Finite Group Databasebeta

← #34294738

Subgroups — #34294738

Order 20224.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772849C211yesmaximal, characteristic
2C2×#19098682C211yesmaximal, characteristic, complemented
3C2×#19098677C211yesmaximal, characteristic, complemented
4#23772118C211yesmaximal, characteristic, complemented
5#23771829C211yesmaximal, characteristic, complemented
6#23764175C211yesmaximal, characteristic, complemented
7#23764051C211yesmaximal, characteristic, complemented
8#23764051C211yesmaximal, characteristic, complemented
9#23763724C211yesmaximal, characteristic, complemented
10#23763724C211yesmaximal, characteristic, complemented
11#23763421C211yesmaximal, characteristic, complemented
12#23763275C211yesmaximal, characteristic, complemented
13#23763245C211yesmaximal, characteristic, complemented
14#23763238C211yesmaximal, characteristic, complemented
15C79×#1980C211yesmaximal, characteristic, complemented
16C2×#14579181C2211yescharacteristic
17C2×#14579181C2211yescharacteristic
18C2×#14579169C2211yescharacteristic
19C2×#14579169C2211yescharacteristic
20C2×#14579168C2211yescharacteristic
21C2×#14579168C2211yescharacteristic
22C4×#11929624C2211yescharacteristic
23#19098782C411yescharacteristic, complemented
24#19098782C411yescharacteristic, complemented
25#19098775C411yescharacteristic, complemented
26#19098775C411yescharacteristic, complemented
27#19098770C411yescharacteristic, complemented
28#19098765C411yescharacteristic, complemented
29#19098760C411yescharacteristic, complemented
30#19098755C411yescharacteristic, complemented
31#19098682—24no—
32#19098677—24no—
33#19098635—21no—
34#19098635—21no—
35#19098635—21no—
36#19098635—21no—
37C2×#14579096C2211yescharacteristic
38C2×#14579096C2211yescharacteristic
39#19098587C2211yescharacteristic
40C2×C4⋊(C79⋊C8)C2211yescharacteristic
41C2×#14579089C2211yescharacteristic
42C2×#14579089C2211yescharacteristic
43#19098559C2211yescharacteristic
44#19098559C2211yescharacteristic
45#19098530C2211yescharacteristic
46#19098530C2211yescharacteristic
47#19098521C2211yescharacteristic
48#19098521C2211yescharacteristic
49#19098517—21no—
50#19098517—21no—
51#19098515—21no—
52C2×#14579072C2211yescharacteristic
53C2×#14579072C2211yescharacteristic
54#97×D79—21no—
55C2×C4×C79⋊C8C2211yescharacteristic
56#19098327C2211yescharacteristic
57#19098327C2211yescharacteristic
58#19098323C2211yescharacteristic
59#19098323C2211yescharacteristic
60#19098318C2211yescharacteristic
61#19098318C2211yescharacteristic
62#532×C79C2211yescharacteristic
63C2×#104×C79C2211yescharacteristic
64C2×#104×C79C2211yescharacteristic
65C2×#104×C79C2211yescharacteristic
66C2×#104×C79C2211yescharacteristic
67C4×M16×C79C2211yescharacteristic
68C4×C4⋊C4×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#14579169—22no—
83#14579169—22no—
84#14579169—22no—
85#14579169D414yescomplemented
86#14579168—22no—
87#14579168—22no—
88#14579168—22no—
89#14579168—22no—
90C2×#11929608—21no—
91C2×#11929608—21no—
92C2×#11929608C2311yescharacteristic
93C2×#11929608C2311yescharacteristic
94C2×#11929607—21no—
95C2×#11929607—21no—
96C22×C79⋊C8—21no—
97C22×C79⋊C8—21no—
98C22×C79⋊C8C2311yescharacteristic
99C22×C79⋊C8C2311yescharacteristic
100C22×C79⋊C8C2311yescharacteristic
101C22×C79⋊C8C2311yescharacteristic
102C2×C8×D79—21no—
103C2×C8×D79—21no—
104C4×Dic158C2×C411yescharacteristic
105C4×Dic158C2×C411yescharacteristic
106C4×D316C2×C411yescharacteristic
107C4×D316C2×C411yescharacteristic
108C4×C22⋊D79—21no—
109C4×C22⋊D79—21no—
110#14579120C2311yescharacteristic
111#14579118—21no—
112C42×D79—21no—
113#14579096—22no—
114#14579096—22no—
115C4⋊(C79⋊C8)—21no—
116C4⋊(C79⋊C8)—21no—
117C4⋊(C79⋊C8)C2×C411yescharacteristic
118C4⋊(C79⋊C8)C2×C411yescharacteristic
119C4⋊(C79⋊C8)C2×C411yescharacteristic
120C4⋊(C79⋊C8)C2×C411yescharacteristic
121#14579089—22no—
122#14579089—22no—
123#14579085C2×C411yescharacteristic
124#14579085C2×C411yescharacteristic
125#14579085C2×C411yescharacteristic
126#14579085C2×C411yescharacteristic
127#14579082C2×C411yescharacteristic
128#14579082C2×C411yescharacteristic
129#14579082C2×C411yescharacteristic
130#14579082C2×C411yescharacteristic
131C22⋊(C79⋊C8)—21no—
132C22⋊(C79⋊C8)—21no—
133C22⋊(C79⋊C8)—21no—
134C22⋊(C79⋊C8)—21no—
135#14579072—22no—
136#14579072D411yescharacteristic
137#14579072D411yescharacteristic
138#14579072D411yescharacteristic
139#14579072D411yescharacteristic
140#14579071—21no—
141#14579071—21no—
142C4×C79⋊C8—22no—
143C8×Dic79—21no—
144C8×Dic79—21no—
145C2×#41×C79C2311yescharacteristic
146C2×#41×C79C2311yescharacteristic
147C2×M16×C79C2311yescharacteristic
148C2×M16×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×C4⋊C4×C79—21no—
158C2×C42×C79C2311yescharacteristic
159C2×C42×C79C2311yescharacteristic
160C2×C42×C79C2311yescharacteristic
161#104×C79—22no—
162#104×C79—22no—
163#104×C79—22no—
164#104×C79—22no—
165#97×C79—21no—
166C4×C8×C79—21no—
167#95×C79—21no—
168#11929624—21no—
169#11929624—21no—
170#11929624C2×D412yes—
171#11929624#4112yes—
172C2×Dic158C22×C411yescharacteristic
173C2×D316C22×C411yescharacteristic
174C2×C22⋊D79—21no—
175C2×C4×D79—21no—
176C2×C4×D79—21no—
177C2×C4×D79—21no—
178#11929614—22no—
179#11929614—22no—
180#11929612—22no—
181#11929612—22no—
182#11929611—22no—
183#11929611—22no—
184#11929609—22no—
185#11929609—22no—
186#11929608—21no—
187#11929608—21no—
188#11929608—21no—
189#11929608—21no—
190#11929608—42no—
191#11929608—42no—
192#11929607—24no—
193#11929607—24no—
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⋊C8—21no—
201C2×C79⋊C8—21no—
202C2×C79⋊C8—42no—
203C2×C79⋊C8—42no—
204C2×C79⋊C8C22×C411yescharacteristic
205C2×C79⋊C8C22×C411yescharacteristic
206C2×C79⋊C8C22×C411yescharacteristic
207C2×C79⋊C8C22×C411yescharacteristic
208C2×C79⋊C8C2×D411yescharacteristic
209C2×C79⋊C8C2×D411yescharacteristic
210C2×C79⋊C8C2×D411yescharacteristic
211C2×C79⋊C8C2×D412yes—
212C2×C79⋊C8C2×D411yescharacteristic
213C2×C79⋊C8#4112yes—
214C8×D79—24no—
215C8×D79—24no—
216C4⋊Dic79C22×C411yescharacteristic
217C4⋊Dic79C22×C411yescharacteristic
218Dic79⋊C4—21no—
219Dic79⋊C4—21no—
220C22⋊Dic79—21no—
221(C2×D79)⋊C4—21no—
222(C2×D79)⋊C4—21no—
223C4×Dic79—21no—
224C4×Dic79—21no—
225C4×Dic79—21no—
226#41×C79—21no—
227#41×C79—21no—
228#41×C79—21no—
229#41×C79—21no—
230#41×C79—21no—
231#41×C79—21no—
232#41×C79—21no—
233#41×C79—21no—
234C2×Q8×C79C22×C411yescharacteristic
235C2×Q8×C79C22×C411yescharacteristic
236C2×D4×C79—21no—
237C2×D4×C79—21no—
238C2×D4×C79—21no—
239C2×D4×C79—21no—
240C2×D4×C79C22×C411yescharacteristic
241C2×D4×C79C22×C411yescharacteristic
242C22×C4×C79—21no—
243C22×C4×C79—21no—
244C22×C4×C79—21no—
245C22×C4×C79—21no—
246C22×C4×C79#4111yescharacteristic
247C22×C4×C79#4111yescharacteristic
248C22×C4×C79C2411yescharacteristic
249M16×C79—21no—
250M16×C79—21no—
251M16×C79C2×D412yes—
252M16×C79#4112yes—
253C2×C8×C79—21no—
254C2×C8×C79—21no—
255C4⋊C4×C79—21no—
256C4⋊C4×C79—21no—
257C4⋊C4×C79—42no—
258C22⋊C4×C79—21no—
259C22⋊C4×C79—21no—
260C22⋊C4×C79—21no—
261C22⋊C4×C79—21no—
262C42×C79—21no—
263C42×C79—21no—
264C42×C79—21no—
265C42×C79—21no—
266C42×C79C22×C411yescharacteristic
267C42×C79C22×C411yescharacteristic
268C42×C79C2×D411yescharacteristic
269C42×C79C2×D411yescharacteristic
270C23×C79—21no—
271C23×C79—21no—
272C23×C79C2×#4111yescharacteristic
273C22×D79—21no—
274Q8×C79—21no—
275Q8×C79—21no—
276Q8×C79—21no—
277Q8×C79—21no—
278D4×C79—21no—
279D4×C79—21no—
280D4×C79—21no—
281D4×C79—21no—
282D4×C79—41no—
283D4×C79—41no—
284D4×C79—41no—
285D4×C79—41no—
286D4×C79—81no—
287D4×C79—81no—
288C2×C4×C79—22no—
289C2×C4×C79—21no—
290C2×C4×C79—21no—
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—41no—
301C2×C4×C79—41no—
302C2×C4×C79C4×D411yescharacteristic
303C2×C4×C79C4×D411yescharacteristic
304C2×C4×C79C4×D411yescharacteristic
305C2×C4×C79C4×D411yescharacteristic
306C2×C4×C79C23×C411yescharacteristic
307C2×C4×C79C22×D411yescharacteristic
308C2×C4×C79C22×D411yescharacteristic
309C2×C4×C79C2×#4111yescharacteristic
310C2×C4×C79C2×#4111yescharacteristic
311C2×C4×C79C2×#4111yescharacteristic
312C22⋊D79—22no—
313C22⋊D79—22no—
314C2×Dic79—21no—
315C2×Dic79—21no—
316C2×Dic79—21no—
317D316—21no—
318D316C4×D412yes—
319C4×D79—22no—
320C4×D79—22no—
321C4×D79—81no—
322C4×D79—81no—
323Dic158—21no—
324Dic158C4×D412yes—
325C8×C79—22no—
326C8×C79—22no—
327C79⋊C8—21no—
328C79⋊C8—21no—
329C79⋊C8—21no—
330C79⋊C8—21no—
331C79⋊C8—21no—
332C79⋊C8—21no—
333C79⋊C8—41no—
334C79⋊C8—41no—
335C79⋊C8#12112yes—
336C79⋊C8#12112yes—
337C22×C79—21no—
338C22×C79—21no—
339C22×C79—41no—
340C22×C79—41no—
341C22×C79—41no—
342C22×C79—41no—
343C22×C79—41no—
344C22×C79—41no—
345C22×C79C2×C4×D411yescharacteristic
346C22×C79#52911yescharacteristic
347C22×C79#53211yescharacteristic
348C2×D79—22no—
349C2×D79—41no—
350C2×D79—41no—
351C4×C79—21no—
352C4×C79—21no—
353C4×C79—21no—
354C4×C79—21no—
355C4×C79—42no—
356C4×C79—41no—
357C4×C79—41no—
358C4×C79—81no—
359C4×C79C2×C4×D411yescharacteristic
360C4×C79C4×#4111yescharacteristic
361C4×C79C2×#12111yescharacteristic
362C4×C79#52511yescharacteristic
363Dic79—22no—
364Dic79—41no—
365Dic79—41no—
366#21519—791nomaximal, Sylow
367C2×C79—21no—
368C2×C79—21no—
369C2×C79—81no—
370C2×C79—81no—
371C2×C79C4×#12111yescharacteristic
372C2×C79#295611yescharacteristic
373C2×C79#295711yescharacteristic
374D79—42no—
375#3035—791no—
376C2×#444—791no—
377C2×#443—791no—
378#2932—791no—
379#2875—791no—
380#1980D7911yescharacteristic, complemented
381#1950—791no—
382#1929—791no—
383#1929—791no—
384#1876—791no—
385#1876—791no—
386#1806—791no—
387#1771—791no—
388#1765—791no—
389#1764—791no—
390C79#2151911yescharacteristic, complemented, Sylow
391C2×#135—791no—
392C2×#135—791no—
393C2×#131—791no—
394C2×#131—791no—
395C2×#131—791no—
396C2×#131—791no—
397#532C2×D7911yescharacteristic
398C4×#41—791no—
399#464—791no—
400#464—791no—
401#463—791no—
402#463—791no—
403#462—791no—
404#461—791no—
405#460—791no—
406#459—791no—
407#444—1584no—
408#443—1584no—
409#435—1581no—
410#435—1581no—
411#435—1581no—
412#435—1581no—
413C2×#108—791no—
414C2×#108—791no—
415#423—791no—
416C2×C4⋊C8—791no—
417C2×#104—791no—
418C2×#104—791no—
419C2×#104C2×D7911yescharacteristic
420C2×#104C2×D7911yescharacteristic
421C2×#104C2×D7911yescharacteristic
422C2×#104C2×D7911yescharacteristic
423#416—791no—
424#416—791no—
425#408—791no—
426#408—791no—
427#405—791no—
428#405—791no—
429#405—1581no—
430#405—1581no—
431C4×M16—1581no—
432C4×M16C2×D7911yescharacteristic
433C2×#97—791no—
434C2×#97—791no—
435C2×#97—1581no—
436C2×C4×C8—791no—
437C4×C4⋊C4C2×D7911yescharacteristic
438#341—791no—
439#341—791no—
440#339—791no—
441#339—791no—
442#336—791no—
443#336—791no—
444C2×#41—791no—
445C2×#41C22×D7911yescharacteristic
446C2×#41C22×D7911yescharacteristic
447#135—1582no—
448#135—1582no—
449#135—1582no—
450#135—1582no—
451C2×Q16—791no—
452C2×Q16—791no—
453C2×SD16—791no—
454C2×SD16—791no—
455C2×SD16—791no—
456C2×SD16—791no—
457C2×D8—791no—
458C2×D8—791no—
459#131—794no—
460#131—1582no—
461#131—1582no—
462#131—1582no—
463#131—1582no—
464#131—1582no—
465#131—1582no—
466#131—1582no—
467C2×M16—791no—
468C2×M16—791no—
469C2×M16—1581no—
470C2×M16—1581no—
471C2×M16—1581no—
472C2×M16—1581no—
473C2×M16C22×D7911yescharacteristic
474C2×M16C22×D7911yescharacteristic
475C22×C8—791no—
476C22×C8—791no—
477C22×C8—791no—
478C22×C8—791no—
479C22×C8—1581no—
480C22×C8—1581no—
481C22×C8—1581no—
482C22×C8—1581no—
483C4⋊Q8C4×D7911yescharacteristic
484#127C4×D7911yescharacteristic
485#124C4×D7911yescharacteristic
486#124C4×D7911yescharacteristic
487#121—21no—
488#121—21no—
489C4×Q8—791no—
490C4×Q8—791no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—791no—
494C4×D4—791no—
495C4×D4—1581no—
496C4×D4—1581no—
497#117—791no—
498#117—1581no—
499C2×C4⋊C4—21no—
500C2×C42—1581no—
501C2×C42C22×D7911yescharacteristic
502C2×C42C22×D7911yescharacteristic
503C2×C42C22×D7911yescharacteristic
504#108—1582no—
505#108—1582no—
506C4⋊C8—791no—
507C4⋊C8—791no—
508C4⋊C8—791no—
509C4⋊C8—791no—
510C4⋊C8—1581no—
511C4⋊C8—1581no—
512#104—22no—
513#104—22no—
514#104—22no—
515#104—22no—
516#104—1582no—
517#104—1582no—
518#103—791no—
519#103—791no—
520#103—791no—
521#103—791no—
522#102—791no—
523#102—791no—
524#102—791no—
525#102—791no—
526C22⋊C8—1581no—
527C22⋊C8—1581no—
528C22⋊C8—1581no—
529C22⋊C8—1581no—
530#97—21no—
531#97—791no—
532#97—791no—
533#97—791no—
534#97—791no—
535#97—1582no—
536#97—1581no—
537#97—1581no—
538C4×C8—21no—
539C4×C8—1582no—
540C4×C8—1581no—
541C4×C8—1581no—
542#95—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—792no—
552#41—792no—
553#41—1581no—
554#41—1581no—
555C2×Q8—791no—
556C2×Q8C2×C4×D7911yescharacteristic
557C2×Q8C2×C4×D7911yescharacteristic
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—791no—
563C2×D4—1581no—
564C2×D4C2×C4×D7911yescharacteristic
565C2×D4C2×C4×D7911yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—1581no—
571C22×C4—1581no—
572C22×C4—1581no—
573C22×C4#1192962311yescharacteristic
574C22×C4#1192962311yescharacteristic
575C22×C4C23×D7911yescharacteristic
576Q16—1582no—
577Q16—1582no—
578SD16—1582no—
579SD16—1582no—
580SD16—1582no—
581SD16—1582no—
582D8—1582no—
583D8—1582no—
584M16—21no—
585M16—21no—
586M16—3162no—
587M16—3162no—
588M16—1584no—
589M16—1584no—
590M16—1581no—
591M16—1581no—
592M16—1581no—
593M16—1581no—
594M16D4×D7912yes—
595M16#1192962312yes—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—3162no—
599C2×C8—3162no—
600C2×C8—792no—
601C2×C8—792no—
602C2×C8—791no—
603C2×C8—791no—
604C2×C8—791no—
605C2×C8—791no—
606C2×C8—791no—
607C2×C8—791no—
608C2×C8—791no—
609C2×C8—791no—
610C2×C8—1584no—
611C2×C8—1584no—
612C2×C8—1581no—
613C2×C8—1581no—
614C2×C8—1581no—
615C2×C8—1581no—
616C2×C8—1581no—
617C2×C8—1581no—
618C2×C8—1581no—
619C2×C8—1581no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—791no—
624C4⋊C4—791no—
625C4⋊C4—1581no—
626C4⋊C4—1581no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—1581no—
632C22⋊C4—1581no—
633C22⋊C4—1581no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—1581no—
639C42—1581no—
640C42—1581no—
641C42C2×C4×D7911yescharacteristic
642C42C2×C4×D7911yescharacteristic
643C42D4×D7911yescharacteristic
644C42D4×D7911yescharacteristic
645C23—21no—
646C23—21no—
647C23—1581no—
648C23C2×#1192962311yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—792no—
654Q8—1581no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—81no—
664D4—81no—
665D4—792no—
666D4—1582no—
667D4—1582no—
668D4—1581no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—6321no—
684C2×C4—6321no—
685C2×C4—1581no—
686C2×C4—1581no—
687C2×C4—1581no—
688C2×C4—1582no—
689C2×C4—1582no—
690C2×C4(C22⋊D79)⋊C411yescharacteristic
691C2×C4(C22⋊D79)⋊C411yescharacteristic
692C2×C4(C22⋊D79)⋊C411yescharacteristic
693C2×C4(C22⋊D79)⋊C411yescharacteristic
694C2×C4C22×C4×D7911yescharacteristic
695C2×C4C2×D4×D7911yescharacteristic
696C2×C4C2×D4×D7911yescharacteristic
697C2×C4#41×D7911yescharacteristic
698C2×C4#41×D7911yescharacteristic
699C2×C4C2×#1192962311yescharacteristic
700C8—22no—
701C8—22no—
702C8—3161no—
703C8—3161no—
704C8—792no—
705C8—792no—
706C8—1581no—
707C8—1581no—
708C8—1581no—
709C8—1581no—
710C8—1581no—
711C8—1581no—
712C22—21no—
713C22—21no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—3161no—
721C22—3161no—
722C22—1582no—
723C22C2×(C22⋊D79)⋊C411yescharacteristic
724C22#1909909211yescharacteristic
725C22#1909911111yescharacteristic
726C4—21no—
727C4—21no—
728C4—21no—
729C4—21no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4—3161no—
735C4—3161no—
736C4—1582no—
737C4C4×D4×D7911yescharacteristic
738C4C4×#1192962311yescharacteristic
739C4#121×D7911yescharacteristic
740C4#1909907311yescharacteristic
741C2—21no—
742C2—21no—
743C2—81no—
744C2—81no—
745C2—3162no—
746C2#2376591611yescharacteristic
747C2#2377230611yescharacteristic
748C2#2377231311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#1980C2
socleC22×C79C2×C4×D4
prime radical#23772849C2
cosocleC22×C4×C79C24
hypercenter#1980D79
hypocenterC79#21519
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. C2×#19098682C2semidirect
3. C2×#19098677C2semidirect
4. #23772118C2semidirect
5. #23771829C2semidirect
6. #23764175C2semidirect
7. #23764051C2semidirect
8. #23764051C2semidirect
9. #23763724C2semidirect
10. #23763724C2semidirect
11. #23763421C2semidirect
12. #23763275C2semidirect
13. #23763245C2semidirect
14. #23763238C2semidirect
15. C79×#1980C2semidirect
23. #19098782C4semidirect
24. #19098782C4semidirect
25. #19098775C4semidirect
26. #19098775C4semidirect
27. #19098770C4semidirect
28. #19098765C4semidirect
29. #19098760C4semidirect
30. #19098755C4semidirect
85. #14579169D4semidirect
380. #1980D79semidirect
390. C79#21519semidirect

Maximal subgroups

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

subgroupindex
#237728492
C2×#190986822
C2×#190986772
#237721182
#237718292
#237641752
#237640512
#237637242
#237634212
#237632752
#237632452
#237632382
C79×#19802
#2151979