Finite Group Databasebeta

← #34310793

Subgroups — #34310793

Order 20224.

864 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772849C211yesmaximal, characteristic
2C2×#19098683C211yesmaximal, characteristic, complemented
3C2×#19098678C211yesmaximal, characteristic, complemented
4#23771965C211yesmaximal, characteristic, complemented
5#23764233C211yesmaximal, characteristic, complemented
6#23764175C211yesmaximal, characteristic, complemented
7#23764114C211yesmaximal, characteristic, complemented
8#23764107C211yesmaximal, characteristic, complemented
9#23763730C211yesmaximal, characteristic, complemented
10#23763730C211yesmaximal, characteristic, complemented
11#23763675C211yesmaximal, characteristic, complemented
12#23763675C211yesmaximal, characteristic, complemented
13#23763259C211yesmaximal, characteristic, complemented
14#23763213C211yesmaximal, characteristic, complemented
15C79×#2935C211yesmaximal, characteristic, complemented
16C2×#14579181C2211yescharacteristic
17C2×#14579181C2211yescharacteristic
18C2×#14579167C2211yescharacteristic
19C2×#14579167C2211yescharacteristic
20C4×#11929624C2211yescharacteristic
21#19098782C411yescharacteristic, complemented
22#19098782C411yescharacteristic, complemented
23#19098775C411yescharacteristic, complemented
24#19098775C411yescharacteristic, complemented
25#19098770C411yescharacteristic, complemented
26#19098765C411yescharacteristic, complemented
27#19098760C411yescharacteristic, complemented
28#19098755C411yescharacteristic, complemented
29#19098683—24no—
30#19098678—24no—
31C2×#14579096C2211yescharacteristic
32C2×#14579096C2211yescharacteristic
33#19098589C2211yescharacteristic
34#19098589C2211yescharacteristic
35#19098588—21no—
36#19098588—21no—
37#19098587C2211yescharacteristic
38#19098585—21no—
39C2×C4⋊(C79⋊C8)C2211yescharacteristic
40C4⋊C8×D79—21no—
41C2×#14579088C2211yescharacteristic
42C2×#14579088C2211yescharacteristic
43C2×#14579088C2211yescharacteristic
44C2×#14579088C2211yescharacteristic
45C2×#14579087C2211yescharacteristic
46C2×#14579087C2211yescharacteristic
47#19098559C2211yescharacteristic
48#19098559C2211yescharacteristic
49C2×#14579071C2211yescharacteristic
50C2×C8×Dic79C2211yescharacteristic
51#19098409C2211yescharacteristic
52#19098327C2211yescharacteristic
53#19098327C2211yescharacteristic
54#19098324C2211yescharacteristic
55#19098324C2211yescharacteristic
56#19098317C2211yescharacteristic
57#19098317C2211yescharacteristic
58C2×#131×C79C2211yescharacteristic
59C2×#131×C79C2211yescharacteristic
60#532×C79C2211yescharacteristic
61#436×C79—21no—
62#435×C79—21no—
63#435×C79—21no—
64C8×D4×C79—21no—
65C2×C4⋊C8×C79C2211yescharacteristic
66#408×C79C2211yescharacteristic
67#408×C79C2211yescharacteristic
68C4×M16×C79C2211yescharacteristic
69C2×#11929624C2311yescharacteristic
70#14579181—22no—
71#14579181—22no—
72#14579181—22no—
73#14579181—22no—
74C2×#11929614C2×C411yescharacteristic
75C2×#11929614C2×C411yescharacteristic
76C2×#11929612C2×C411yescharacteristic
77C2×#11929612C2×C411yescharacteristic
78C2×#11929611C2×C411yescharacteristic
79C2×#11929611C2×C411yescharacteristic
80C2×#11929609C2×C411yescharacteristic
81C2×#11929609C2×C411yescharacteristic
82#14579167—22no—
83#14579167—22no—
84#14579167—41no—
85#14579167—41no—
86C2×#11929608C2311yescharacteristic
87C2×#11929608C2311yescharacteristic
88C2×#11929607—21no—
89C2×#11929607—21no—
90C22×C79⋊C8C2311yescharacteristic
91C22×C79⋊C8C2311yescharacteristic
92C2×C8×D79—21no—
93C2×C8×D79—21no—
94C4×Dic158C2×C411yescharacteristic
95C4×Dic158C2×C411yescharacteristic
96C4×D316C2×C411yescharacteristic
97C4×D316C2×C411yescharacteristic
98C4×C22⋊D79—21no—
99C4×C22⋊D79—21no—
100#14579120C2311yescharacteristic
101#14579118—21no—
102C2×C4×Dic79C2311yescharacteristic
103C2×C4×Dic79C2311yescharacteristic
104C42×D79—21no—
105#14579096—22no—
106#14579096—22no—
107C4⋊(C79⋊C8)—21no—
108C4⋊(C79⋊C8)—21no—
109C4⋊(C79⋊C8)C2×C411yescharacteristic
110C4⋊(C79⋊C8)C2×C411yescharacteristic
111C4⋊(C79⋊C8)C2×C411yescharacteristic
112C4⋊(C79⋊C8)C2×C411yescharacteristic
113Dic79⋊C8—21no—
114Dic79⋊C8—21no—
115Dic79⋊C8—21no—
116Dic79⋊C8—21no—
117#14579088—22no—
118#14579088—22no—
119#14579088—41no—
120#14579088—41no—
121#14579087—22no—
122#14579087D414yescomplemented
123#14579085C2×C411yescharacteristic
124#14579085C2×C411yescharacteristic
125#14579085C2×C411yescharacteristic
126#14579085C2×C411yescharacteristic
127#14579082C2×C411yescharacteristic
128#14579082C2×C411yescharacteristic
129#14579082C2×C411yescharacteristic
130#14579082C2×C411yescharacteristic
131#14579071—22no—
132C8×Dic79—22no—
133C79⋊#95—21no—
134C79⋊#95—21no—
135C2×#41×C79C2311yescharacteristic
136C2×#41×C79C2311yescharacteristic
137#131×C79—22no—
138#131×C79—22no—
139#131×C79—41no—
140#131×C79—41no—
141C2×M16×C79—21no—
142C2×M16×C79—21no—
143C2×M16×C79C2311yescharacteristic
144C2×M16×C79C2311yescharacteristic
145C22×C8×C79—21no—
146C22×C8×C79—21no—
147C22×C8×C79C2311yescharacteristic
148C22×C8×C79C2311yescharacteristic
149C4⋊Q8×C79C2×C411yescharacteristic
150#127×C79C2×C411yescharacteristic
151#124×C79C2×C411yescharacteristic
152#124×C79C2×C411yescharacteristic
153#121×C79—21no—
154#121×C79—21no—
155C4×D4×C79—21no—
156C4×D4×C79—21no—
157C2×C42×C79C2311yescharacteristic
158C4⋊C8×C79D411yescharacteristic
159C4⋊C8×C79D411yescharacteristic
160C4⋊C8×C79D411yescharacteristic
161C4⋊C8×C79D411yescharacteristic
162C22⋊C8×C79—21no—
163C22⋊C8×C79—21no—
164C22⋊C8×C79—21no—
165C22⋊C8×C79—21no—
166#97×C79—21no—
167C4×C8×C79—21no—
168#11929624—21no—
169#11929624—21no—
170#11929624C2×D412yes—
171#11929624#4112yes—
172C2×Dic158C22×C411yescharacteristic
173C2×D316C22×C411yescharacteristic
174C2×C22⋊D79—21no—
175C22×Dic79—21no—
176C22×Dic79—21no—
177C2×C4×D79—21no—
178C2×C4×D79—21no—
179C2×C4×D79—21no—
180#11929614—22no—
181#11929614—22no—
182#11929612—22no—
183#11929612—22no—
184#11929611—22no—
185#11929611—22no—
186#11929609—22no—
187#11929609—22no—
188#11929608—21no—
189#11929608—21no—
190#11929608—21no—
191#11929608—21no—
192#11929607—42no—
193#11929607—42no—
194C2×C79⋊C8—21no—
195C2×C79⋊C8—21no—
196C2×C79⋊C8—21no—
197C2×C79⋊C8—21no—
198C2×C79⋊C8—21no—
199C2×C79⋊C8—21no—
200C2×C79⋊C8C22×C411yescharacteristic
201C2×C79⋊C8C22×C411yescharacteristic
202C2×C79⋊C8C22×C411yescharacteristic
203C2×C79⋊C8C22×C411yescharacteristic
204C8×D79—42no—
205C8×D79—42no—
206C4⋊Dic79C22×C411yescharacteristic
207C4⋊Dic79C22×C411yescharacteristic
208Dic79⋊C4—21no—
209Dic79⋊C4—21no—
210C22⋊Dic79—21no—
211(C2×D79)⋊C4—21no—
212(C2×D79)⋊C4—21no—
213C4×Dic79—21no—
214C4×Dic79—21no—
215C4×Dic79—21no—
216C4×Dic79—21no—
217C4×Dic79—21no—
218C4×Dic79—21no—
219C4×Dic79C2×D412yes—
220#41×C79—21no—
221#41×C79—21no—
222#41×C79—21no—
223#41×C79—21no—
224#41×C79—21no—
225#41×C79—21no—
226#41×C79—21no—
227#41×C79—21no—
228C2×Q8×C79C22×C411yescharacteristic
229C2×Q8×C79C22×C411yescharacteristic
230C2×D4×C79—21no—
231C2×D4×C79—21no—
232C2×D4×C79—21no—
233C2×D4×C79—21no—
234C2×D4×C79C22×C411yescharacteristic
235C2×D4×C79C22×C411yescharacteristic
236C22×C4×C79—21no—
237C22×C4×C79—21no—
238C22×C4×C79#4111yescharacteristic
239C22×C4×C79#4111yescharacteristic
240C22×C4×C79C2411yescharacteristic
241M16×C79—21no—
242M16×C79—21no—
243M16×C79—21no—
244M16×C79—42no—
245M16×C79—42no—
246M16×C79C2×D412yes—
247C2×C8×C79—21no—
248C2×C8×C79—21no—
249C2×C8×C79—21no—
250C2×C8×C79—21no—
251C2×C8×C79—21no—
252C2×C8×C79—21no—
253C2×C8×C79—42no—
254C2×C8×C79—42no—
255C2×C8×C79C2×D411yescharacteristic
256C2×C8×C79C2×D411yescharacteristic
257C2×C8×C79C2×D411yescharacteristic
258C2×C8×C79C2×D411yescharacteristic
259C4⋊C4×C79—21no—
260C4⋊C4×C79—21no—
261C22⋊C4×C79—21no—
262C22⋊C4×C79—21no—
263C22⋊C4×C79—21no—
264C22⋊C4×C79—21no—
265C42×C79C22×C411yescharacteristic
266C42×C79C22×C411yescharacteristic
267C42×C79C2×D411yescharacteristic
268C42×C79C2×D411yescharacteristic
269C23×C79—21no—
270C23×C79—21no—
271C23×C79C2×#4111yescharacteristic
272C22×D79—21no—
273Q8×C79—21no—
274Q8×C79—21no—
275Q8×C79—21no—
276Q8×C79—21no—
277D4×C79—21no—
278D4×C79—21no—
279D4×C79—21no—
280D4×C79—21no—
281D4×C79—42no—
282D4×C79—41no—
283D4×C79—41no—
284D4×C79—41no—
285D4×C79—41no—
286D4×C79—81no—
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×C79C4×D411yescharacteristic
296C2×C4×C79C4×D411yescharacteristic
297C2×C4×C79C4×D411yescharacteristic
298C2×C4×C79C4×D411yescharacteristic
299C2×C4×C79C23×C411yescharacteristic
300C2×C4×C79C22×D411yescharacteristic
301C2×C4×C79C22×D411yescharacteristic
302C2×C4×C79C2×#4111yescharacteristic
303C2×C4×C79H(5,𝔽2)11yescharacteristic
304C2×C4×C792−1+411yescharacteristic
305C22⋊D79—22no—
306C22⋊D79—22no—
307C2×Dic79—21no—
308C2×Dic79—21no—
309C2×Dic79—21no—
310C2×Dic79—22no—
311C2×Dic79—41no—
312C2×Dic79—41no—
313C2×Dic79—41no—
314C2×Dic79—41no—
315C2×Dic79—41no—
316D316—21no—
317D316C4×D412yes—
318C4×D79—22no—
319C4×D79—22no—
320C4×D79—42no—
321C4×D79—81no—
322Dic158—21no—
323Dic158C4×D412yes—
324C8×C79—21no—
325C8×C79—21no—
326C8×C79—21no—
327C8×C79—21no—
328C8×C79—22no—
329C8×C79—41no—
330C79⋊C8—21no—
331C79⋊C8—21no—
332C79⋊C8—21no—
333C79⋊C8—21no—
334C79⋊C8—41no—
335C79⋊C8—41no—
336C22×C79—21no—
337C22×C79—21no—
338C22×C79—41no—
339C22×C79—41no—
340C22×C79—41no—
341C22×C79—41no—
342C22×C79—41no—
343C22×C79—41no—
344C22×C79C2×C4×D411yescharacteristic
345C22×C79#54711yescharacteristic
346C22×C79#55311yescharacteristic
347C2×D79—22no—
348C2×D79—41no—
349C2×D79—41no—
350C4×C79—21no—
351C4×C79—21no—
352C4×C79—21no—
353C4×C79—21no—
354C4×C79—41no—
355C4×C79—41no—
356C4×C79C2×C4×D411yescharacteristic
357C4×C79#52011yescharacteristic
358C4×C79D4211yescharacteristic
359C4×C79#54811yescharacteristic
360Dic79—22no—
361Dic79—42no—
362Dic79—41no—
363Dic79—41no—
364Dic79—81no—
365#23017—791nomaximal, Sylow
366C2×C79—21no—
367C2×C79—21no—
368C2×C79—81no—
369C2×C79—81no—
370C2×C79#236111yescharacteristic
371C2×C79#295511yescharacteristic
372C2×C79#295711yescharacteristic
373D79—42no—
374#3035—791no—
375C2×#444—791no—
376C2×#443—791no—
377#2935D7911yescharacteristic, complemented
378#2906—791no—
379#1963—791no—
380#1950—791no—
381#1938—791no—
382#1937—791no—
383#1876—791no—
384#1876—791no—
385#1866—791no—
386#1866—791no—
387#1768—791no—
388#1759—791no—
389C79#2301711yescharacteristic, complemented, Sylow
390C2×#135—791no—
391C2×#135—791no—
392C2×#131—791no—
393C2×#131—791no—
394C2×#131C2×D7911yescharacteristic
395C2×#131C2×D7911yescharacteristic
396#532C2×D7911yescharacteristic
397C4×#41—791no—
398#464—791no—
399#464—791no—
400#463—791no—
401#463—791no—
402#462—791no—
403#461—791no—
404#460—791no—
405#459—791no—
406#444—1584no—
407#443—1584no—
408#436—21no—
409#435—21no—
410#435—21no—
411C8×D4—21no—
412C2×#108—791no—
413C2×#108—791no—
414#424—791no—
415#424—791no—
416#424—1581no—
417#424—1581no—
418#423—791no—
419#423—1581no—
420C2×C4⋊C8—791no—
421C2×C4⋊C8—1581no—
422C2×C4⋊C8C2×D7911yescharacteristic
423C2×#104—791no—
424C2×#104—791no—
425C2×#104—791no—
426C2×#104—791no—
427C2×#104—791no—
428C2×#104—791no—
429#416—791no—
430#416—791no—
431#408C2×D7911yescharacteristic
432#408C2×D7911yescharacteristic
433C4×M16C2×D7911yescharacteristic
434C2×#97—791no—
435C2×C4×C8—791no—
436#376—791no—
437#341—791no—
438#341—791no—
439#339—791no—
440#339—791no—
441#336—791no—
442#336—791no—
443C2×#41—791no—
444C2×#41C22×D7911yescharacteristic
445C2×#41C22×D7911yescharacteristic
446#135—1582no—
447#135—1582no—
448#135—1582no—
449#135—1582no—
450C2×Q16—791no—
451C2×Q16—791no—
452C2×SD16—791no—
453C2×SD16—791no—
454C2×SD16—791no—
455C2×SD16—791no—
456C2×D8—791no—
457C2×D8—791no—
458#131—22no—
459#131—22no—
460#131—41no—
461#131—41no—
462#131—3161no—
463#131—3161no—
464#131—1582no—
465#131—1582no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—791no—
469C2×M16—791no—
470C2×M16—1581no—
471C2×M16—1581no—
472C2×M16C22×D7911yescharacteristic
473C2×M16C22×D7911yescharacteristic
474C22×C8—21no—
475C22×C8—21no—
476C22×C8—791no—
477C22×C8—791no—
478C22×C8—1581no—
479C22×C8—1581no—
480C22×C8C22×D7911yescharacteristic
481C22×C8C22×D7911yescharacteristic
482C4⋊Q8C4×D7911yescharacteristic
483#127C4×D7911yescharacteristic
484#124C4×D7911yescharacteristic
485#124C4×D7911yescharacteristic
486#121—21no—
487#121—21no—
488C4×Q8—791no—
489C4×Q8—791no—
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—791no—
493C4×D4—791no—
494C4×D4—1581no—
495C4×D4—1581no—
496#117—791no—
497#117—1581no—
498C2×C42—791no—
499C2×C42—791no—
500C2×C42—1581no—
501C2×C42C22×D7911yescharacteristic
502#108—1582no—
503#108—1582no—
504C4⋊C8—791no—
505C4⋊C8—791no—
506C4⋊C8—791no—
507C4⋊C8—791no—
508C4⋊C8—1581no—
509C4⋊C8—1581no—
510C4⋊C8—1581no—
511C4⋊C8—1581no—
512C4⋊C8—1581no—
513C4⋊C8—1581no—
514C4⋊C8C22⋊D7911yescharacteristic
515C4⋊C8C22⋊D7911yescharacteristic
516C4⋊C8C22⋊D7911yescharacteristic
517C4⋊C8C22⋊D7911yescharacteristic
518#104—3161no—
519#104—3161no—
520#104—794no—
521#104—1582no—
522#104—1582no—
523#104—1582no—
524#103—791no—
525#103—791no—
526#103—791no—
527#103—791no—
528#102—791no—
529#102—791no—
530#102—791no—
531#102—791no—
532C22⋊C8—21no—
533C22⋊C8—21no—
534C22⋊C8—21no—
535C22⋊C8—21no—
536#97—21no—
537#97—1582no—
538C4×C8—21no—
539C4×C8—1582no—
540#95—1581no—
541#95—1581no—
542#41—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—792no—
551#41—792no—
552#41—1581no—
553#41—1581no—
554C2×Q8—791no—
555C2×Q8C2×C4×D7911yescharacteristic
556C2×Q8C2×C4×D7911yescharacteristic
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—791no—
562C2×D4—1581no—
563C2×D4C2×C4×D7911yescharacteristic
564C2×D4C2×C4×D7911yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—1581no—
568C22×C4—1581no—
569C22×C4—1581no—
570C22×C4—1581no—
571C22×C4—1581no—
572C22×C4#1192962411yescharacteristic
573C22×C4#1192962411yescharacteristic
574C22×C4C23×D7911yescharacteristic
575Q16—1582no—
576Q16—1582no—
577SD16—1582no—
578SD16—1582no—
579SD16—1582no—
580SD16—1582no—
581D8—1582no—
582D8—1582no—
583M16—21no—
584M16—21no—
585M16—21no—
586M16—42no—
587M16—42no—
588M16—3162no—
589M16—3162no—
590M16—1581no—
591M16—1581no—
592M16—1581no—
593M16—1581no—
594M16D4×D7912yes—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—42no—
602C2×C8—42no—
603C2×C8—3162no—
604C2×C8—3162no—
605C2×C8—791no—
606C2×C8—791no—
607C2×C8—791no—
608C2×C8—791no—
609C2×C8—1581no—
610C2×C8—1581no—
611C2×C8—1581no—
612C2×C8—1581no—
613C2×C8—1581no—
614C2×C8—1581no—
615C2×C8C2×C22⋊D7911yescharacteristic
616C2×C8C2×C22⋊D7911yescharacteristic
617C2×C8C2×C22⋊D7911yescharacteristic
618C2×C8C2×C22⋊D7911yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—791no—
622C4⋊C4—791no—
623C4⋊C4—1581no—
624C4⋊C4—1581no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—1581no—
630C22⋊C4—1581no—
631C22⋊C4—1581no—
632C42—792no—
633C42—1581no—
634C42—1581no—
635C42—1581no—
636C42—1581no—
637C42—1581no—
638C42—1581no—
639C42C2×C4×D7911yescharacteristic
640C42C2×C4×D7911yescharacteristic
641C42C2×C22⋊D7911yescharacteristic
642C42C2×C22⋊D7911yescharacteristic
643C23—21no—
644C23—21no—
645C23—1581no—
646C23C2×#1192962411yescharacteristic
647Q8—21no—
648Q8—21no—
649Q8—21no—
650Q8—21no—
651Q8—792no—
652Q8—1581no—
653D4—21no—
654D4—21no—
655D4—21no—
656D4—21no—
657D4—42no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—81no—
663D4—792no—
664D4—1582no—
665D4—1582no—
666D4—1581no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—3162no—
676C2×C4—3161no—
677C2×C4—3161no—
678C2×C4—3161no—
679C2×C4—3161no—
680C2×C4—3161no—
681C2×C4—6321no—
682C2×C4—1582no—
683C2×C4—1581no—
684C2×C4—1581no—
685C2×C4—1581no—
686C2×C4—1582no—
687C2×C4—1582no—
688C2×C4C4×C22⋊D7911yescharacteristic
689C2×C4C4×C22⋊D7911yescharacteristic
690C2×C4C4×C22⋊D7911yescharacteristic
691C2×C4C4×C22⋊D7911yescharacteristic
692C2×C4C22×C4×D7911yescharacteristic
693C2×C4C2×D4×D7911yescharacteristic
694C2×C4C22×C22⋊D7911yescharacteristic
695C2×C4#41×D7911yescharacteristic
696C2×C4#1457920611yescharacteristic
697C2×C4#1457920811yescharacteristic
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—22no—
703C8—41no—
704C8—3161no—
705C8—3161no—
706C8—1581no—
707C8—1581no—
708C8—1581no—
709C8—1581no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—3161no—
719C22—3161no—
720C22—1582no—
721C22C2×C4×C22⋊D7911yescharacteristic
722C22#1909921811yescharacteristic
723C22#1909926311yescharacteristic
724C4—21no—
725C4—21no—
726C4—21no—
727C4—21no—
728C4—41no—
729C4—41no—
730C4—3162no—
731C4—3161no—
732C4—3161no—
733C4—6321no—
734C4—1582no—
735C4C4×D4×D7911yescharacteristic
736C4#1909904211yescharacteristic
737C4D4×C22⋊D7911yescharacteristic
738C4#1909922011yescharacteristic
739C2—21no—
740C2—21no—
741C2—81no—
742C2—81no—
743C2—3162no—
744C2#2376641211yescharacteristic
745C2#2377230111yescharacteristic
746C2#2377231511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2935C2
socleC22×C79C2×C4×D4
prime radical#23772849C2
cosocleC22×C4×C79C24
hypercenter#2935D79
hypocenterC79#23017
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. C2×#19098683C2semidirect
3. C2×#19098678C2semidirect
4. #23771965C2semidirect
5. #23764233C2semidirect
6. #23764175C2semidirect
7. #23764114C2semidirect
8. #23764107C2semidirect
9. #23763730C2semidirect
10. #23763730C2semidirect
11. #23763675C2semidirect
12. #23763675C2semidirect
13. #23763259C2semidirect
14. #23763213C2semidirect
15. C79×#2935C2semidirect
21. #19098782C4semidirect
22. #19098782C4semidirect
23. #19098775C4semidirect
24. #19098775C4semidirect
25. #19098770C4semidirect
26. #19098765C4semidirect
27. #19098760C4semidirect
28. #19098755C4semidirect
122. #14579087D4semidirect
377. #2935D79semidirect
389. C79#23017semidirect

Maximal subgroups

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

subgroupindex
#237728492
C2×#190986832
C2×#190986782
#237719652
#237642332
#237641752
#237641142
#237641072
#237637302
#237636752
#237632592
#237632132
C79×#29352
#2301779