Finite Group Databasebeta

← #34298521

Subgroups — #34298521

Order 20224.

1030 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098531C211yesmaximal, characteristic
2C2×#19098528C211yesmaximal, characteristic
3#23765886C211yesmaximal, characteristic
4#23763584C211yesmaximal, characteristic, complemented
5#23763584C211yesmaximal, characteristic, complemented
6#23763583C211yesmaximal, characteristic, complemented
7#23763580C211yesmaximal, characteristic, complemented
8#23763577C211yesmaximal, characteristic, complemented
9#23763576C211yesmaximal, characteristic, complemented
10#23763576C211yesmaximal, characteristic, complemented
11#23763383C211yesmaximal, characteristic, complemented
12#23763381C211yesmaximal, characteristic, complemented
13#23763379C211yesmaximal, characteristic, complemented
14#23763377C211yesmaximal, characteristic, complemented
15C79×#1851C211yesmaximal, characteristic, complemented
16C22×#11929624C2211yescharacteristic
17C22×#11929607C2211yescharacteristic
18C23×C79⋊C8C2211yescharacteristic
19C22×C8×D79C2211yescharacteristic
20C2×#14579118C2211yescharacteristic
21C2×C42×D79C2211yescharacteristic
22C2×C4⋊(C79⋊C8)C2211yescharacteristic
23C2×C4⋊(C79⋊C8)C2211yescharacteristic
24C2×Dic79⋊C8C2211yescharacteristic
25C2×Dic79⋊C8C2211yescharacteristic
26C2×Dic79⋊C8C2211yescharacteristic
27C2×Dic79⋊C8C2211yescharacteristic
28#19098531—24no—
29#19098528—24no—
30C2×C22⋊(C79⋊C8)C2211yescharacteristic
31C2×(C2×D79)⋊C8C2211yescharacteristic
32C2×(C2×D79)⋊C8C2211yescharacteristic
33C2×(C2×D79)⋊C8C2211yescharacteristic
34C2×(C2×D79)⋊C8C2211yescharacteristic
35C2×(C2×D79)⋊C8C2211yescharacteristic
36C2×(C2×D79)⋊C8C2211yescharacteristic
37#19098467C411yescharacteristic
38#19098467C411yescharacteristic
39#19098463C411yescharacteristic
40#19098463C411yescharacteristic
41#19098441C411yescharacteristic
42#19098441C411yescharacteristic
43#19098439C411yescharacteristic
44#19098439C411yescharacteristic
45C4×(C2×D79)⋊C4C2211yescharacteristic
46C4×(C2×D79)⋊C4C2211yescharacteristic
47C4×C22⋊Dic79C2211yescharacteristic
48#19098318C2211yescharacteristic
49#19098318C2211yescharacteristic
50#19098317C2211yescharacteristic
51#19098317C2211yescharacteristic
52#19098317C2211yescharacteristic
53#19098317C2211yescharacteristic
54C22×M16×C79C2211yescharacteristic
55C2×C4⋊C8×C79C2211yescharacteristic
56C2×C4⋊C8×C79C2211yescharacteristic
57C2×C22⋊C8×C79C2211yescharacteristic
58C4×C22⋊C4×C79C2211yescharacteristic
59#336×C79C2211yescharacteristic
60#336×C79C2211yescharacteristic
61C2×#11929624—41no—
62C2×#11929624—41no—
63C2×#11929624—41no—
64C2×#11929624—41no—
65C2×#11929624D414yes—
66C2×#11929624Q814yes—
67C22×Dic158C2×C411yescharacteristic
68C22×D316C2×C411yescharacteristic
69C22×C22⋊D79C2×C411yescharacteristic
70C22×C22⋊D79C2×C411yescharacteristic
71C22×C4×D79C2×C411yescharacteristic
72C22×C4×D79C2×C411yescharacteristic
73C22×C4×D79C2311yescharacteristic
74C22×C4×D79C2311yescharacteristic
75C2×#11929607—22no—
76C2×#11929607—41no—
77C2×#11929607—41no—
78C22×C79⋊C8—22no—
79C22×C79⋊C8—41no—
80C22×C79⋊C8—41no—
81C22×C79⋊C8C2311yescharacteristic
82C22×C79⋊C8C2311yescharacteristic
83C22×C79⋊C8C2311yescharacteristic
84C22×C79⋊C8C2311yescharacteristic
85C2×C8×D79—22no—
86C2×C8×D79—41no—
87C2×C8×D79—41no—
88#14579118—41no—
89#14579118—41no—
90C2×Dic79⋊C4C2×C411yescharacteristic
91C2×Dic79⋊C4C2×C411yescharacteristic
92C2×C22⋊Dic79C2×C411yescharacteristic
93C2×C22⋊Dic79C2×C411yescharacteristic
94C2×(C2×D79)⋊C4C2×C411yescharacteristic
95C2×(C2×D79)⋊C4C2×C411yescharacteristic
96C2×(C2×D79)⋊C4C2×C411yescharacteristic
97C2×(C2×D79)⋊C4C2×C411yescharacteristic
98C2×(C2×D79)⋊C4C2×C411yescharacteristic
99C2×(C2×D79)⋊C4C2×C411yescharacteristic
100C2×C4×Dic79C2×C411yescharacteristic
101C2×C4×Dic79C2×C411yescharacteristic
102C2×C4×Dic79C2311yescharacteristic
103C2×C4×Dic79C2311yescharacteristic
104C42×D79—41no—
105C42×D79—41no—
106C4⋊(C79⋊C8)—41no—
107C4⋊(C79⋊C8)—41no—
108Dic79⋊C8—41no—
109Dic79⋊C8—41no—
110Dic79⋊C8—41no—
111Dic79⋊C8—41no—
112C22⋊(C79⋊C8)—22no—
113(C2×D79)⋊C8—22no—
114(C2×D79)⋊C8—22no—
115(C2×D79)⋊C8—22no—
116(C2×D79)⋊C8—22no—
117(C2×D79)⋊C8—22no—
118(C2×D79)⋊C8—22no—
119C79⋊#95C2×C411yescharacteristic
120C79⋊#95C2×C411yescharacteristic
121C79⋊#95C2×C411yescharacteristic
122C79⋊#95C2×C411yescharacteristic
123C79⋊#95C2×C411yescharacteristic
124C79⋊#95C2×C411yescharacteristic
125C23×C4×C79C2311yescharacteristic
126C2×M16×C79—22no—
127C2×M16×C79—41no—
128C2×M16×C79—41no—
129C22×C8×C79C2311yescharacteristic
130C22×C8×C79C2311yescharacteristic
131C22×C8×C79C2311yescharacteristic
132C22×C8×C79C2311yescharacteristic
133C2×C22⋊C4×C79C2×C411yescharacteristic
134C2×C22⋊C4×C79C2×C411yescharacteristic
135C2×C42×C79C2311yescharacteristic
136C2×C42×C79C2311yescharacteristic
137C4⋊C8×C79—41no—
138C4⋊C8×C79—41no—
139C22⋊C8×C79—22no—
140#95×C79C2×C411yescharacteristic
141#95×C79C2×C411yescharacteristic
142C23×D79C22×C411yescharacteristic
143C23×D79C22×C411yescharacteristic
144#11929624—44no—
145#11929624—44no—
146#11929624—44no—
147#11929624—44no—
148C2×Dic158—41no—
149C2×Dic158—41no—
150C2×Dic158C4⋊C414yes—
151C2×D316—41no—
152C2×D316—41no—
153C2×D316C4⋊C414yes—
154C2×C22⋊D79—41no—
155C2×C22⋊D79—41no—
156C2×C22⋊D79—41no—
157C2×C22⋊D79—41no—
158C2×C22⋊D79C4⋊C414yes—
159C2×C22⋊D79C4⋊C414yes—
160C22×Dic79C22×C411yescharacteristic
161C22×Dic79C22×C411yescharacteristic
162C22×Dic79C22×C411yescharacteristic
163C22×Dic79C22×C411yescharacteristic
164C22×Dic79C22×C411yescharacteristic
165C22×Dic79C22×C411yescharacteristic
166C2×C4×D79—22no—
167C2×C4×D79—22no—
168C2×C4×D79—21no—
169C2×C4×D79—21no—
170C2×C4×D79—21no—
171C2×C4×D79—21no—
172C2×C4×D79—21no—
173C2×C4×D79—21no—
174C2×C4×D79—21no—
175C2×C4×D79—21no—
176C2×C4×D79—41no—
177C2×C4×D79—41no—
178C2×C4×D79—41no—
179C2×C4×D79—41no—
180C2×C4×D79C2×D412yes—
181C2×C4×D79C2×D412yes—
182C2×C4×D79C2×Q812yes—
183C2×C4×D79C2×Q812yes—
184#11929607—44no—
185C2×C79⋊C8—21no—
186C2×C79⋊C8—21no—
187C2×C79⋊C8—21no—
188C2×C79⋊C8—21no—
189C2×C79⋊C8—21no—
190C2×C79⋊C8—21no—
191C2×C79⋊C8—21no—
192C2×C79⋊C8—21no—
193C2×C79⋊C8—21no—
194C2×C79⋊C8—21no—
195C2×C79⋊C8—21no—
196C2×C79⋊C8—21no—
197C2×C79⋊C8—44no—
198C8×D79—44no—
199Dic79⋊C4—41no—
200Dic79⋊C4—41no—
201C22⋊Dic79—22no—
202C22⋊Dic79—41no—
203(C2×D79)⋊C4—22no—
204(C2×D79)⋊C4—22no—
205(C2×D79)⋊C4—41no—
206(C2×D79)⋊C4—41no—
207(C2×D79)⋊C4—41no—
208(C2×D79)⋊C4—41no—
209C4×Dic79—21no—
210C4×Dic79—21no—
211C4×Dic79—21no—
212C4×Dic79—21no—
213C4×Dic79—41no—
214C4×Dic79—41no—
215C24×C79C22×C411yescharacteristic
216C22×C4×C79—21no—
217C22×C4×C79—21no—
218C22×C4×C79—21no—
219C22×C4×C79—21no—
220C22×C4×C79C22×C411yescharacteristic
221C22×C4×C79C22×C411yescharacteristic
222C22×C4×C79C22×C411yescharacteristic
223C22×C4×C79C22×C411yescharacteristic
224C22×C4×C79C22×C411yescharacteristic
225C22×C4×C79C2×D412yes—
226C22×C4×C79C2×Q812yes—
227C22×C4×C79C2411yescharacteristic
228M16×C79—44no—
229C2×C8×C79—21no—
230C2×C8×C79—21no—
231C2×C8×C79—21no—
232C2×C8×C79—21no—
233C2×C8×C79—21no—
234C2×C8×C79—21no—
235C2×C8×C79—21no—
236C2×C8×C79—21no—
237C2×C8×C79—21no—
238C2×C8×C79—21no—
239C2×C8×C79—21no—
240C2×C8×C79—21no—
241C22⋊C4×C79—22no—
242C22⋊C4×C79—41no—
243C42×C79—21no—
244C42×C79—21no—
245C42×C79—21no—
246C42×C79—21no—
247C23×C79—21no—
248C23×C79—21no—
249C23×C79—21no—
250C23×C79—21no—
251C23×C79—21no—
252C23×C79—21no—
253C23×C79C2×C4⋊C412yes—
254C23×C79C23×C411yescharacteristic
255C22×D79—21no—
256C22×D79—21no—
257C22×D79—21no—
258C22×D79—21no—
259C22×D79—21no—
260C22×D79—21no—
261C22×D79—21no—
262C22×D79—21no—
263C22×D79—21no—
264C22×D79—21no—
265C22×D79—21no—
266C22×D79—21no—
267C22×D79C2×C4⋊C412yes—
268C22×D79C2×C4⋊C412yes—
269C2×C4×C79—21no—
270C2×C4×C79—21no—
271C2×C4×C79—21no—
272C2×C4×C79—21no—
273C2×C4×C79—22no—
274C2×C4×C79—22no—
275C2×C4×C79—22no—
276C2×C4×C79—22no—
277C2×C4×C79—21no—
278C2×C4×C79—21no—
279C2×C4×C79—21no—
280C2×C4×C79—21no—
281C2×C4×C79—21no—
282C2×C4×C79—21no—
283C2×C4×C79—21no—
284C2×C4×C79—21no—
285C2×C4×C79—21no—
286C2×C4×C79C2×C4⋊C412yes—
287C2×C4×C79#13112yes—
288C2×C4×C79C22×D411yescharacteristic
289C2×C4×C79C22×Q811yescharacteristic
290C2×C4×C79H(5,𝔽2)11yescharacteristic
291C2×C4×C79H(5,𝔽2)11yescharacteristic
292C2×C4×C79H(5,𝔽2)11yescharacteristic
293C2×C4×C79H(5,𝔽2)11yescharacteristic
294C22⋊D79—44no—
295C22⋊D79—44no—
296C2×Dic79—21no—
297C2×Dic79—21no—
298C2×Dic79—21no—
299C2×Dic79—21no—
300C2×Dic79—21no—
301C2×Dic79—21no—
302C2×Dic79—21no—
303C2×Dic79—21no—
304C2×Dic79—21no—
305C2×Dic79—21no—
306C2×Dic79—21no—
307C2×Dic79—21no—
308C2×Dic79—21no—
309C2×Dic79—21no—
310C2×Dic79—21no—
311C2×Dic79C2×C4⋊C412yes—
312C2×Dic79C2×C4⋊C412yes—
313C2×Dic79#13112yes—
314D316—44no—
315C4×D79—22no—
316C4×D79—22no—
317C4×D79—22no—
318C4×D79—22no—
319C4×D79—22no—
320C4×D79—22no—
321C4×D79—22no—
322C4×D79—22no—
323C4×D79—44no—
324C4×D79—44no—
325Dic158—44no—
326C8×C79—41no—
327C8×C79—41no—
328C8×C79—41no—
329C8×C79—41no—
330C79⋊C8—41no—
331C79⋊C8—41no—
332C79⋊C8—41no—
333C79⋊C8—41no—
334C22×C79—22no—
335C22×C79—22no—
336C22×C79—22no—
337C22×C79—41no—
338C22×C79—41no—
339C22×C79—41no—
340C22×C79—41no—
341C22×C79C22×C4⋊C411yescharacteristic
342C22×C79#51811yescharacteristic
343C22×C79#51811yescharacteristic
344C22×C79C2×#13111yescharacteristic
345C22×C79C2×#13111yescharacteristic
346C22×C79#56811yescharacteristic
347C22×C79#56811yescharacteristic
348C2×D79—22no—
349C2×D79—22no—
350C2×D79—22no—
351C2×D79—22no—
352C2×D79—22no—
353C2×D79—22no—
354C2×D79—41no—
355C2×D79—41no—
356C2×D79—41no—
357C2×D79—41no—
358C2×D79—41no—
359C2×D79—41no—
360C2×D79—41no—
361C2×D79—41no—
362C4×C79—22no—
363C4×C79—22no—
364C4×C79—41no—
365C4×C79—41no—
366C4×C79—41no—
367C4×C79#53411yescharacteristic
368C4×C79#53411yescharacteristic
369C4×C79#54311yescharacteristic
370C4×C79#54311yescharacteristic
371Dic79—22no—
372Dic79—22no—
373Dic79—22no—
374Dic79—41no—
375Dic79—41no—
376Dic79—41no—
377#21937—791nomaximal, Sylow
378C2×C79—42no—
379C2×C79#231511yescharacteristic
380C2×C79#290611yescharacteristic
381C2×C79#290611yescharacteristic
382C2×C79#297711yescharacteristic
383C2×C79#297811yescharacteristic
384C2×C79#298111yescharacteristic
385C2×C79#298111yescharacteristic
386D79—42no—
387D79—42no—
388C2×#408—791no—
389C2×#408—791no—
390#2297—791no—
391#1851—791no—
392#1851—791no—
393#1851—791no—
394#1851D7911yescharacteristic, complemented
395#1850—791no—
396#1850—791no—
397#1850—791no—
398#1850—791no—
399#1798—791no—
400#1798—791no—
401#1797—791no—
402#1797—791no—
403C79#2193711yescharacteristic, complemented, Sylow
404C22×#41—791no—
405C22×M16—791no—
406C22×M16C2×D7911yescharacteristic
407C23×C8—791no—
408C23×C8—791no—
409C2×#117—791no—
410C22×C42—791no—
411C2×C4⋊C8—791no—
412C2×C4⋊C8—791no—
413C2×C4⋊C8—791no—
414C2×C4⋊C8—791no—
415C2×C4⋊C8—791no—
416C2×C4⋊C8—791no—
417C2×C4⋊C8C2×D7911yescharacteristic
418C2×C4⋊C8C2×D7911yescharacteristic
419#408—1584no—
420#408—1584no—
421C2×C22⋊C8—791no—
422C2×C22⋊C8—791no—
423C2×C22⋊C8—791no—
424C2×C22⋊C8—791no—
425C2×C22⋊C8—791no—
426C2×C22⋊C8—791no—
427C2×C22⋊C8—791no—
428C2×C22⋊C8C2×D7911yescharacteristic
429#391—791no—
430#391—791no—
431#390—791no—
432#390—791no—
433#386—791no—
434#386—791no—
435#386—791no—
436#386—791no—
437C4×C22⋊C4—791no—
438C4×C22⋊C4—791no—
439C4×C22⋊C4—791no—
440C4×C22⋊C4C2×D7911yescharacteristic
441#336—791no—
442#336—791no—
443#336—791no—
444#336—791no—
445#336—791no—
446#336—791no—
447#336C2×D7911yescharacteristic
448#336C2×D7911yescharacteristic
449C2×#41—3161no—
450C2×#41—3161no—
451C2×#41—3161no—
452C2×#41—3161no—
453C2×#41—794no—
454C2×#41—794no—
455C22×Q8—791no—
456C22×D4—791no—
457C22×D4—791no—
458C22×D4—791no—
459C23×C4—791no—
460C23×C4—791no—
461C23×C4—791no—
462C23×C4—791no—
463C23×C4C22×D7911yescharacteristic
464C2×M16—22no—
465C2×M16—41no—
466C2×M16—41no—
467C2×M16—3161no—
468C2×M16—3161no—
469C2×M16—1582no—
470C22×C8—3161no—
471C22×C8—3161no—
472C22×C8—3161no—
473C22×C8—3161no—
474C22×C8—791no—
475C22×C8—791no—
476C22×C8—791no—
477C22×C8—791no—
478C22×C8—1582no—
479C22×C8—1582no—
480C22×C8C22×D7911yescharacteristic
481C22×C8C22×D7911yescharacteristic
482C22×C8C22×D7911yescharacteristic
483C22×C8C22×D7911yescharacteristic
484#117—3161no—
485#117—3161no—
486C2×C4⋊C4—791no—
487C2×C4⋊C4—791no—
488C2×C22⋊C4—791no—
489C2×C22⋊C4—791no—
490C2×C22⋊C4—791no—
491C2×C22⋊C4—791no—
492C2×C22⋊C4—791no—
493C2×C22⋊C4—791no—
494C2×C22⋊C4—791no—
495C2×C22⋊C4—791no—
496C2×C22⋊C4C4×D7911yescharacteristic
497C2×C22⋊C4C4×D7911yescharacteristic
498C2×C42—3161no—
499C2×C42—3161no—
500C2×C42—791no—
501C2×C42—791no—
502C2×C42—791no—
503C2×C42—791no—
504C2×C42C22×D7911yescharacteristic
505C2×C42C22×D7911yescharacteristic
506C4⋊C8—41no—
507C4⋊C8—41no—
508C4⋊C8—3161no—
509C4⋊C8—3161no—
510C4⋊C8—3161no—
511C4⋊C8—3161no—
512C4⋊C8—3161no—
513C4⋊C8—3161no—
514C22⋊C8—22no—
515C22⋊C8—1582no—
516C22⋊C8—1582no—
517C22⋊C8—1582no—
518C22⋊C8—1582no—
519C22⋊C8—1582no—
520C22⋊C8—1582no—
521C22⋊C8—1582no—
522#95—791no—
523#95—791no—
524#95—791no—
525#95—791no—
526#95—791no—
527#95—791no—
528#95C4×D7911yescharacteristic
529#95C4×D7911yescharacteristic
530C24—791no—
531C24—791no—
532C24C2×C4×D7911yescharacteristic
533#41—3164no—
534#41—3164no—
535#41—3164no—
536#41—3164no—
537C2×Q8—3161no—
538C2×Q8—3161no—
539C2×Q8—794no—
540C2×D4—3161no—
541C2×D4—3161no—
542C2×D4—3161no—
543C2×D4—3161no—
544C2×D4—3161no—
545C2×D4—3161no—
546C2×D4—794no—
547C2×D4—794no—
548C2×D4—794no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—3161no—
554C22×C4—3161no—
555C22×C4—3161no—
556C22×C4—3161no—
557C22×C4—791no—
558C22×C4—791no—
559C22×C4—791no—
560C22×C4—792no—
561C22×C4—792no—
562C22×C4—792no—
563C22×C4—792no—
564C22×C4—791no—
565C22×C4—791no—
566C22×C4—791no—
567C22×C4—1582no—
568C22×C4—1582no—
569C22×C4—1581no—
570C22×C4—1581no—
571C22×C4—1581no—
572C22×C4—1581no—
573C22×C4—1581no—
574C22×C4—1581no—
575C22×C4—1581no—
576C22×C4—1581no—
577C22×C4C2×C4×D7911yescharacteristic
578C22×C4C2×C4×D7911yescharacteristic
579C22×C4C2×C4×D7911yescharacteristic
580C22×C4C2×C4×D7911yescharacteristic
581C22×C4C2×C4×D7911yescharacteristic
582C22×C4D4×D7912yes—
583C22×C4Q8×D7912yes—
584C22×C4C23×D7911yescharacteristic
585M16—44no—
586M16—3164no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—3164no—
600C2×C8—3164no—
601C2×C8—1581no—
602C2×C8—1581no—
603C2×C8—1581no—
604C2×C8—1581no—
605C2×C8—1581no—
606C2×C8—1581no—
607C2×C8—1581no—
608C2×C8—1581no—
609C2×C8—1581no—
610C2×C8—1581no—
611C2×C8—1581no—
612C2×C8—1581no—
613C4⋊C4—3161no—
614C4⋊C4—3161no—
615C22⋊C4—22no—
616C22⋊C4—41no—
617C22⋊C4—3161no—
618C22⋊C4—3161no—
619C22⋊C4—3161no—
620C22⋊C4—3161no—
621C22⋊C4—3161no—
622C22⋊C4—1582no—
623C22⋊C4—1582no—
624C22⋊C4—1582no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—3161no—
630C42—3161no—
631C42—1581no—
632C42—1581no—
633C42—1581no—
634C42—1581no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—792no—
642C23—792no—
643C23—1581no—
644C23—1581no—
645C23—1581no—
646C23—1581no—
647C23—1581no—
648C23—1581no—
649C23—1581no—
650C23—1581no—
651C23—1581no—
652C23—1581no—
653C23—1581no—
654C23—1581no—
655C23C4⋊C4×D7912yes—
656C23C22×C4×D7911yescharacteristic
657Q8—3164no—
658D4—3164no—
659D4—3164no—
660D4—3164no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—3164no—
679C2×C4—3164no—
680C2×C4—792no—
681C2×C4—792no—
682C2×C4—792no—
683C2×C4—1581no—
684C2×C4—1581no—
685C2×C4—1581no—
686C2×C4—1581no—
687C2×C4—1581no—
688C2×C4—1581no—
689C2×C4—1581no—
690C2×C4—1581no—
691C2×C4—1581no—
692C2×C4—1581no—
693C2×C4—1581no—
694C2×C4—1581no—
695C2×C4—1581no—
696C2×C4—1581no—
697C2×C4—1581no—
698C2×C4—1582no—
699C2×C4—1582no—
700C2×C4—1582no—
701C2×C4—1582no—
702C2×C4—1582no—
703C2×C4—1582no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4C4⋊C4×D7912yes—
707C2×C4#1457916912yes—
708C2×C4C2×D4×D7911yescharacteristic
709C2×C4C2×Q8×D7911yescharacteristic
710C2×C4#1457920611yescharacteristic
711C2×C4#1457920611yescharacteristic
712C2×C4#1457920711yescharacteristic
713C2×C4#1457920711yescharacteristic
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C8—3161no—
719C8—3161no—
720C8—3161no—
721C8—3161no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—3161no—
730C22—3161no—
731C22—3161no—
732C22—3161no—
733C22—3161no—
734C22—3161no—
735C22—3161no—
736C22—3161no—
737C22—1582no—
738C22—1582no—
739C22—1582no—
740C22—1582no—
741C22—1582no—
742C22—1582no—
743C22C2×C4⋊C4×D7911yescharacteristic
744C22#1909903511yescharacteristic
745C22#1909903511yescharacteristic
746C22#131×D7911yescharacteristic
747C22C2×#1457916911yescharacteristic
748C22#1909932811yescharacteristic
749C22#1909932911yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—3161no—
756C4—3161no—
757C4—3161no—
758C4—1582no—
759C4—1582no—
760C4—1582no—
761C4#1909912311yescharacteristic
762C4#1909912411yescharacteristic
763C4#1909918811yescharacteristic
764C4#1909918811yescharacteristic
765C2—42no—
766C2—3162no—
767C2—3162no—
768C2#2376601111yescharacteristic
769C2#2377196711yescharacteristic
770C2#2377196911yescharacteristic
771C2#2377245111yescharacteristic
772C2#2377245711yescharacteristic
773C2#2377247211yescharacteristic
774C2#2377247711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D79
commutator, socleC23×C79C23×C4
FittingC79×#1851C2
prime radicalC22×#11929624C22
cosocleC22×C4×C79C24
hypercenter#1851D79
hypocenterC79#21937
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
4. #23763584C2semidirect
5. #23763584C2semidirect
6. #23763583C2semidirect
7. #23763580C2semidirect
8. #23763577C2semidirect
9. #23763576C2semidirect
10. #23763576C2semidirect
11. #23763383C2semidirect
12. #23763381C2semidirect
13. #23763379C2semidirect
14. #23763377C2semidirect
15. C79×#1851C2semidirect
394. #1851D79semidirect
403. C79#21937semidirect

Maximal subgroups

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

subgroupindex
C2×#190985312
C2×#190985282
#237658862
#237635842
#237635832
#237635802
#237635772
#237635762
#237633832
#237633812
#237633792
#237633772
C79×#18512
#2193779