Finite Group Databasebeta

← C2×#23774182 #35158822

Subgroups — C2×#23774182 #35158822

Order 20224.

2374 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099076C211yesmaximal, characteristic
2C2×C22⋊Q8×D79C211yesmaximal, characteristic, complemented
3#23774182C2116yesmaximal, direct product factor
4C2×#19098906C211yesmaximal, characteristic, complemented
5C2×#19098902C211yesmaximal, characteristic, complemented
6C2×#19098892C211yesmaximal, characteristic, complemented
7C2×#19098878C211yesmaximal, characteristic, complemented
8C2×#19098802C211yesmaximal, characteristic, complemented
9C2×#19098794C211yesmaximal, characteristic, complemented
10C2×#19098792C211yesmaximal, characteristic, complemented
11C2×#19098728C211yesmaximal, characteristic, complemented
12C2×#19098724C211yesmaximal, characteristic, complemented
13C2×#19098717C211yesmaximal, characteristic, complemented
14C2×#19098703C211yesmaximal, characteristic, complemented
15C22×(C2×D79)⋊C8C211yesmaximal, characteristic, complemented
16C2×#467×C79C211yesmaximal, characteristic, complemented
17C22×#11929625C2211yescharacteristic
18C22×Q8×D79C2211yescharacteristic
19C23×C4×D79C2211yescharacteristic
20C22×#11929614C2211yescharacteristic, complemented
21C22×#11929613C2211yescharacteristic, complemented
22C22×#11929611C2211yescharacteristic, complemented
23C23×C79⋊C8C2211yescharacteristic
24#19099076—24no—
25#19099076C2218yes—
26C2×#14579146—21no—
27C2×#14579141C2211yescharacteristic
28C2×#14579140C2211yescharacteristic
29C2×#14579139—21no—
30C2×#14579138—21no—
31C2×#14579137C2211yescharacteristic
32C2×#14579137C2211yescharacteristic
33C22⋊Q8×D79—24no—
34C22⋊Q8×D79C2218yescomplemented
35C2×#14579136C2211yescharacteristic
36C2×#14579135C2211yescharacteristic
37C2×#14579131—21no—
38C2×#14579123—21no—
39C2×(C22⋊D79)⋊C4—21no—
40C2×#14579119C2211yescharacteristic
41C2×C4⋊C4×D79—21no—
42C2×C4⋊C4×D79C2211yescharacteristic
43C2×C22⋊C4×D79—21no—
44#19098906C2218yescomplemented
45#19098902C2218yescomplemented
46#19098892C2218yescomplemented
47#19098878C2218yescomplemented
48#19098802C2218yescomplemented
49#19098794C2218yescomplemented
50#19098792C2218yescomplemented
51#19098728C2218yescomplemented
52#19098724C2218yescomplemented
53#19098717C2218yescomplemented
54#19098703C2218yescomplemented
55C2×#14579094C2211yescharacteristic, complemented
56C2×#14579093C2211yescharacteristic, complemented
57C2×#14579092C2211yescharacteristic, complemented
58C2×#14579086C2211yescharacteristic, complemented
59C2×#14579085C2211yescharacteristic, complemented
60C2×#14579085C2211yescharacteristic, complemented
61C2×#14579084C2211yescharacteristic, complemented
62C2×#14579083C2211yescharacteristic, complemented
63C2×#14579081C2211yescharacteristic, complemented
64C2×(C2×D79)⋊C8C2211yescharacteristic
65C2×(C2×D79)⋊C8C2211yescharacteristic
66C2×(C2×D79)⋊C8C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×(C2×D79)⋊C8C2218yescomplemented
69C22×Q16×C79C2211yescharacteristic, complemented
70C23×C8×C79C2211yescharacteristic
71C2×C22⋊Q8×C79C2211yescharacteristic
72C2×C22⋊Q8×C79C2211yescharacteristic
73#467×C79C2218yescomplemented
74C2×#107×C79C2211yescharacteristic, complemented
75C2×#103×C79C2211yescharacteristic, complemented
76C2×#103×C79C2211yescharacteristic, complemented
77C24×D79D411yescharacteristic
78C2×#11929625—22no—
79C2×#11929625—42no—
80C2×#11929625—42no—
81C2×#11929625C2314yes—
82C22×Dic158—21no—
83C22×Dic158C2311yescharacteristic
84C2×Q8×D79—22no—
85C2×Q8×D79—42no—
86C2×Q8×D79—42no—
87C2×Q8×D79C2314yes—
88C22×D316—21no—
89C22×D316—21no—
90C22×D316C2311yescharacteristic
91C22×C22⋊D79—21no—
92C23×Dic79D411yescharacteristic
93C22×C4×D79—21no—
94C22×C4×D79—21no—
95C22×C4×D79—21no—
96C22×C4×D79—42no—
97C22×C4×D79—42no—
98C22×C4×D79D411yescharacteristic
99C22×C4×D79D414yes—
100C22×C4×D79D411yescharacteristic
101C22×C4×D79C2311yescharacteristic
102C22×C4×D79C2311yescharacteristic
103C22×C4×D79C2314yes—
104C2×#11929614—42no—
105C2×#11929614C2314yescomplemented
106C2×#11929613—42no—
107C2×#11929613C2314yescomplemented
108C2×#11929611—42no—
109C2×#11929611C2314yescomplemented
110C22×C79⋊C8—42no—
111C22×C79⋊C8C2311yescharacteristic
112C22×C79⋊C8C2311yescharacteristic
113C22×C79⋊C8C2314yes—
114#14579146—28no—
115#14579141—22no—
116#14579141C2314yes—
117#14579140—22no—
118#14579140C2314yes—
119#14579139—28no—
120#14579138—28no—
121#14579137—22no—
122#14579137—22no—
123#14579137C2314yes—
124#14579137C2314yes—
125#14579136—22no—
126#14579136C2314yes—
127#14579135—22no—
128#14579135C2314yes—
129#14579131—28no—
130#14579123—28no—
131(C22⋊D79)⋊C4—28no—
132#14579119—22no—
133#14579119C2314yes—
134C2×C4⋊Dic79—21no—
135C2×C4⋊Dic79C2311yescharacteristic
136C2×C4⋊Dic79C2311yescharacteristic
137C2×Dic79⋊C4—21no—
138C2×Dic79⋊C4—21no—
139C2×Dic79⋊C4—21no—
140C2×Dic79⋊C4—21no—
141C4⋊C4×D79—28no—
142C4⋊C4×D79—22no—
143C4⋊C4×D79C2314yes—
144C2×C22⋊Dic79—21no—
145C2×(C2×D79)⋊C4—21no—
146C2×(C2×D79)⋊C4—21no—
147C2×(C2×D79)⋊C4—21no—
148C2×(C2×D79)⋊C4—21no—
149C2×(C2×D79)⋊C4—21no—
150C2×(C2×D79)⋊C4—21no—
151C22⋊C4×D79—28no—
152C2×C4×Dic79—21no—
153#14579094C2314yescomplemented
154#14579093C2314yescomplemented
155#14579092C2314yescomplemented
156#14579086C2314yescomplemented
157#14579085C2314yescomplemented
158#14579085C2314yescomplemented
159#14579084C2314yescomplemented
160#14579083C2314yescomplemented
161#14579081C2314yescomplemented
162(C2×D79)⋊C8C2314yes—
163(C2×D79)⋊C8C2314yes—
164(C2×D79)⋊C8C2314yes—
165(C2×D79)⋊C8C2314yes—
166C22×Q8×C79C2311yescharacteristic
167C22×Q8×C79C2311yescharacteristic
168C23×C4×C79C2311yescharacteristic
169C2×Q16×C79—42no—
170C2×Q16×C79C2314yescomplemented
171C22×C8×C79—42no—
172C22×C8×C79C2311yescharacteristic
173C22×C8×C79C2311yescharacteristic
174C22×C8×C79C2314yes—
175C22⋊Q8×C79—22no—
176C22⋊Q8×C79—22no—
177C22⋊Q8×C79C2314yes—
178C22⋊Q8×C79C2314yes—
179C2×C4⋊C4×C79—21no—
180C2×C4⋊C4×C79—21no—
181C2×C4⋊C4×C79C2311yescharacteristic
182C2×C4⋊C4×C79C2311yescharacteristic
183C2×C22⋊C4×C79—21no—
184C2×C22⋊C4×C79—21no—
185#107×C79C2314yescomplemented
186#103×C79C2314yescomplemented
187#103×C79C2314yescomplemented
188C23×D79—24no—
189C23×D79—24no—
190C23×D79—21no—
191C23×D79—42no—
192C23×D79C2×D411yescharacteristic
193C23×D79C2×D414yes—
194C23×D79C2×D411yescharacteristic
195#11929625—44no—
196#11929625—44no—
197#11929625—48no—
198C2×Dic158—24no—
199C2×Dic158—21no—
200C2×Dic158—22no—
201C2×Dic158—22no—
202C2×Dic158—44no—
203C2×Dic158C2412yes—
204Q8×D79—44no—
205Q8×D79—44no—
206Q8×D79—48no—
207C2×D316—24no—
208C2×D316—24no—
209C2×D316—21no—
210C2×D316—22no—
211C2×D316—22no—
212C2×D316—44no—
213C2×D316—44no—
214C2×D316C2412yes—
215C2×C22⋊D79—24no—
216C2×C22⋊D79—44no—
217C22×Dic79—21no—
218C22×Dic79—21no—
219C22×Dic79—21no—
220C22×Dic79—42no—
221C22×Dic79C2×D411yescharacteristic
222C22×Dic79C2×D411yescharacteristic
223C22×Dic79C2×D414yes—
224C2×C4×D79—24no—
225C2×C4×D79—24no—
226C2×C4×D79—24no—
227C2×C4×D79—22no—
228C2×C4×D79—22no—
229C2×C4×D79—22no—
230C2×C4×D79—22no—
231C2×C4×D79—42no—
232C2×C4×D79—42no—
233C2×C4×D79—48no—
234C2×C4×D79—44no—
235C2×C4×D79—44no—
236C2×C4×D79—44no—
237C2×C4×D79—44no—
238C2×C4×D79—44no—
239C2×C4×D79C2×D412yes—
240C2×C4×D79C2×D412yes—
241C2×C4×D79C2×D414yes—
242C2×C4×D79C2×D414yes—
243C2×C4×D79C2412yes—
244C2×C4×D79C2412yes—
245#11929614—44no—
246#11929613—44no—
247#11929611—44no—
248C2×C79⋊C8—22no—
249C2×C79⋊C8—22no—
250C2×C79⋊C8—44no—
251C2×C79⋊C8C2412yes—
252C2×C79⋊C8C2412yes—
253C4⋊Dic79—24no—
254C4⋊Dic79—21no—
255C4⋊Dic79—21no—
256C4⋊Dic79C2412yes—
257C4⋊Dic79C2412yes—
258Dic79⋊C4—24no—
259Dic79⋊C4—24no—
260Dic79⋊C4—24no—
261Dic79⋊C4—24no—
262C22⋊Dic79—24no—
263(C2×D79)⋊C4—24no—
264(C2×D79)⋊C4—24no—
265(C2×D79)⋊C4—24no—
266(C2×D79)⋊C4—24no—
267(C2×D79)⋊C4—24no—
268(C2×D79)⋊C4—24no—
269C4×Dic79—24no—
270C24×C79C2×D411yescharacteristic
271C2×Q8×C79—21no—
272C2×Q8×C79—21no—
273C2×Q8×C79—22no—
274C2×Q8×C79—22no—
275C2×Q8×C79—22no—
276C2×Q8×C79—22no—
277C2×Q8×C79C2412yes—
278C2×Q8×C79C2412yes—
279C22×C4×C79—22no—
280C22×C4×C79—22no—
281C22×C4×C79—21no—
282C22×C4×C79—21no—
283C22×C4×C79—21no—
284C22×C4×C79—21no—
285C22×C4×C79C2×D411yescharacteristic
286C22×C4×C79C2×D412yes—
287C22×C4×C79C2412yes—
288C22×C4×C79C2411yescharacteristic
289Q16×C79—44no—
290C2×C8×C79—22no—
291C2×C8×C79—22no—
292C2×C8×C79—44no—
293C2×C8×C79C2412yes—
294C2×C8×C79C2412yes—
295C4⋊C4×C79—24no—
296C4⋊C4×C79—24no—
297C4⋊C4×C79—21no—
298C4⋊C4×C79—21no—
299C4⋊C4×C79C2412yes—
300C4⋊C4×C79C2412yes—
301C22⋊C4×C79—24no—
302C22⋊C4×C79—24no—
303C23×C79—22no—
304C23×C79—22no—
305C23×C79#13714yes—
306C23×C79C22×D412yes—
307C23×C79C22×D411yescharacteristic
308C22×D79—22no—
309C22×D79—22no—
310C22×D79—22no—
311C22×D79—22no—
312C22×D79—28no—
313C22×D79—22no—
314C22×D79—28no—
315C22×D79—22no—
316C22×D79—44no—
317C22×D79—416no—
318C22×D79—42no—
319C22×D79—42no—
320C22×D79—42no—
321C22×D79#13514yes—
322C22×D79C22×D412yes—
323C22×D79C22×D412yes—
324Q8×C79—22no—
325Q8×C79—22no—
326Q8×C79—22no—
327Q8×C79—22no—
328Q8×C79—42no—
329Q8×C79—42no—
330C2×C4×C79—22no—
331C2×C4×C79—24no—
332C2×C4×C79—22no—
333C2×C4×C79—22no—
334C2×C4×C79—22no—
335C2×C4×C79—22no—
336C2×C4×C79—22no—
337C2×C4×C79—22no—
338C2×C4×C79—42no—
339C2×C4×C79—42no—
340C2×C4×C79—42no—
341C2×C4×C79—42no—
342C2×C4×C79C22×D412yes—
343C2×C4×C79C22×D411yescharacteristic
344C2×C4×C79H(5,𝔽2)12yes—
345C2×C4×C79H(5,𝔽2)12yes—
346C2×C4×C79C2511yescharacteristic
347C22⋊D79—48no—
348C2×Dic79—22no—
349C2×Dic79—22no—
350C2×Dic79—22no—
351C2×Dic79—22no—
352C2×Dic79—22no—
353C2×Dic79—44no—
354C2×Dic79—42no—
355C2×Dic79—42no—
356C2×Dic79—42no—
357C2×Dic79C22×D412yes—
358C2×Dic79C22×D412yes—
359D316—22no—
360D316—22no—
361D316—48no—
362D316—48no—
363D316—42no—
364C4×D79—24no—
365C4×D79—24no—
366C4×D79—22no—
367C4×D79—22no—
368C4×D79—22no—
369C4×D79—22no—
370C4×D79—44no—
371C4×D79—44no—
372C4×D79—48no—
373C4×D79—48no—
374C4×D79—48no—
375Dic158—22no—
376Dic158—22no—
377Dic158—48no—
378Dic158—42no—
379C8×C79—22no—
380C8×C79—22no—
381C79⋊C8—22no—
382C79⋊C8—22no—
383C22×C79—22no—
384C22×C79—28no—
385C22×C79—22no—
386C22×C79#53412yes—
387C22×C79C2×#13512yes—
388C22×C79C2×#13714yes—
389C22×C79C2×#13712yes—
390C22×C79C23×D411yescharacteristic
391C2×D79—22no—
392C2×D79—28no—
393C2×D79—22no—
394C2×D79—22no—
395C2×D79—22no—
396C2×D79—22no—
397C2×D79—416no—
398C2×D79—44no—
399C2×D79—42no—
400C2×D79—42no—
401C2×D79—42no—
402C2×D79—84no—
403C2×D79C2×#13514yes—
404C4×C79—22no—
405C4×C79—42no—
406C4×C79—42no—
407C4×C79—42no—
408C4×C79—42no—
409C4×C79#53412yes—
410C4×C79C2×H(5,𝔽2)11yescharacteristic
411C4×C79C2×H(5,𝔽2)11yescharacteristic
412Dic79—22no—
413Dic79—22no—
414Dic79—42no—
415Dic79—42no—
416Dic79—42no—
417C2×#3190—791nomaximal, Sylow
418C2×C79—24no—
419C2×C79#319014yescomplemented
420C2×C79C2×#53411yescharacteristic
421C2×C79C22×#13511yescharacteristic
422C2×C79C22×#13711yescharacteristic
423D79—24no—
424D79—42no—
425D79—82no—
426C2×#525—791no—
427C22×C22⋊Q8—791no—
428#3190—7916no—
429C2×#485—791no—
430C2×#485—791no—
431C2×#483—791no—
432C2×#480—791no—
433C2×#467—791no—
434C2×#467D7911yescharacteristic, complemented
435C2×#465—791no—
436C2×#465—791no—
437C2×#452—791no—
438C2×#452—791no—
439C2×#451—791no—
440C2×#448—791no—
441C22×C22⋊C8—791no—
442C79C2×#319011yescharacteristic, complemented, Sylow
443C22×#41—791no—
444C23×Q8—791no—
445C24×C4—791no—
446C22×Q16—791no—
447C22×Q16C2×D7911yescharacteristic, complemented
448C22×SD16—791no—
449C22×SD16—791no—
450C23×C8—791no—
451C23×C8C2×D7911yescharacteristic
452#525—798no—
453#525—1584no—
454C2×#123—1581no—
455C2×C22⋊Q8—791no—
456C2×C22⋊Q8—791no—
457C2×C22⋊Q8—791no—
458C2×C22⋊Q8—798no—
459C2×C22⋊Q8—791no—
460C2×C22⋊Q8—1581no—
461C2×C22⋊Q8—1581no—
462C2×C22⋊Q8—1584no—
463C2×C22⋊Q8C2×D7911yescharacteristic
464C2×C22⋊Q8C2×D7911yescharacteristic
465C2×#121—791no—
466C2×#121—791no—
467C2×#120—1581no—
468C2×C4×D4—1581no—
469C2×C4×D4—1581no—
470C2×#117—791no—
471C22×C4⋊C4—791no—
472C22×C4⋊C4—1581no—
473C22×C22⋊C4—1581no—
474#485—798no—
475#485—798no—
476#483—798no—
477#480—798no—
478#467—798no—
479#467C2×D7918yescomplemented
480#465—798no—
481#465—798no—
482#452—798no—
483#452—798no—
484#451—798no—
485#448—798no—
486C2×#107—791no—
487C2×#107C2×D7911yescharacteristic, complemented
488C2×#106—791no—
489C2×#106—791no—
490C2×#103—791no—
491C2×#103—791no—
492C2×#103—791no—
493C2×#103—791no—
494C2×#103C2×D7911yescharacteristic, complemented
495C2×#103C2×D7911yescharacteristic, complemented
496C2×#102—791no—
497C2×#102—791no—
498C2×C22⋊C8—791no—
499C2×C22⋊C8—791no—
500C2×C22⋊C8—791no—
501C2×C22⋊C8—791no—
502C2×C22⋊C8—798no—
503C25—791no—
504C2×#41—3162no—
505C2×#41—3162no—
506C2×#41—794no—
507C2×#41—1582no—
508C22×Q8—3162no—
509C22×Q8—3162no—
510C22×Q8—794no—
511C22×Q8—791no—
512C22×Q8—1581no—
513C22×Q8—1582no—
514C22×Q8C22×D7911yescharacteristic
515C22×Q8C22×D7911yescharacteristic
516C22×D4—791no—
517C22×D4—1581no—
518C22×D4—1581no—
519C22×D4—1581no—
520C23×C4—3162no—
521C23×C4—3162no—
522C23×C4—791no—
523C23×C4—791no—
524C23×C4—791no—
525C23×C4—794no—
526C23×C4—794no—
527C23×C4—791no—
528C23×C4—791no—
529C23×C4—1581no—
530C23×C4—1581no—
531C23×C4—1581no—
532C23×C4C22×D7911yescharacteristic
533C2×Q16—42no—
534C2×Q16—3162no—
535C2×Q16—794no—
536C2×Q16C22×D7914yescomplemented
537C2×SD16—3162no—
538C2×SD16—3162no—
539C2×SD16—794no—
540C2×SD16—794no—
541C22×C8—42no—
542C22×C8—3162no—
543C22×C8—794no—
544C22×C8—791no—
545C22×C8—791no—
546C22×C8C22×D7911yescharacteristic
547C22×C8C22×D7911yescharacteristic
548C22×C8C22×D7914yes—
549#123—1588no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—794no—
553C22⋊Q8—794no—
554C22⋊Q8—794no—
555C22⋊Q8—794no—
556C22⋊Q8—1588no—
557C22⋊Q8—1588no—
558C22⋊Q8—1582no—
559C22⋊Q8—1582no—
560C22⋊Q8—1582no—
561C22⋊Q8—1582no—
562C22⋊Q8C22×D7914yes—
563C22⋊Q8C22×D7914yes—
564#121—794no—
565#121—794no—
566#121—1582no—
567#121—1582no—
568#120—1588no—
569C4×D4—1588no—
570C4×D4—1588no—
571#117—794no—
572#117—1582no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—791no—
576C2×C4⋊C4—791no—
577C2×C4⋊C4—794no—
578C2×C4⋊C4—1582no—
579C2×C4⋊C4—1588no—
580C2×C4⋊C4—1581no—
581C2×C4⋊C4—1581no—
582C2×C4⋊C4—1581no—
583C2×C4⋊C4—1581no—
584C2×C4⋊C4—1581no—
585C2×C4⋊C4C22×D7911yescharacteristic
586C2×C4⋊C4C22×D7911yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—1588no—
590C2×C22⋊C4—1581no—
591C2×C22⋊C4—1581no—
592C2×C22⋊C4—1581no—
593C2×C22⋊C4—1581no—
594C2×C22⋊C4—1581no—
595C2×C22⋊C4—1581no—
596C2×C22⋊C4—1581no—
597C2×C42—1581no—
598#107—794no—
599#107C22×D7914yescomplemented
600#106—794no—
601#106—794no—
602#103—794no—
603#103—794no—
604#103—794no—
605#103—794no—
606#103C22×D7914yescomplemented
607#103C22×D7914yescomplemented
608#102—794no—
609#102—794no—
610C22⋊C8—794no—
611C22⋊C8—794no—
612C22⋊C8—794no—
613C22⋊C8—794no—
614C24—3162no—
615C24—794no—
616C24—791no—
617C24—791no—
618C24—1584no—
619C24—1581no—
620C24—1584no—
621C24D4×D7911yescharacteristic
622#41—3168no—
623#41—3164no—
624#41—3164no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—3164no—
632C2×Q8—3164no—
633C2×Q8—3164no—
634C2×Q8—3168no—
635C2×Q8—792no—
636C2×Q8—1584no—
637C2×Q8—1582no—
638C2×Q8—1582no—
639C2×Q8—1581no—
640C2×Q8C23×D7912yes—
641C2×Q8C23×D7912yes—
642C2×D4—3164no—
643C2×D4—3164no—
644C2×D4—3164no—
645C2×D4—792no—
646C2×D4—1584no—
647C2×D4—1584no—
648C2×D4—1584no—
649C2×D4—1582no—
650C2×D4—1582no—
651C2×D4—1581no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—3162no—
659C22×C4—3162no—
660C22×C4—3164no—
661C22×C4—3164no—
662C22×C4—3168no—
663C22×C4—3164no—
664C22×C4—3164no—
665C22×C4—3164no—
666C22×C4—3162no—
667C22×C4—794no—
668C22×C4—794no—
669C22×C4—794no—
670C22×C4—791no—
671C22×C4—791no—
672C22×C4—792no—
673C22×C4—792no—
674C22×C4—792no—
675C22×C4—792no—
676C22×C4—1584no—
677C22×C4—1584no—
678C22×C4—1584no—
679C22×C4—1581no—
680C22×C4—1581no—
681C22×C4—1581no—
682C22×C4—1582no—
683C22×C4—1582no—
684C22×C4—1582no—
685C22×C4—1582no—
686C22×C4D4×D7912yes—
687C22×C4D4×D7911yescharacteristic
688C22×C4C23×D7912yes—
689C22×C4C23×D7911yescharacteristic
690Q16—44no—
691Q16—3164no—
692SD16—3164no—
693SD16—3164no—
694C2×C8—22no—
695C2×C8—22no—
696C2×C8—44no—
697C2×C8—3164no—
698C2×C8—792no—
699C2×C8—792no—
700C2×C8—1582no—
701C2×C8—1582no—
702C2×C8C23×D7912yes—
703C2×C8C23×D7912yes—
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—792no—
709C4⋊C4—792no—
710C4⋊C4—1584no—
711C4⋊C4—1584no—
712C4⋊C4—1584no—
713C4⋊C4—1584no—
714C4⋊C4—1584no—
715C4⋊C4—1581no—
716C4⋊C4—1581no—
717C4⋊C4C23×D7912yes—
718C4⋊C4C23×D7912yes—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—1584no—
722C22⋊C4—1584no—
723C22⋊C4—1584no—
724C22⋊C4—1584no—
725C22⋊C4—1584no—
726C22⋊C4—1584no—
727C22⋊C4—1584no—
728C42—1584no—
729C23—22no—
730C23—22no—
731C23—31616no—
732C23—3164no—
733C23—3162no—
734C23—3162no—
735C23—3162no—
736C23—794no—
737C23—792no—
738C23—792no—
739C23—1588no—
740C23—1582no—
741C23—1582no—
742C23—1588no—
743C23—1582no—
744C23—1582no—
745C23—1582no—
746C23—1582no—
747C23#1457919314yes—
748C23C2×D4×D7912yes—
749C23C2×D4×D7911yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8—42no—
755Q8—42no—
756Q8—3168no—
757Q8—3162no—
758Q8—1582no—
759Q8—1582no—
760D4—3168no—
761D4—3168no—
762D4—3168no—
763D4—3162no—
764D4—1582no—
765D4—1582no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—3164no—
779C2×C4—3164no—
780C2×C4—3168no—
781C2×C4—3168no—
782C2×C4—3168no—
783C2×C4—3162no—
784C2×C4—3162no—
785C2×C4—3162no—
786C2×C4—3164no—
787C2×C4—792no—
788C2×C4—792no—
789C2×C4—1582no—
790C2×C4—1582no—
791C2×C4—1582no—
792C2×C4—1582no—
793C2×C4—1582no—
794C2×C4—1582no—
795C2×C4—1582no—
796C2×C4—1582no—
797C2×C4—1582no—
798C2×C4—1584no—
799C2×C4—1584no—
800C2×C4C2×D4×D7912yes—
801C2×C4C2×D4×D7911yescharacteristic
802C2×C4#1457920612yes—
803C2×C4#1457920712yes—
804C2×C4C24×D7911yescharacteristic
805C8—22no—
806C8—22no—
807C8—1582no—
808C8—1582no—
809C22—22no—
810C22—22no—
811C22—28no—
812C22—31616no—
813C22—3164no—
814C22—3162no—
815C22—3162no—
816C22—3162no—
817C22—794no—
818C22—6324no—
819C22—1582no—
820C22—1582no—
821C22—1582no—
822C22—1582no—
823C22—1582no—
824C22—1588no—
825C22#1909912112yes—
826C22#135×D7912yes—
827C22C2×#1457919314yes—
828C22C2×#1457919312yes—
829C22C22×D4×D7911yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—3162no—
836C4—3162no—
837C4—3162no—
838C4—1582no—
839C4—1582no—
840C4#1909912112yes—
841C4C2×#1457920611yescharacteristic
842C4C2×#1457920711yescharacteristic
843C2—24no—
844C2—3162no—
845C2—6322no—
846C2—1584no—
847C2#2377418214yesdirect product factor
848C2C2×#1909912111yescharacteristic
849C2C2×#135×D7911yescharacteristic
850C2C22×#1457919311yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#467×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099076C2
hypercenterC2×#467D79
hypocenterC79C2×#3190
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊Q8×D79C2semidirect
3. #23774182C2direct (N × H)
4. C2×#19098906C2semidirect
5. C2×#19098902C2semidirect
6. C2×#19098892C2semidirect
7. C2×#19098878C2semidirect
8. C2×#19098802C2semidirect
9. C2×#19098794C2semidirect
10. C2×#19098792C2semidirect
11. C2×#19098728C2semidirect
12. C2×#19098724C2semidirect
13. C2×#19098717C2semidirect
14. C2×#19098703C2semidirect
15. C22×(C2×D79)⋊C8C2semidirect
16. C2×#467×C79C2semidirect
20. C22×#11929614C22semidirect
21. C22×#11929613C22semidirect
22. C22×#11929611C22semidirect
34. C22⋊Q8×D79C22semidirect
44. #19098906C22semidirect
45. #19098902C22semidirect
46. #19098892C22semidirect
47. #19098878C22semidirect
48. #19098802C22semidirect
49. #19098794C22semidirect
50. #19098792C22semidirect
51. #19098728C22semidirect
52. #19098724C22semidirect
53. #19098717C22semidirect
54. #19098703C22semidirect
55. C2×#14579094C22semidirect
56. C2×#14579093C22semidirect
57. C2×#14579092C22semidirect
58. C2×#14579086C22semidirect
59. C2×#14579085C22semidirect
60. C2×#14579085C22semidirect
61. C2×#14579084C22semidirect
62. C2×#14579083C22semidirect
63. C2×#14579081C22semidirect
68. C2×(C2×D79)⋊C8C22semidirect
69. C22×Q16×C79C22semidirect
73. #467×C79C22semidirect
74. C2×#107×C79C22semidirect
75. C2×#103×C79C22semidirect
76. C2×#103×C79C22semidirect
105. C2×#11929614C23semidirect
107. C2×#11929613C23semidirect
109. C2×#11929611C23semidirect
153. #14579094C23semidirect
154. #14579093C23semidirect
155. #14579092C23semidirect
156. #14579086C23semidirect
157. #14579085C23semidirect
158. #14579085C23semidirect
159. #14579084C23semidirect
160. #14579083C23semidirect
161. #14579081C23semidirect
170. C2×Q16×C79C23semidirect
185. #107×C79C23semidirect
186. #103×C79C23semidirect
187. #103×C79C23semidirect
419. C2×C79#3190semidirect
434. C2×#467D79semidirect
442. C79C2×#3190semidirect
447. C22×Q16C2×D79semidirect
479. #467C2×D79semidirect
487. C2×#107C2×D79semidirect
494. C2×#103C2×D79semidirect
495. C2×#103C2×D79semidirect
536. C2×Q16C22×D79semidirect
599. #107C22×D79semidirect
606. #103C22×D79semidirect
607. #103C22×D79semidirect
847. C2#23774182direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190990762
C2×C22⋊Q8×D792
#237741822
C2×#190989062
C2×#190989022
C2×#190988922
C2×#190988782
C2×#190988022
C2×#190987942
C2×#190987922
C2×#190987282
C2×#190987242
C2×#190987172
C2×#190987032
C22×(C2×D79)⋊C82
C2×#467×C792
C2×#319079