Finite Group Databasebeta

← #34290780

Subgroups — #34290780

Order 20224.

1050 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098610C211yesmaximal, characteristic, complemented
2C2×#104×D79C211yesmaximal, characteristic
3#23771915C211yesmaximal, characteristic
4#23771842C211yesmaximal, characteristic
5#23771816C211yesmaximal, characteristic, complemented
6#23764051C211yesmaximal, characteristic, complemented
7#23764050C211yesmaximal, characteristic, complemented
8#23764049C211yesmaximal, characteristic, complemented
9#23764048C211yesmaximal, characteristic, complemented
10#23764047C211yesmaximal, characteristic, complemented
11#23764046C211yesmaximal, characteristic, complemented
12#23764045C211yesmaximal, characteristic, complemented
13#339×D79C211yesmaximal, characteristic, complemented
14#23763092C211yesmaximal, characteristic, complemented
15C79×#1929C211yesmaximal, characteristic, complemented
16C2×#41×D79C2211yescharacteristic
17C22×#11929607C2211yescharacteristic
18C22×#11929607C2211yescharacteristic
19C2×M16×D79C2211yescharacteristic
20C2×M16×D79C2211yescharacteristic
21#117×D79C2211yescharacteristic
22C2×C42×D79C2211yescharacteristic
23#19098610—24no—
24C2×#14579097C2211yescharacteristic, complemented
25C2×#14579096C2211yescharacteristic, complemented
26C2×#14579096C2211yescharacteristic, complemented
27C2×#14579089C2211yescharacteristic
28C2×#14579088C2211yescharacteristic
29C2×#14579087C2211yescharacteristic
30#104×D79—24no—
31#19098570C411yescharacteristic, complemented
32#19098570C411yescharacteristic, complemented
33#19098566C411yescharacteristic, complemented
34#19098566C411yescharacteristic, complemented
35#19098563C411yescharacteristic, complemented
36#19098563C411yescharacteristic, complemented
37#19098561C411yescharacteristic, complemented
38#19098561C411yescharacteristic, complemented
39#19098560C2211yescharacteristic
40#19098559C2211yescharacteristic
41#19098557C2211yescharacteristic
42#19098531C2211yescharacteristic
43#19098530C2211yescharacteristic
44#19098529C2211yescharacteristic
45#19098528—21no—
46#19098528—21no—
47#19098525—21no—
48#19098525—21no—
49#19098521C2211yescharacteristic, complemented
50#19098520—21no—
51#19098519C2211yescharacteristic, complemented
52#19098518C2211yescharacteristic, complemented
53#19098517—21no—
54#19098515—21no—
55C4×#11929607—21no—
56#19098324C2211yescharacteristic, complemented
57#19098323C2211yescharacteristic, complemented
58#19098322C2211yescharacteristic, complemented
59#19098318C2211yescharacteristic, complemented
60#19098317C2211yescharacteristic, complemented
61#19098317C2211yescharacteristic, complemented
62C2×#108×C79C2211yescharacteristic, complemented
63C2×#104×C79C2211yescharacteristic
64#416×C79C2211yescharacteristic
65#408×C79C2211yescharacteristic
66#405×C79C2211yescharacteristic, complemented
67#339×C79C2211yescharacteristic, complemented
68#336×C79C2211yescharacteristic, complemented
69C2×#11929625C2×C411yescharacteristic
70C2×#11929624—21no—
71C2×#11929624C2311yescharacteristic
72C2×#11929623—21no—
73C2×#11929623C2×C411yescharacteristic
74#41×D79—22no—
75#41×D79—22no—
76#41×D79—22no—
77#41×D79—22no—
78C2×Q8×D79C2×C411yescharacteristic
79C2×D4×D79—21no—
80C2×D4×D79C2×C411yescharacteristic
81C22×C4×D79—21no—
82C22×C4×D79—21no—
83C22×C4×D79C2311yescharacteristic
84C2×#11929608C2311yescharacteristic
85C2×#11929608C2311yescharacteristic
86C2×#11929607—21no—
87C2×#11929607—22no—
88C2×#11929607—22no—
89C2×#11929607—22no—
90C2×#11929607—22no—
91C2×#11929607—21no—
92C2×#11929607C2×C411yescharacteristic
93C2×#11929607C2×C411yescharacteristic
94C2×#11929607C2×C411yescharacteristic
95C2×#11929607C2×C411yescharacteristic
96C2×#11929607D411yescharacteristic
97C2×#11929607D411yescharacteristic
98C2×#11929607D411yescharacteristic
99C2×#11929607D411yescharacteristic
100M16×D79—22no—
101M16×D79—22no—
102M16×D79—22no—
103M16×D79D414yes—
104C22×C79⋊C8C2311yescharacteristic
105C22×C79⋊C8C2311yescharacteristic
106C2×C8×D79—21no—
107C2×C8×D79—21no—
108#14579120C2311yescharacteristic
109#14579119C2×C411yescharacteristic
110#14579119C2×C411yescharacteristic
111#14579118—21no—
112#14579117—21no—
113C4⋊C4×D79C2×C411yescharacteristic
114C4⋊C4×D79C2×C411yescharacteristic
115C22⋊C4×D79—21no—
116C2×C4×Dic79—21no—
117C2×C4×Dic79C2311yescharacteristic
118C42×D79—21no—
119C42×D79—22no—
120C42×D79—22no—
121#14579097—22no—
122#14579096—22no—
123#14579096—22no—
124#14579089—22no—
125#14579088—22no—
126#14579087—22no—
127#14579086C2×C411yescharacteristic, complemented
128#14579086C2×C411yescharacteristic, complemented
129#14579085C2×C411yescharacteristic, complemented
130#14579085C2×C411yescharacteristic, complemented
131#14579084C2×C411yescharacteristic, complemented
132#14579084C2×C411yescharacteristic, complemented
133#14579083C2×C411yescharacteristic, complemented
134#14579083C2×C411yescharacteristic, complemented
135#14579082C2×C411yescharacteristic, complemented
136#14579082C2×C411yescharacteristic, complemented
137#14579081C2×C411yescharacteristic, complemented
138#14579081C2×C411yescharacteristic, complemented
139C22⋊(C79⋊C8)—21no—
140C22⋊(C79⋊C8)—21no—
141(C2×D79)⋊C8—21no—
142(C2×D79)⋊C8—21no—
143(C2×D79)⋊C8—21no—
144(C2×D79)⋊C8—21no—
145#14579072—21no—
146#14579071—21no—
147#14579071—21no—
148C4×C79⋊C8—21no—
149C8×Dic79—21no—
150C8×Dic79—21no—
151C2×#41×C79C2311yescharacteristic
152C2×M16×C79C2311yescharacteristic
153C2×M16×C79C2311yescharacteristic
154C22×C8×C79C2311yescharacteristic
155C22×C8×C79C2311yescharacteristic
156#117×C79C2311yescharacteristic
157C2×C42×C79C2311yescharacteristic
158#108×C79—22no—
159#104×C79—22no—
160#103×C79C2×C411yescharacteristic, complemented
161#103×C79C2×C411yescharacteristic, complemented
162#102×C79C2×C411yescharacteristic, complemented
163#102×C79C2×C411yescharacteristic, complemented
164C22⋊C8×C79—21no—
165C22⋊C8×C79—21no—
166#97×C79—21no—
167C4×C8×C79—21no—
168C23×D79—21no—
169C23×D79#4111yescharacteristic
170#11929625—22no—
171#11929625—22no—
172#11929624—21no—
173#11929624—21no—
174#11929624—21no—
175#11929624—21no—
176#11929624—42no—
177#11929624—42no—
178#11929623—22no—
179#11929623—22no—
180#11929623—42no—
181#11929623—42no—
182C2×Dic158—21no—
183C2×Dic158C22×C411yescharacteristic
184Q8×D79—22no—
185Q8×D79—22no—
186C2×D316—21no—
187C2×D316C22×C411yescharacteristic
188C2×C22⋊D79—21no—
189C2×C22⋊D79—21no—
190C2×C22⋊D79—21no—
191D4×D79—22no—
192D4×D79—22no—
193D4×D79—42no—
194D4×D79—42no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79#4111yescharacteristic
198C2×C4×D79—21no—
199C2×C4×D79—21no—
200C2×C4×D79—21no—
201C2×C4×D79—21no—
202C2×C4×D79—21no—
203C2×C4×D79—42no—
204C2×C4×D79—42no—
205C2×C4×D79—42no—
206C2×C4×D79—42no—
207C2×C4×D79—42no—
208C2×C4×D79C22×C411yescharacteristic
209C2×C4×D79C22×C411yescharacteristic
210C2×C4×D79C2×D411yescharacteristic
211C2×C4×D79C2×D411yescharacteristic
212C2×C4×D79C2×D412yes—
213C2×C4×D79#4112yes—
214C2×C4×D79#4112yes—
215C2×C4×D79#4112yes—
216#11929608—21no—
217#11929608—21no—
218#11929608—21no—
219#11929608C2×D412yes—
220#11929607—22no—
221#11929607—22no—
222#11929607—22no—
223#11929607—22no—
224#11929607—24no—
225#11929607—22no—
226#11929607—22no—
227#11929607—22no—
228#11929607—22no—
229#11929607—42no—
230C2×C79⋊C8—21no—
231C2×C79⋊C8—21no—
232C2×C79⋊C8—21no—
233C2×C79⋊C8—21no—
234C2×C79⋊C8—21no—
235C2×C79⋊C8—21no—
236C2×C79⋊C8C22×C411yescharacteristic
237C2×C79⋊C8C22×C411yescharacteristic
238C2×C79⋊C8C2×D411yescharacteristic
239C2×C79⋊C8C2×D411yescharacteristic
240C8×D79—24no—
241C8×D79—42no—
242C4⋊Dic79C22×C411yescharacteristic
243C4⋊Dic79C22×C411yescharacteristic
244Dic79⋊C4—21no—
245Dic79⋊C4—21no—
246C22⋊Dic79—21no—
247(C2×D79)⋊C4—21no—
248(C2×D79)⋊C4—21no—
249C4×Dic79—21no—
250C4×Dic79—21no—
251C4×Dic79—21no—
252C4×Dic79—21no—
253C4×Dic79—21no—
254C4×Dic79—42no—
255#41×C79—21no—
256#41×C79—21no—
257#41×C79—21no—
258#41×C79—21no—
259C2×Q8×C79C22×C411yescharacteristic
260C2×D4×C79—21no—
261C2×D4×C79C22×C411yescharacteristic
262C22×C4×C79—21no—
263C22×C4×C79—21no—
264C22×C4×C79C2411yescharacteristic
265M16×C79—21no—
266M16×C79—21no—
267M16×C79—21no—
268M16×C79C2×D412yes—
269C2×C8×C79—21no—
270C2×C8×C79—21no—
271C2×C8×C79—21no—
272C2×C8×C79—21no—
273C2×C8×C79—21no—
274C2×C8×C79—21no—
275C2×C8×C79C22×C411yescharacteristic
276C2×C8×C79C22×C411yescharacteristic
277C2×C8×C79C2×D411yescharacteristic
278C2×C8×C79C2×D411yescharacteristic
279C4⋊C4×C79C22×C411yescharacteristic
280C4⋊C4×C79C22×C411yescharacteristic
281C22⋊C4×C79—21no—
282C42×C79—21no—
283C42×C79—21no—
284C42×C79—21no—
285C23×C79—21no—
286C23×C79C2×#4111yescharacteristic
287C22×D79—21no—
288C22×D79—41no—
289C22×D79—41no—
290C22×D79—42no—
291C22×D79—81no—
292C22×D79—81no—
293C22×D79C4×D411yescharacteristic
294C22×D79C4×D411yescharacteristic
295C22×D79#12412yes—
296C22×D79#12612yes—
297Q8×C79—21no—
298Q8×C79—21no—
299D4×C79—21no—
300D4×C79—21no—
301D4×C79—41no—
302D4×C79—41no—
303C2×C4×C79—22no—
304C2×C4×C79—21no—
305C2×C4×C79—21no—
306C2×C4×C79—21no—
307C2×C4×C79—41no—
308C2×C4×C79—41no—
309C2×C4×C79—41no—
310C2×C4×C79—41no—
311C2×C4×C79C23×C411yescharacteristic
312C2×C4×C79C22×D411yescharacteristic
313C2×C4×C79C22×D411yescharacteristic
314C2×C4×C79C2×#4111yescharacteristic
315C2×C4×C79C2×#4111yescharacteristic
316C2×C4×C79C2×#4111yescharacteristic
317C22⋊D79—41no—
318C22⋊D79—41no—
319C22⋊D79—42no—
320C22⋊D79—42no—
321C2×Dic79—22no—
322C2×Dic79—21no—
323C2×Dic79—21no—
324C2×Dic79—21no—
325C2×Dic79—41no—
326C2×Dic79—41no—
327C2×Dic79—42no—
328C2×Dic79C4×D411yescharacteristic
329C2×Dic79C4×D411yescharacteristic
330C2×Dic79#12412yes—
331C2×Dic79#12612yes—
332D316—21no—
333D316—21no—
334D316—42no—
335C4×D79—48no—
336C4×D79—42no—
337C4×D79—41no—
338C4×D79—41no—
339C4×D79—42no—
340C4×D79—81no—
341C4×D79—81no—
342C4×D79#11712yes—
343C4×D79#11712yes—
344C4×D79C4×D412yes—
345C4×D79C4×D412yes—
346C4×D79#12112yes—
347C4×D79#12112yes—
348C4×D79#12312yes—
349C4×D79#12312yes—
350Dic158—21no—
351Dic158—21no—
352Dic158—42no—
353C8×C79—21no—
354C8×C79—21no—
355C8×C79—22no—
356C8×C79—21no—
357C8×C79—21no—
358C8×C79—41no—
359C79⋊C8—21no—
360C79⋊C8—21no—
361C79⋊C8—22no—
362C79⋊C8—21no—
363C79⋊C8—21no—
364C79⋊C8—41no—
365C22×C79—21no—
366C22×C79—21no—
367C22×C79—41no—
368C22×C79—41no—
369C22×C79—41no—
370C22×C79C2×C4×D411yescharacteristic
371C22×C79C2×#12411yescharacteristic
372C22×C79C2×#12611yescharacteristic
373C2×D79—21no—
374C2×D79—21no—
375C2×D79—21no—
376C2×D79—21no—
377C2×D79—42no—
378C2×D79—42no—
379C2×D79—41no—
380C2×D79—41no—
381C2×D79—41no—
382C2×D79—84no—
383C2×D79#38812yes—
384C2×D79#38812yes—
385C4×C79—42no—
386C4×C79—41no—
387C4×C79—41no—
388C4×C79—41no—
389C4×C79C2×#11711yescharacteristic
390C4×C79C2×C4×D411yescharacteristic
391C4×C79C2×#12111yescharacteristic
392C4×C79C2×#12311yescharacteristic
393Dic79—42no—
394Dic79—41no—
395Dic79—41no—
396Dic79—41no—
397Dic79#38812yes—
398Dic79#38812yes—
399#21071—791nomaximal, Sylow
400C2×C79—21no—
401C2×C79—21no—
402C2×C79—81no—
403C2×C79C2×#38811yescharacteristic
404C2×C79#295611yescharacteristic
405C2×C79#295611yescharacteristic
406D79—22no—
407D79—22no—
408D79—81no—
409C2×#430—791no—
410C22×#104—791no—
411#2896—791no—
412#2879—791no—
413#2873—791no—
414#1929—791no—
415#1929—791no—
416#1929—791no—
417#1929—791no—
418#1929—791no—
419#1929—791no—
420#1929—791no—
421#1929D7911yescharacteristic, complemented
422C2×#339—791no—
423#1728—791no—
424C79#2107111yescharacteristic, complemented, Sylow
425C22×#41—791no—
426C22×M16—791no—
427C22×M16—791no—
428C22×M16—791no—
429C22×M16—791no—
430C2×#117—791no—
431C22×C42—791no—
432#430—1584no—
433C2×#108—791no—
434C2×#108—791no—
435C2×#108—791no—
436C2×#108C2×D7911yescharacteristic, complemented
437C2×#104—791no—
438C2×#104—791no—
439C2×#104—791no—
440C2×#104—1584no—
441C2×#104C2×D7911yescharacteristic
442#419—791no—
443#419—791no—
444#418—791no—
445#418—791no—
446#417—791no—
447#417—791no—
448#417—791no—
449#417—791no—
450#416—791no—
451#416—791no—
452#416—791no—
453#416C2×D7911yescharacteristic
454#408—791no—
455#408—791no—
456#408—791no—
457#408—1581no—
458#408—1581no—
459#408C2×D7911yescharacteristic
460#407—1581no—
461#407—1581no—
462#405—791no—
463#405—791no—
464#405—791no—
465#405—1581no—
466#405—1581no—
467#405C2×D7911yescharacteristic, complemented
468C4×M16—1581no—
469C4×M16—1581no—
470#339—791no—
471#339—791no—
472#339—791no—
473#339C2×D7911yescharacteristic, complemented
474#336—791no—
475#336—791no—
476#336—791no—
477#336C2×D7911yescharacteristic, complemented
478C2×#41—791no—
479C2×#41—791no—
480C2×#41—791no—
481C2×#41—1581no—
482C2×#41—1582no—
483C2×#41—1582no—
484C2×#41—1582no—
485C2×#41—1582no—
486C2×#41—1581no—
487C2×#41C22×D7911yescharacteristic
488C22×Q8—791no—
489C22×D4—791no—
490C22×D4—1581no—
491C23×C4—791no—
492C23×C4—1581no—
493C23×C4—1581no—
494C2×M16—791no—
495C2×M16—791no—
496C2×M16—791no—
497C2×M16—791no—
498C2×M16—791no—
499C2×M16—791no—
500C2×M16—791no—
501C2×M16—791no—
502C2×M16—791no—
503C2×M16—794no—
504C2×M16—791no—
505C2×M16—1581no—
506C2×M16—1581no—
507C2×M16—1582no—
508C2×M16—1582no—
509C2×M16—1582no—
510C2×M16—1582no—
511C2×M16—1582no—
512C2×M16—1582no—
513C2×M16—1582no—
514C2×M16C22×D7911yescharacteristic
515C2×M16C22×D7911yescharacteristic
516C22×C8—791no—
517C22×C8—791no—
518C22×C8—1581no—
519C22×C8—1581no—
520C22×C8C22×D7911yescharacteristic
521C22×C8C22×D7911yescharacteristic
522#117—791no—
523#117—791no—
524#117—791no—
525#117—1581no—
526#117—1581no—
527#117C22×D7911yescharacteristic
528C2×C4⋊C4—791no—
529C2×C4⋊C4—791no—
530C2×C22⋊C4—1581no—
531C2×C42—791no—
532C2×C42—1582no—
533C2×C42—1582no—
534C2×C42—1581no—
535C2×C42—1581no—
536C2×C42C22×D7911yescharacteristic
537#108—22no—
538#108—1582no—
539#108—1582no—
540#108—1582no—
541#104—22no—
542#104—1582no—
543#104—1582no—
544#104—1582no—
545#103—791no—
546#103—791no—
547#103—791no—
548#103—791no—
549#103—791no—
550#103—791no—
551#103C4×D7911yescharacteristic, complemented
552#103C4×D7911yescharacteristic, complemented
553#102—791no—
554#102—791no—
555#102—791no—
556#102—791no—
557#102—791no—
558#102—791no—
559#102C4×D7911yescharacteristic, complemented
560#102C4×D7911yescharacteristic, complemented
561C22⋊C8—21no—
562C22⋊C8—21no—
563C22⋊C8—1581no—
564C22⋊C8—1581no—
565C22⋊C8—1581no—
566C22⋊C8—1581no—
567C22⋊C8—1581no—
568C22⋊C8—1581no—
569#97—21no—
570#97—1581no—
571#97—1581no—
572#97—1581no—
573C4×C8—21no—
574C4×C8—1581no—
575C4×C8—1581no—
576C4×C8—1581no—
577C24—791no—
578C24—1581no—
579#41—21no—
580#41—21no—
581#41—21no—
582#41—21no—
583#41—3162no—
584#41—3162no—
585#41—3162no—
586#41—3162no—
587#41—1582no—
588#41—1582no—
589#41—1582no—
590#41—1582no—
591#41—1581no—
592#41—1581no—
593#41—1581no—
594#41—1581no—
595C2×Q8—791no—
596C2×Q8—1581no—
597C2×Q8—1582no—
598C2×Q8—1582no—
599C2×Q8C2×C4×D7911yescharacteristic
600C2×D4—21no—
601C2×D4—3162no—
602C2×D4—3162no—
603C2×D4—791no—
604C2×D4—1581no—
605C2×D4—1582no—
606C2×D4—1582no—
607C2×D4—1581no—
608C2×D4—1581no—
609C2×D4—1581no—
610C2×D4C2×C4×D7911yescharacteristic
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—3162no—
614C22×C4—3162no—
615C22×C4—3162no—
616C22×C4—3162no—
617C22×C4—3162no—
618C22×C4—791no—
619C22×C4—792no—
620C22×C4—792no—
621C22×C4—792no—
622C22×C4—791no—
623C22×C4—791no—
624C22×C4—792no—
625C22×C4—791no—
626C22×C4—791no—
627C22×C4—1581no—
628C22×C4—1581no—
629C22×C4—1581no—
630C22×C4—1581no—
631C22×C4—1581no—
632C22×C4—1581no—
633C22×C4—1581no—
634C22×C4C23×D7911yescharacteristic
635M16—21no—
636M16—21no—
637M16—21no—
638M16—3162no—
639M16—792no—
640M16—1582no—
641M16—1582no—
642M16—1582no—
643M16—1582no—
644M16—1584no—
645M16—1582no—
646M16—1582no—
647M16—1582no—
648M16—1582no—
649M16—1581no—
650M16—1581no—
651M16—1581no—
652M16D4×D7912yes—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—3162no—
660C2×C8—791no—
661C2×C8—791no—
662C2×C8—791no—
663C2×C8—791no—
664C2×C8—1584no—
665C2×C8—1581no—
666C2×C8—1581no—
667C2×C8—1581no—
668C2×C8—1581no—
669C2×C8—1581no—
670C2×C8—1581no—
671C2×C8C2×C4×D7911yescharacteristic
672C2×C8C2×C4×D7911yescharacteristic
673C2×C8D4×D7911yescharacteristic
674C2×C8D4×D7911yescharacteristic
675C4⋊C4—791no—
676C4⋊C4—791no—
677C4⋊C4—1581no—
678C4⋊C4—1581no—
679C4⋊C4C2×C4×D7911yescharacteristic
680C4⋊C4C2×C4×D7911yescharacteristic
681C22⋊C4—21no—
682C22⋊C4—1581no—
683C22⋊C4—1581no—
684C22⋊C4—1581no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—3162no—
689C42—1581no—
690C42—1581no—
691C42—1581no—
692C42—1581no—
693C42—1581no—
694C23—21no—
695C23—3161no—
696C23—3161no—
697C23—3162no—
698C23—792no—
699C23—792no—
700C23—791no—
701C23—791no—
702C23—6321no—
703C23—6321no—
704C23—1581no—
705C23#41×D7911yescharacteristic
706Q8—21no—
707Q8—21no—
708Q8—3162no—
709Q8—1581no—
710Q8—1581no—
711D4—21no—
712D4—21no—
713D4—41no—
714D4—41no—
715D4—3162no—
716D4—3162no—
717D4—3161no—
718D4—3161no—
719D4—3162no—
720D4—1581no—
721D4—1581no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—3168no—
731C2×C4—3162no—
732C2×C4—3162no—
733C2×C4—3161no—
734C2×C4—3161no—
735C2×C4—3162no—
736C2×C4—3161no—
737C2×C4—3161no—
738C2×C4—791no—
739C2×C4—791no—
740C2×C4—792no—
741C2×C4—792no—
742C2×C4—792no—
743C2×C4—792no—
744C2×C4—792no—
745C2×C4—792no—
746C2×C4—792no—
747C2×C4—792no—
748C2×C4—792no—
749C2×C4—792no—
750C2×C4—6321no—
751C2×C4—6321no—
752C2×C4—1582no—
753C2×C4—1581no—
754C2×C4—1581no—
755C2×C4—1581no—
756C2×C4C22×C4×D7911yescharacteristic
757C2×C4C2×D4×D7911yescharacteristic
758C2×C4C2×D4×D7911yescharacteristic
759C2×C4#41×D7911yescharacteristic
760C2×C4#41×D7911yescharacteristic
761C2×C4#41×D7911yescharacteristic
762C8—21no—
763C8—21no—
764C8—22no—
765C8—21no—
766C8—21no—
767C8—41no—
768C8—3161no—
769C8—1581no—
770C8—1581no—
771C8—1582no—
772C8—1581no—
773C8—1581no—
774C22—21no—
775C22—21no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—3162no—
780C22—3162no—
781C22—3161no—
782C22—3161no—
783C22—3161no—
784C22—792no—
785C22—792no—
786C22—6324no—
787C22—1581no—
788C22—1581no—
789C22—1581no—
790C22—1581no—
791C22C4×D4×D7911yescharacteristic
792C22#124×D7911yescharacteristic
793C22#126×D7911yescharacteristic
794C4—42no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—3162no—
799C4—3161no—
800C4—3161no—
801C4—3161no—
802C4—792no—
803C4—792no—
804C4#117×D7911yescharacteristic
805C4C4×D4×D7911yescharacteristic
806C4#121×D7911yescharacteristic
807C4#123×D7911yescharacteristic
808C2—21no—
809C2—21no—
810C2—81no—
811C2—6321no—
812C2—1582no—
813C2—1582no—
814C2#388×D7911yescharacteristic
815C2#2377230511yescharacteristic
816C2#2377230811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#1929C2
socleC22×C79C2×C4×D4
prime radicalC2×#41×D79C22
cosocleC22×C4×C79C24
hypercenter#1929D79
hypocenterC79#21071
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
1. C2×#19098610C2semidirect
5. #23771816C2semidirect
6. #23764051C2semidirect
7. #23764050C2semidirect
8. #23764049C2semidirect
9. #23764048C2semidirect
10. #23764047C2semidirect
11. #23764046C2semidirect
12. #23764045C2semidirect
13. #339×D79C2semidirect
14. #23763092C2semidirect
15. C79×#1929C2semidirect
24. C2×#14579097C22semidirect
25. C2×#14579096C22semidirect
26. C2×#14579096C22semidirect
31. #19098570C4semidirect
32. #19098570C4semidirect
33. #19098566C4semidirect
34. #19098566C4semidirect
35. #19098563C4semidirect
36. #19098563C4semidirect
37. #19098561C4semidirect
38. #19098561C4semidirect
49. #19098521C22semidirect
51. #19098519C22semidirect
52. #19098518C22semidirect
56. #19098324C22semidirect
57. #19098323C22semidirect
58. #19098322C22semidirect
59. #19098318C22semidirect
60. #19098317C22semidirect
61. #19098317C22semidirect
62. C2×#108×C79C22semidirect
66. #405×C79C22semidirect
67. #339×C79C22semidirect
68. #336×C79C22semidirect
127. #14579086C2×C4semidirect
128. #14579086C2×C4semidirect
129. #14579085C2×C4semidirect
130. #14579085C2×C4semidirect
131. #14579084C2×C4semidirect
132. #14579084C2×C4semidirect
133. #14579083C2×C4semidirect
134. #14579083C2×C4semidirect
135. #14579082C2×C4semidirect
136. #14579082C2×C4semidirect
137. #14579081C2×C4semidirect
138. #14579081C2×C4semidirect
160. #103×C79C2×C4semidirect
161. #103×C79C2×C4semidirect
162. #102×C79C2×C4semidirect
163. #102×C79C2×C4semidirect
421. #1929D79semidirect
424. C79#21071semidirect
436. C2×#108C2×D79semidirect
467. #405C2×D79semidirect
473. #339C2×D79semidirect
477. #336C2×D79semidirect
551. #103C4×D79semidirect
552. #103C4×D79semidirect
559. #102C4×D79semidirect
560. #102C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190986102
C2×#104×D792
#237719152
#237718422
#237718162
#237640512
#237640502
#237640492
#237640482
#237640472
#237640462
#237640452
#339×D792
#237630922
C79×#19292
#2107179