7911yescharacteristic, complemented
432#417Dic7911yescharacteristic, complemented
433#417Dic7911yescharacteristic, complemented
434#417Dic7911yescharacteristic, complemented
435#417Dic7911yescharacteristic, complemented
436#416C2×D7911yescharacteristic
437#416C2×D7911yescharacteristic
438#416C2×D7911yescharacteristic
439#416C2×D7911yescharacteristic
440#408—791no—
441#408—791no—
442#408—1581no—
443#408—1581no—
444#407—791no—
445#407—791no—
446#407—1581no—
447C2×C22⋊C8—791no—
448C2×C22⋊C8—1581no—
449#405—791no—
450#405—791no—
451C2×#97—791no—
452C2×C4×C8—791no—
453C4×C22⋊C4—791no—
454#341—791no—
455#341—791no—
456#339—791no—
457#339—791no—
458#339—791no—
459#339—791no—
460#336—791no—
461#336—791no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C2×Dic7911yescharacteristic
469C2×#41C2×Dic7911yescharacteristic
470C2×#41C22×D7911yescharacteristic
471C2×#41C22×D7911yescharacteristic
472C22×Q8C2×Dic7911yescharacteristic
473C22×D4—21no—
474C22×D4C2×Dic7911yescharacteristic
475C23×C4—21no—
476C23×C4C22×D7911yescharacteristic
477#131—3161no—
478#131—3161no—
479#131—1582no—
480#131—1582no—
481C2×M16—41no—
482C2×M16—41no—
483C2×M16—791no—
484C2×M16—791no—
485C2×M16—791no—
486C2×M16—791no—
487C2×M16—1581no—
488C2×M16—1581no—
489C2×M16C2×Dic7911yescharacteristic
490C2×M16C2×Dic7911yescharacteristic
491C2×M16C2×Dic7911yescharacteristic
492C2×M16C2×Dic7911yescharacteristic
493C22×C8—791no—
494C22×C8—791no—
495C22×C8—1581no—
496C22×C8—1581no—
497C22×C8C22×D7911yescharacteristic
498C22×C8C22×D7911yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×Dic7911yescharacteristic
502#117C2×Dic7911yescharacteristic
503#117C22×D7911yescharacteristic
504#117C22×D7911yescharacteristic
505C2×C4⋊C4C2×Dic7911yescharacteristic
506C2×C4⋊C4C2×Dic7911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1581no—
509C2×C42—21no—
510C2×C42—791no—
511C2×C42—791no—
512#108—3161no—
513#108—3161no—
514C4⋊C8—1581no—
515C4⋊C8—1581no—
516C4⋊C8—1581no—
517C4⋊C8—1581no—
518#104—3161no—
519#104—3161no—
520#104—1582no—
521#104—1582no—
522#103C2×Dic7911yescharacteristic
523#103C2×Dic7911yescharacteristic
524#103C2×Dic7911yescharacteristic
525#103C2×Dic7911yescharacteristic
526#103C2×Dic7911yescharacteristic
527#103C2×Dic7911yescharacteristic
528#103C2×Dic7911yescharacteristic
529#103C2×Dic7911yescharacteristic
530#102C2×Dic7911yescharacteristic
531#102C2×Dic7911yescharacteristic
532#102C2×Dic7911yescharacteristic
533#102C2×Dic7911yescharacteristic
534#102C2×Dic7911yescharacteristic
535#102C2×Dic7911yescharacteristic
536#102C2×Dic7911yescharacteristic
537#102C2×Dic7911yescharacteristic
538C22⋊C8—791no—
539C22⋊C8—791no—
540C22⋊C8—791no—
541C22⋊C8—791no—
542C22⋊C8—1581no—
543C22⋊C8—1581no—
544C22⋊C8—1581no—
545C22⋊C8—1581no—
546C22⋊C8—1581no—
547C22⋊C8—1581no—
548C22⋊C8—1581no—
549C22⋊C8—1581no—
550#97—3161no—
551#97—1581no—
552#97—1581no—
553C4×C8—3161no—
554C4×C8—1581no—
555C4×C8—1581no—
556#95—1581no—
557C24—21no—
558C24#1192962311yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#1192962412yes—
574#41#1192962412yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×Dic7911yescharacteristic
579C2×Q8C22×Dic7911yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×Dic7911yescharacteristic
590C2×D4C22×Dic7911yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—1581no—
605C22×C4—1581no—
606C22×C4C22×Dic7911yescharacteristic
607C22×C4C22×Dic7911yescharacteristic
608C22×C4D4×D7911yescharacteristic
609C22×C4D4×D7911yescharacteristic
610C22×C4#1192962311yescharacteristic
611C22×C4C23×D7911yescharacteristic
612M16—41no—
613M16—41no—
614M16—41no—
615M16—41no—
616M16—3162no—
617M16—3162no—
618M16—1581no—
619M16—1581no—
620M16—1581no—
621M16—1581no—
622M16—1581no—
623M16—1581no—
624M16—1581no—
625M16—1581no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—3162no—
631C2×C8—3162no—
632C2×C8—791no—
633C2×C8—791no—
634C2×C8—791no—
635C2×C8—791no—
636C2×C8—1581no—
637C2×C8—1581no—
638C2×C8—1581no—
639C2×C8—1581no—
640C2×C8—1581no—
641C2×C8—1581no—
642C2×C8—1581no—
643C2×C8—1581no—
644C2×C8C22×Dic7911yescharacteristic
645C2×C8C22×Dic7911yescharacteristic
646C2×C8C22×Dic7911yescharacteristic
647C2×C8C22×Dic7911yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×Dic7911yescharacteristic
651C4⋊C4C22×Dic7911yescharacteristic
652C4⋊C4C22×Dic7911yescharacteristic
653C4⋊C4C22×Dic7911yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—3162no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—1581no—
664C42—1581no—
665C42—1581no—
666C42—1581no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23D4×Dic7911yescharacteristic
677C23D4×Dic7911yescharacteristic
678C23C2×#1192962311yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1457912012yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1457912012yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—81no—
720C2×C4—3161no—
721C2×C4—3161no—
722C2×C4—3161no—
723C2×C4—3161no—
724C2×C4—3161no—
725C2×C4—1582no—
726C2×C4D4×Dic7911yescharacteristic
727C2×C4D4×Dic7911yescharacteristic
728C2×C4C23×Dic7911yescharacteristic
729C2×C4C2×D4×D7911yescharacteristic
730C2×C4C2×#1192962411yescharacteristic
731C2×C4C2×#1192962411yescharacteristic
732C2×C4#1457920611yescharacteristic
733C2×C4#1457920611yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—3161no—
739C8—3161no—
740C8—3161no—
741C8—3161no—
742C8—1581no—
743C8—1581no—
744C8—1581no—
745C8—1581no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×D4×Dic7911yescharacteristic
764C22#1909923911yescharacteristic
765C22#1909923911yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—3162no—
775C4—6321no—
776C4C2×#1457912011yescharacteristic
777C4#1909903811yescharacteristic
778C4#1909920311yescharacteristic
779C4#1909920311yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2376624911yescharacteristic
787C2#2377230311yescharacteristic
788C2#2377231011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2896C2
socleC22×C79C2×C4×D4
prime radicalC22×#41×C79C22
cosocleC22×C4×C79C24
hypercenter#2896D79
hypocenterC79#22588
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. #23772058C2semidirect
3. #23764113C2semidirect
4. #23764106C2semidirect
5. #23764050C2semidirect
6. #23764050C2semidirect
7. #23763677C2semidirect
8. #23763677C2semidirect
9. #23763499C2semidirect
10. #23763442C2semidirect
12. #23763247C2semidirect
13. #23763240C2semidirect
14. #23763181C2semidirect
22. C2×#14579097C22semidirect
23. C2×#14579097C22semidirect
24. #19098590C22semidirect
25. #19098590C22semidirect
39. #19098519C22semidirect
40. #19098519C22semidirect
41. C2×#14579071C22semidirect
42. C2×C8×Dic79C22semidirect
44. #19098328C22semidirect
45. #19098328C22semidirect
46. #19098322C22semidirect
47. #19098322C22semidirect
48. #19098322C22semidirect
49. #19098322C22semidirect
50. #19098317C22semidirect
51. #19098317C22semidirect
55. #419×C79C4semidirect
56. #419×C79C4semidirect
57. #418×C79C4semidirect
58. #418×C79C4semidirect
59. #417×C79C4semidirect
60. #417×C79C4semidirect
61. #417×C79C4semidirect
62. #417×C79C4semidirect
410. C79#22588semidirect
428. #419Dic79semidirect
429. #419Dic79semidirect
430. #418Dic79semidirect
431. #418Dic79semidirect
432. #417Dic79semidirect
433. #417Dic79semidirect
434. #417Dic79semidirect
435. #417Dic79semidirect

Maximal subgroups

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

subgroupindex
#237720582
#237718492
#237641132
#237641062
#237640502
#237636772
#237634992
#237634422
#237633442
#237632472
#237632402
#237631812
C79×#28962
#2258879