Finite Group Databasebeta

← C2×#23774503 #35159658

Subgroups — C2×#23774503 #35159658

Order 20224.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099139C211yesmaximal, characteristic, complemented
2#23774503C2116yesmaximal, direct product factor
3C2×#19098958C211yesmaximal, characteristic, complemented
4C2×#19098945C211yesmaximal, characteristic, complemented
5C2×#19098925C211yesmaximal, characteristic, complemented
6C2×#19098915C211yesmaximal, characteristic, complemented
7C2×#19098785C211yesmaximal, characteristic, complemented
8C2×#19098773C211yesmaximal, characteristic, complemented
9C2×#19098778C211yesmaximal, characteristic, complemented
10C2×#19098768C211yesmaximal, characteristic, complemented
11C2×#19098723C211yesmaximal, characteristic, complemented
12C2×#19098706C211yesmaximal, characteristic
13C2×#19098718C211yesmaximal, characteristic, complemented
14C2×#19098701C211yesmaximal, characteristic, complemented
15C2×#19098624C211yesmaximal, characteristic, complemented
16C2×#542×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C23×Dic158C2211yescharacteristic
19C22×#11929614C2211yescharacteristic
20C22×#11929614C2211yescharacteristic
21C22×#11929614C2211yescharacteristic
22C22×#11929612C2211yescharacteristic
23C22×#11929612C2211yescharacteristic
24C22×#11929612C2211yescharacteristic
25C22×#11929611C2211yescharacteristic
26C22×#11929609C2211yescharacteristic
27#19099139—24no—
28#19099139C2218yescomplemented
29C2×#14579161C2211yescharacteristic
30C2×#14579161C2211yescharacteristic
31C2×#14579149C2211yescharacteristic
32C2×#14579149C2211yescharacteristic
33C2×#14579145—21no—
34C2×#14579145—21no—
35C2×#14579141—21no—
36C2×#14579141—21no—
37#19098958C2218yescomplemented
38#19098945C2218yescomplemented
39#19098925C2218yescomplemented
40#19098915C2218yescomplemented
41#19098785C2218yescomplemented
42#19098778C2218yescomplemented
43#19098773C2218yescomplemented
44#19098768C2218yescomplemented
45#19098723C2218yescomplemented
46#19098718C2218yescomplemented
47#19098706C2218yes—
48#19098701C2218yescomplemented
49#19098624C2218yescomplemented
50C2×C4⋊(C79⋊C8)C2211yescharacteristic
51C2×C4⋊(C79⋊C8)C2211yescharacteristic
52C2×#14579084C2211yescharacteristic
53C2×#14579084C2211yescharacteristic
54C2×#14579084C2211yescharacteristic
55C2×#14579084C2211yescharacteristic
56C2×#14579084C2211yescharacteristic
57C2×#14579084C2211yescharacteristic
58C2×#14579081C2211yescharacteristic
59C2×#14579081C2211yescharacteristic
60C2×C22⋊(C79⋊C8)C2211yescharacteristic
61C2×C22⋊(C79⋊C8)C2211yescharacteristic
62C2×#14579072C2211yescharacteristic
63C2×C4×C79⋊C8C2211yescharacteristic
64#542×C79—24no—
65#542×C79C2218yescomplemented
66C2×C4⋊Q8×C79C2211yescharacteristic
67C2×#126×C79—21no—
68C2×#124×C79—21no—
69C2×#124×C79C2211yescharacteristic
70C2×#123×C79—21no—
71C2×C22⋊Q8×C79—21no—
72C2×C22⋊Q8×C79C2211yescharacteristic
73C2×#121×C79C2211yescharacteristic
74C2×C4×Q8×C79C2211yescharacteristic
75C2×C4×D4×C79C2211yescharacteristic
76C2×#117×C79C2211yescharacteristic
77C2×#11929624—22no—
78C2×#11929624—42no—
79C2×#11929624—42no—
80C2×#11929624C2314yes—
81C22×Dic158—22no—
82C22×Dic158—21no—
83C22×Dic158—42no—
84C22×Dic158—42no—
85C22×Dic158C2311yescharacteristic
86C22×Dic158C2311yescharacteristic
87C22×Dic158C2311yescharacteristic
88C22×Dic158C2314yes—
89C22×D316C2311yescharacteristic
90C22×C22⋊D79—21no—
91C23×Dic79—21no—
92C22×C4×D79—21no—
93C2×#11929614—42no—
94C2×#11929614—42no—
95C2×#11929614—42no—
96C2×#11929614C2314yes—
97C2×#11929614C2314yes—
98C2×#11929614C2314yes—
99C2×#11929612—42no—
100C2×#11929612—42no—
101C2×#11929612—42no—
102C2×#11929612C2314yes—
103C2×#11929612C2314yes—
104C2×#11929612C2314yes—
105C2×#11929611—42no—
106C2×#11929611C2314yes—
107C2×#11929609—42no—
108C2×#11929609C2314yes—
109C22×C79⋊C8C2311yescharacteristic
110C22×C79⋊C8C2311yescharacteristic
111C22×C79⋊C8C2311yescharacteristic
112C22×C79⋊C8C2311yescharacteristic
113#14579161—22no—
114#14579161—22no—
115#14579161C2314yes—
116#14579161C2314yes—
117#14579149—22no—
118#14579149—22no—
119#14579149C2314yes—
120#14579149C2314yes—
121#14579145—28no—
122#14579145—28no—
123#14579141—28no—
124#14579141—28no—
125C2×C4⋊Dic79—21no—
126C2×C4⋊Dic79—21no—
127C2×C4⋊Dic79—21no—
128C2×C4⋊Dic79—21no—
129C2×(C2×D79)⋊C4—21no—
130C2×(C2×D79)⋊C4—21no—
131C2×(C2×D79)⋊C4—21no—
132C2×(C2×D79)⋊C4—21no—
133C4⋊(C79⋊C8)C2314yes—
134C4⋊(C79⋊C8)C2314yes—
135#14579084C2314yes—
136#14579084C2314yes—
137#14579084C2314yes—
138#14579084C2314yes—
139#14579084C2314yes—
140#14579084C2314yes—
141#14579081C2314yes—
142#14579081C2314yes—
143C22⋊(C79⋊C8)C2314yes—
144C22⋊(C79⋊C8)C2314yes—
145#14579072C2314yes—
146C4×C79⋊C8C2314yes—
147C22×Q8×C79—21no—
148C22×Q8×C79C2311yescharacteristic
149C22×D4×C79—21no—
150C22×D4×C79C2311yescharacteristic
151C23×C4×C79—21no—
152C23×C4×C79C2311yescharacteristic
153C4⋊Q8×C79—22no—
154C4⋊Q8×C79C2314yes—
155#126×C79—28no—
156#124×C79—28no—
157#124×C79—22no—
158#124×C79C2314yes—
159#123×C79—28no—
160C22⋊Q8×C79—22no—
161C22⋊Q8×C79—28no—
162C22⋊Q8×C79C2314yes—
163#121×C79—22no—
164#121×C79C2314yes—
165C4×Q8×C79—22no—
166C4×Q8×C79C2314yes—
167C4×D4×C79—22no—
168C4×D4×C79C2314yes—
169#117×C79D414yes—
170#117×C79C2314yes—
171C2×C4⋊C4×C79—21no—
172C2×C4⋊C4×C79—21no—
173C2×C4⋊C4×C79—21no—
174C2×C4⋊C4×C79D411yescharacteristic
175C2×C4⋊C4×C79D411yescharacteristic
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C4⋊C4×C79C2311yescharacteristic
178C2×C22⋊C4×C79—21no—
179C2×C22⋊C4×C79—21no—
180C2×C22⋊C4×C79—21no—
181C2×C22⋊C4×C79—21no—
182C2×C22⋊C4×C79—21no—
183C2×C22⋊C4×C79D411yescharacteristic
184C2×C22⋊C4×C79D411yescharacteristic
185C2×C42×C79—21no—
186C2×C42×C79C2311yescharacteristic
187C2×C42×C79C2311yescharacteristic
188C23×D79—21no—
189#11929624—44no—
190#11929624—44no—
191#11929624—48no—
192C2×Dic158—24no—
193C2×Dic158—21no—
194C2×Dic158—21no—
195C2×Dic158—21no—
196C2×Dic158—22no—
197C2×Dic158—22no—
198C2×Dic158—22no—
199C2×Dic158—22no—
200C2×Dic158—22no—
201C2×Dic158—22no—
202C2×Dic158—44no—
203C2×Dic158—44no—
204C2×Dic158—44no—
205C2×Dic158—48no—
206C2×Dic158C2412yes—
207C2×Dic158C2412yes—
208C2×Dic158C2412yes—
209C2×D316—21no—
210C2×D316—22no—
211C2×D316—22no—
212C2×D316C2412yes—
213C2×C22⋊D79—24no—
214C2×C22⋊D79—44no—
215C22×Dic79—21no—
216C22×Dic79—21no—
217C22×Dic79—24no—
218C22×Dic79—21no—
219C22×Dic79—44no—
220C2×C4×D79—24no—
221C2×C4×D79—44no—
222#11929614—44no—
223#11929614—44no—
224#11929614—44no—
225#11929612—44no—
226#11929612—44no—
227#11929612—44no—
228#11929611—44no—
229#11929609—44no—
230C2×C79⋊C8—22no—
231C2×C79⋊C8—22no—
232C2×C79⋊C8—22no—
233C2×C79⋊C8—22no—
234C2×C79⋊C8C2412yes—
235C2×C79⋊C8C2412yes—
236C2×C79⋊C8C2412yes—
237C2×C79⋊C8C2412yes—
238C4⋊Dic79—24no—
239C4⋊Dic79—24no—
240C4⋊Dic79—24no—
241C4⋊Dic79—24no—
242(C2×D79)⋊C4—24no—
243(C2×D79)⋊C4—24no—
244(C2×D79)⋊C4—24no—
245(C2×D79)⋊C4—24no—
246C24×C79—21no—
247C24×C79C2×D411yescharacteristic
248C2×Q8×C79—21no—
249C2×Q8×C79—24no—
250C2×Q8×C79—22no—
251C2×Q8×C79—22no—
252C2×Q8×C79—82no—
253C2×Q8×C79C2412yes—
254C2×D4×C79—24no—
255C2×D4×C79—21no—
256C2×D4×C79—22no—
257C2×D4×C79—22no—
258C2×D4×C79—82no—
259C2×D4×C79C2412yes—
260C22×C4×C79—22no—
261C22×C4×C79—22no—
262C22×C4×C79—21no—
263C22×C4×C79—21no—
264C22×C4×C79—21no—
265C22×C4×C79—24no—
266C22×C4×C79—82no—
267C22×C4×C79C2×D412yes—
268C22×C4×C79C2×D411yescharacteristic
269C22×C4×C79C2×D411yescharacteristic
270C22×C4×C79C2×D411yescharacteristic
271C22×C4×C79C2×D411yescharacteristic
272C22×C4×C79C2×D411yescharacteristic
273C22×C4×C79C2412yes—
274C22×C4×C79C2411yescharacteristic
275C4⋊C4×C79—24no—
276C4⋊C4×C79—24no—
277C4⋊C4×C79—24no—
278C4⋊C4×C79—21no—
279C4⋊C4×C79—21no—
280C4⋊C4×C79C2×D414yes—
281C4⋊C4×C79C2×D414yes—
282C4⋊C4×C79C2412yes—
283C4⋊C4×C79C2412yes—
284C22⋊C4×C79—24no—
285C22⋊C4×C79—24no—
286C22⋊C4×C79—24no—
287C22⋊C4×C79—24no—
288C22⋊C4×C79—24no—
289C22⋊C4×C79C2×D414yes—
290C22⋊C4×C79C2×D414yes—
291C42×C79—24no—
292C42×C79C2×D412yes—
293C42×C79C2×D412yes—
294C42×C79C2412yes—
295C42×C79C2412yes—
296C23×C79—22no—
297C23×C79—22no—
298C23×C79—22no—
299C23×C79—22no—
300C23×C79—42no—
301C23×C79—42no—
302C23×C79—42no—
303C23×C79C22×D412yes—
304C23×C79C22×D411yescharacteristic
305C22×D79—22no—
306C22×D79—42no—
307C22×D79—42no—
308C22×D79—42no—
309Q8×C79—22no—
310Q8×C79—22no—
311Q8×C79—42no—
312Q8×C79—84no—
313D4×C79—22no—
314D4×C79—22no—
315D4×C79—42no—
316D4×C79—84no—
317C2×C4×C79—22no—
318C2×C4×C79—22no—
319C2×C4×C79—22no—
320C2×C4×C79—22no—
321C2×C4×C79—22no—
322C2×C4×C79—24no—
323C2×C4×C79—22no—
324C2×C4×C79—22no—
325C2×C4×C79—22no—
326C2×C4×C79—22no—
327C2×C4×C79—22no—
328C2×C4×C79—42no—
329C2×C4×C79—42no—
330C2×C4×C79—42no—
331C2×C4×C79—84no—
332C2×C4×C79C22×D412yes—
333C2×C4×C79C22×D412yes—
334C2×C4×C79C22×D412yes—
335C2×C4×C79C22×D412yes—
336C2×C4×C79C22×D412yes—
337C2×C4×C79C22×D411yescharacteristic
338C2×C4×C79H(5,𝔽2)12yes—
339C2×C4×C79H(5,𝔽2)12yes—
340C2×C4×C79C2511yescharacteristic
341C22⋊D79—48no—
342C2×Dic79—22no—
343C2×Dic79—22no—
344C2×Dic79—22no—
345C2×Dic79—48no—
346C2×Dic79—42no—
347C2×Dic79—42no—
348C2×Dic79—42no—
349D316—22no—
350D316—22no—
351D316—42no—
352C4×D79—48no—
353Dic158—22no—
354Dic158—22no—
355Dic158—22no—
356Dic158—22no—
357Dic158—22no—
358Dic158—22no—
359Dic158—48no—
360Dic158—42no—
361Dic158—42no—
362Dic158—42no—
363C79⋊C8—22no—
364C79⋊C8—22no—
365C79⋊C8—22no—
366C79⋊C8—22no—
367C22×C79—22no—
368C22×C79—22no—
369C22×C79—22no—
370C22×C79—44no—
371C22×C79—42no—
372C22×C79—42no—
373C22×C79—42no—
374C22×C79—84no—
375C22×C79#53512yes—
376C22×C79#57712yes—
377C22×C79#57812yes—
378C22×C79C23×D411yescharacteristic
379C2×D79—42no—
380C2×D79—42no—
381C2×D79—42no—
382C2×D79—84no—
383C4×C79—22no—
384C4×C79—22no—
385C4×C79—22no—
386C4×C79—22no—
387C4×C79—22no—
388C4×C79—42no—
389C4×C79—42no—
390C4×C79—42no—
391C4×C79#53512yes—
392C4×C79C2×H(5,𝔽2)11yescharacteristic
393C4×C79C2×H(5,𝔽2)11yescharacteristic
394Dic79—42no—
395Dic79—42no—
396Dic79—42no—
397C2×#3225—791nomaximal, Sylow
398C2×C79—42no—
399C2×C79—82no—
400C2×C79#322514yescomplemented
401C2×C79C2×#53511yescharacteristic
402C2×C79C2×#57711yescharacteristic
403C2×C79C2×#57811yescharacteristic
404D79—82no—
405C2×#542D7911yescharacteristic, complemented
406C2×#536—791no—
407#3225—7916no—
408C2×#497—791no—
409C2×#495—791no—
410C2×#489—791no—
411C2×#487—791no—
412C2×#464—791no—
413C2×#462—791no—
414C2×#463—791no—
415C2×#461—791no—
416C2×#452—791no—
417C2×#449—791no—
418C2×#451—791no—
419C2×#448—791no—
420C2×#433—791no—
421C79C2×#322511yescharacteristic, complemented, Sylow
422C22×#41—791no—
423C23×Q8—791no—
424C22×Q16—791no—
425C22×Q16—791no—
426C22×Q16—791no—
427C22×SD16—791no—
428C22×SD16—791no—
429C22×SD16—791no—
430C22×SD16—791no—
431C22×D8—791no—
432#542—24no—
433#542C2×D7918yescomplemented
434#536—798no—
435#536—1584no—
436C2×C4⋊Q8—791no—
437C2×C4⋊Q8—791no—
438C2×C4⋊Q8C2×D7911yescharacteristic
439C2×#126—21no—
440C2×#124—21no—
441C2×#124—791no—
442C2×#124—791no—
443C2×#124C2×D7911yescharacteristic
444C2×#123—21no—
445C2×#123—1581no—
446C2×#123—1581no—
447C2×C22⋊Q8—21no—
448C2×C22⋊Q8—1581no—
449C2×C22⋊Q8—1581no—
450C2×C22⋊Q8C2×D7911yescharacteristic
451C2×#121C2×D7911yescharacteristic
452C2×C4×Q8C2×D7911yescharacteristic
453C2×C4×D4C2×D7911yescharacteristic
454C2×#117C2×D7911yescharacteristic
455#497—798no—
456#495—798no—
457#489—798no—
458#487—798no—
459#464—798no—
460#463—798no—
461#462—798no—
462#461—798no—
463#452—798no—
464#451—798no—
465#449—798no—
466#448—798no—
467#433—798no—
468C2×C4⋊C8—791no—
469C2×C4⋊C8—791no—
470C2×#103—791no—
471C2×#103—791no—
472C2×#103—791no—
473C2×#103—791no—
474C2×#103—791no—
475C2×#103—791no—
476C2×#102—791no—
477C2×#102—791no—
478C2×C22⋊C8—791no—
479C2×C22⋊C8—791no—
480C2×#97—791no—
481C2×C4×C8—791no—
482C2×#41—3162no—
483C2×#41—3162no—
484C2×#41—794no—
485C2×#41—1582no—
486C22×Q8—21no—
487C22×Q8—3162no—
488C22×Q8—3162no—
489C22×Q8—794no—
490C22×Q8—791no—
491C22×Q8—791no—
492C22×Q8—791no—
493C22×Q8—1581no—
494C22×Q8—1582no—
495C22×Q8C22×D7911yescharacteristic
496C22×D4—21no—
497C22×D4—791no—
498C22×D4—1581no—
499C22×D4C22×D7911yescharacteristic
500C23×C4—21no—
501C23×C4—1581no—
502C23×C4—1581no—
503C23×C4C22×D7911yescharacteristic
504C2×Q16—3162no—
505C2×Q16—3162no—
506C2×Q16—3162no—
507C2×Q16—794no—
508C2×Q16—794no—
509C2×Q16—794no—
510C2×SD16—3162no—
511C2×SD16—3162no—
512C2×SD16—3162no—
513C2×SD16—3162no—
514C2×SD16—794no—
515C2×SD16—794no—
516C2×SD16—794no—
517C2×SD16—794no—
518C2×D8—3162no—
519C2×D8—794no—
520C22×C8—791no—
521C22×C8—791no—
522C22×C8—791no—
523C22×C8—791no—
524C4⋊Q8—22no—
525C4⋊Q8—794no—
526C4⋊Q8—794no—
527C4⋊Q8—1582no—
528C4⋊Q8—1582no—
529C4⋊Q8C22×D7914yes—
530#126—28no—
531#124—28no—
532#124—22no—
533#124—794no—
534#124—794no—
535#124—1582no—
536#124—1582no—
537#124C22×D7914yes—
538#123—28no—
539#123—1588no—
540#123—1588no—
541C22⋊Q8—22no—
542C22⋊Q8—28no—
543C22⋊Q8—1588no—
544C22⋊Q8—1588no—
545C22⋊Q8C22×D7914yes—
546#121—22no—
547#121C22×D7914yes—
548C4×Q8—22no—
549C4×Q8C22×D7914yes—
550C4×D4—22no—
551C4×D4C22×D7914yes—
552#117C22⋊D7914yes—
553#117C22×D7914yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—1581no—
558C2×C4⋊C4—1581no—
559C2×C4⋊C4—1581no—
560C2×C4⋊C4—1581no—
561C2×C4⋊C4C22⋊D7911yescharacteristic
562C2×C4⋊C4C22⋊D7911yescharacteristic
563C2×C4⋊C4C22×D7911yescharacteristic
564C2×C4⋊C4C22×D7911yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1581no—
571C2×C22⋊C4—1581no—
572C2×C22⋊C4—1581no—
573C2×C22⋊C4—1581no—
574C2×C22⋊C4C22⋊D7911yescharacteristic
575C2×C22⋊C4C22⋊D7911yescharacteristic
576C2×C42—21no—
577C2×C42C22×D7911yescharacteristic
578C2×C42C22×D7911yescharacteristic
579C4⋊C8—794no—
580C4⋊C8—794no—
581#103—794no—
582#103—794no—
583#103—794no—
584#103—794no—
585#103—794no—
586#103—794no—
587#102—794no—
588#102—794no—
589C22⋊C8—794no—
590C22⋊C8—794no—
591#97—794no—
592C4×C8—794no—
593C24—21no—
594C24—1581no—
595C24C2×C22⋊D7911yescharacteristic
596#41—3168no—
597#41—3164no—
598#41—3164no—
599C2×Q8—21no—
600C2×Q8—24no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—82no—
604C2×Q8—3164no—
605C2×Q8—3168no—
606C2×Q8—3164no—
607C2×Q8—3164no—
608C2×Q8—792no—
609C2×Q8—792no—
610C2×Q8—792no—
611C2×Q8—1582no—
612C2×Q8—1582no—
613C2×Q8—1582no—
614C2×Q8—1582no—
615C2×Q8—1582no—
616C2×Q8—1582no—
617C2×Q8—1584no—
618C2×Q8—1581no—
619C2×Q8—1581no—
620C2×Q8—1581no—
621C2×Q8C23×D7912yes—
622C2×D4—24no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—21no—
626C2×D4—82no—
627C2×D4—3164no—
628C2×D4—792no—
629C2×D4—1584no—
630C2×D4—1582no—
631C2×D4—1582no—
632C2×D4—1581no—
633C2×D4C23×D7912yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—82no—
641C22×C4—3164no—
642C22×C4—3164no—
643C22×C4—1584no—
644C22×C4—1581no—
645C22×C4—1581no—
646C22×C4—1581no—
647C22×C4—1584no—
648C22×C4C2×C22⋊D7912yes—
649C22×C4C2×C22⋊D7911yescharacteristic
650C22×C4C2×C22⋊D7911yescharacteristic
651C22×C4C2×C22⋊D7911yescharacteristic
652C22×C4C2×C22⋊D7911yescharacteristic
653C22×C4C2×C22⋊D7911yescharacteristic
654C22×C4C23×D7912yes—
655C22×C4C23×D7911yescharacteristic
656Q16—3164no—
657Q16—3164no—
658Q16—3164no—
659SD16—3164no—
660SD16—3164no—
661SD16—3164no—
662SD16—3164no—
663D8—3164no—
664C2×C8—792no—
665C2×C8—792no—
666C2×C8—792no—
667C2×C8—792no—
668C2×C8—1582no—
669C2×C8—1582no—
670C2×C8—1582no—
671C2×C8—1582no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—1584no—
678C4⋊C4—1584no—
679C4⋊C4—1584no—
680C4⋊C4—1584no—
681C4⋊C4C2×C22⋊D7914yes—
682C4⋊C4C2×C22⋊D7914yes—
683C4⋊C4C23×D7912yes—
684C4⋊C4C23×D7912yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—1584no—
691C22⋊C4—1584no—
692C22⋊C4—1584no—
693C22⋊C4—1584no—
694C22⋊C4C2×C22⋊D7914yes—
695C22⋊C4C2×C22⋊D7914yes—
696C42—24no—
697C42C2×C22⋊D7912yes—
698C42C2×C22⋊D7912yes—
699C42C23×D7912yes—
700C42C23×D7912yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—3162no—
709C23—3162no—
710C23—3162no—
711C23—1582no—
712C23C22×C22⋊D7912yes—
713C23C22×C22⋊D7911yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—84no—
718Q8—3168no—
719Q8—3162no—
720Q8—3162no—
721Q8—3162no—
722Q8—1582no—
723Q8—1582no—
724Q8—1582no—
725Q8—1582no—
726Q8—1582no—
727Q8—1582no—
728D4—22no—
729D4—22no—
730D4—42no—
731D4—84no—
732D4—3168no—
733D4—3162no—
734D4—1582no—
735D4—1582no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—84no—
751C2×C4—3168no—
752C2×C4—3168no—
753C2×C4—3162no—
754C2×C4—3162no—
755C2×C4—3162no—
756C2×C4—1582no—
757C2×C4—1582no—
758C2×C4—1582no—
759C2×C4C22×C22⋊D7912yes—
760C2×C4C22×C22⋊D7912yes—
761C2×C4C22×C22⋊D7912yes—
762C2×C4C22×C22⋊D7912yes—
763C2×C4C22×C22⋊D7912yes—
764C2×C4C22×C22⋊D7911yescharacteristic
765C2×C4#1457920712yes—
766C2×C4#1457920712yes—
767C2×C4C24×D7911yescharacteristic
768C8—1582no—
769C8—1582no—
770C8—1582no—
771C8—1582no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—3162no—
781C22—3162no—
782C22—3162no—
783C22—6324no—
784C22#1909912712yes—
785C22#1909937412yes—
786C22#1909937812yes—
787C22C23×C22⋊D7911yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—3162no—
797C4—3162no—
798C4—3162no—
799C4#1909912712yes—
800C4C2×#1457920711yescharacteristic
801C4C2×#1457920711yescharacteristic
802C2—42no—
803C2—82no—
804C2—6322no—
805C2#2377450314yesdirect product factor
806C2C2×#1909912711yescharacteristic
807C2C2×#1909937411yescharacteristic
808C2C2×#1909937811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#542×C79C2
socleC23×C79C22×D4
prime radicalC2×#19098706C2
hypercenterC2×#542D79
hypocenterC79C2×#3225
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#19099139C2semidirect
2. #23774503C2direct (N × H)
3. C2×#19098958C2semidirect
4. C2×#19098945C2semidirect
5. C2×#19098925C2semidirect
6. C2×#19098915C2semidirect
7. C2×#19098785C2semidirect
8. C2×#19098773C2semidirect
9. C2×#19098778C2semidirect
10. C2×#19098768C2semidirect
11. C2×#19098723C2semidirect
13. C2×#19098718C2semidirect
14. C2×#19098701C2semidirect
15. C2×#19098624C2semidirect
16. C2×#542×C79C2semidirect
28. #19099139C22semidirect
37. #19098958C22semidirect
38. #19098945C22semidirect
39. #19098925C22semidirect
40. #19098915C22semidirect
41. #19098785C22semidirect
42. #19098778C22semidirect
43. #19098773C22semidirect
44. #19098768C22semidirect
45. #19098723C22semidirect
46. #19098718C22semidirect
48. #19098701C22semidirect
49. #19098624C22semidirect
65. #542×C79C22semidirect
400. C2×C79#3225semidirect
405. C2×#542D79semidirect
421. C79C2×#3225semidirect
433. #542C2×D79semidirect
805. C2#23774503direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991392
#237745032
C2×#190989582
C2×#190989452
C2×#190989252
C2×#190989152
C2×#190987852
C2×#190987732
C2×#190987782
C2×#190987682
C2×#190987232
C2×#190987062
C2×#190987182
C2×#190987012
C2×#190986242
C2×#542×C792
C2×#322579