Finite Group Databasebeta

← C2×#23773364 #35156103

Subgroups — C2×#23773364 #35156103

Order 20224.

2170 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099136C211yesmaximal, characteristic
2C2×#19099043C211yesmaximal, characteristic
3#23773364C2116yesmaximal, direct product factor
4C2×#19098899C211yesmaximal, characteristic, complemented
5C2×#19098897C211yesmaximal, characteristic, complemented
6C2×#19098906C211yesmaximal, characteristic, complemented
7C2×#19098904C211yesmaximal, characteristic, complemented
8C2×#19098903C211yesmaximal, characteristic, complemented
9C2×#19098895C211yesmaximal, characteristic, complemented
10C2×#19098891C211yesmaximal, characteristic, complemented
11C2×#19098602C211yesmaximal, characteristic, complemented
12C2×#19098600C211yesmaximal, characteristic, complemented
13C2×#19098570C211yesmaximal, characteristic, complemented
14C2×#103×D79C211yesmaximal, characteristic, complemented
15C2×#19098528C211yesmaximal, characteristic
16C2×#485×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C22×Q8×D79C2211yescharacteristic
19C22×#11929607C2211yescharacteristic
20C22×C8×D79C2211yescharacteristic
21#19099136—24no—
22#19099136C2218yes—
23C2×#14579160—21no—
24C2×#14579147—21no—
25C2×#14579146—21no—
26C2×#14579143—21no—
27C2×#14579141C2211yescharacteristic
28C2×#14579140C2211yescharacteristic
29C2×#14579137C2211yescharacteristic
30#19099043—24no—
31#19099043C2218yes—
32C2×C4×Dic158—21no—
33C2×C4×D316—21no—
34C2×(C22⋊D79)⋊C4—21no—
35C2×(C22⋊D79)⋊C4—21no—
36C2×#14579119C2211yescharacteristic
37C2×#14579119C2211yescharacteristic
38C2×#14579119C2211yescharacteristic
39C22×C4⋊Dic79C2211yescharacteristic
40C2×C4⋊C4×D79C2211yescharacteristic
41C2×C4⋊C4×D79C2211yescharacteristic
42#19098906C2218yescomplemented
43#19098904C2218yescomplemented
44#19098903C2218yescomplemented
45#19098899C2218yescomplemented
46#19098897C2218yescomplemented
47#19098895C2218yescomplemented
48#19098891C2218yescomplemented
49#19098602C2218yescomplemented
50#19098600C2218yescomplemented
51C2×#14579095C2211yescharacteristic
52C2×#14579095C2211yescharacteristic
53C2×#14579094C2211yescharacteristic
54C2×#14579092C2211yescharacteristic
55C2×#14579092C2211yescharacteristic
56C2×#14579092C2211yescharacteristic
57#19098570C2218yescomplemented
58C2×#14579086C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579085C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579084C2211yescharacteristic
63C2×#14579084C2211yescharacteristic
64#103×D79C2218yescomplemented
65#19098528C2218yes—
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×(C2×D79)⋊C8C2211yescharacteristic
69C2×C22⋊Q8×C79C2211yescharacteristic
70C2×#117×C79C2211yescharacteristic
71#485×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×C22⋊C8×C79C2211yescharacteristic
77C2×#11929624—24no—
78C2×#11929624—24no—
79C2×#11929624D414yes—
80C2×#11929624C2314yes—
81C22×Dic158—21no—
82C22×Dic158D411yescharacteristic
83C22×Dic158C2311yescharacteristic
84C2×Q8×D79—22no—
85C2×Q8×D79—24no—
86C2×Q8×D79—24no—
87C2×Q8×D79C2314yes—
88C22×D316D411yescharacteristic
89C22×C22⋊D79D411yescharacteristic
90C22×C22⋊D79D411yescharacteristic
91C23×Dic79—21no—
92C22×C4×D79—21no—
93C22×C4×D79—21no—
94C22×C4×D79—21no—
95C22×C4×D79C2311yescharacteristic
96C22×C4×D79C2311yescharacteristic
97C2×#11929607—24no—
98C2×#11929607C2314yes—
99C22×C79⋊C8C2311yescharacteristic
100C22×C79⋊C8C2311yescharacteristic
101C2×C8×D79—24no—
102C2×C8×D79C2314yes—
103#14579160—28no—
104#14579147—28no—
105#14579146—28no—
106#14579143—28no—
107#14579141—22no—
108#14579141C2314yes—
109#14579140—22no—
110#14579140C2314yes—
111#14579137—22no—
112#14579137C2314yes—
113C4×Dic158—28no—
114C4×D316—28no—
115(C22⋊D79)⋊C4—28no—
116(C22⋊D79)⋊C4—28no—
117#14579119—22no—
118#14579119—22no—
119#14579119—22no—
120#14579119C2314yes—
121#14579119C2314yes—
122#14579119C2314yes—
123C2×C4⋊Dic79—21no—
124C2×C4⋊Dic79—22no—
125C2×C4⋊Dic79—21no—
126C2×C4⋊Dic79C2314yes—
127C2×C4⋊Dic79C2311yescharacteristic
128C2×C4⋊Dic79C2311yescharacteristic
129C2×C4⋊Dic79C2311yescharacteristic
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×Dic79⋊C4—21no—
134C4⋊C4×D79—22no—
135C4⋊C4×D79—22no—
136C4⋊C4×D79C2314yes—
137C4⋊C4×D79C2314yes—
138C2×C22⋊Dic79—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4—21no—
142C2×(C2×D79)⋊C4—21no—
143C2×(C2×D79)⋊C4—21no—
144C2×C4×Dic79—21no—
145C2×C4×Dic79—21no—
146C2×C4×Dic79—21no—
147#14579095C2314yes—
148#14579095C2314yes—
149#14579094C2314yes—
150#14579092C2314yes—
151#14579092C2314yes—
152#14579092C2314yes—
153#14579086C2314yes—
154#14579086C2314yes—
155#14579085C2314yes—
156#14579085C2314yes—
157#14579084C2314yes—
158#14579084C2314yes—
159C22⋊(C79⋊C8)C2314yes—
160(C2×D79)⋊C8C2314yes—
161(C2×D79)⋊C8C2314yes—
162C22×Q8×C79C2311yescharacteristic
163C23×C4×C79C2311yescharacteristic
164C22×C8×C79C2311yescharacteristic
165C22×C8×C79C2311yescharacteristic
166C22⋊Q8×C79—22no—
167C22⋊Q8×C79C2314yes—
168#117×C79—22no—
169#117×C79C2314yes—
170C2×C4⋊C4×C79—21no—
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176C2×C42×C79—21no—
177#107×C79C2314yes—
178#106×C79C2314yes—
179#103×C79C2314yes—
180#103×C79C2314yes—
181C22⋊C8×C79C2314yes—
182C23×D79C2×D411yescharacteristic
183C23×D79C2×D411yescharacteristic
184#11929624—216no—
185#11929624—28no—
186#11929624—28no—
187C2×Dic158—24no—
188C2×Dic158—24no—
189C2×Dic158—21no—
190C2×Dic158—22no—
191C2×Dic158—22no—
192C2×Dic158—44no—
193C2×Dic158C2×D414yes—
194C2×Dic158C2412yes—
195Q8×D79—28no—
196Q8×D79—28no—
197Q8×D79—48no—
198C2×D316—24no—
199C2×D316C2×D414yes—
200C2×C22⋊D79—24no—
201C2×C22⋊D79—24no—
202C2×C22⋊D79C2×D414yes—
203C2×C22⋊D79C2×D414yes—
204C22×Dic79—21no—
205C22×Dic79—21no—
206C22×Dic79—21no—
207C22×Dic79—21no—
208C22×Dic79—24no—
209C22×Dic79—82no—
210C22×Dic79C2×D411yescharacteristic
211C22×Dic79C2×D411yescharacteristic
212C2×C4×D79—24no—
213C2×C4×D79—24no—
214C2×C4×D79—24no—
215C2×C4×D79—22no—
216C2×C4×D79—22no—
217C2×C4×D79—44no—
218C2×C4×D79—82no—
219C2×C4×D79—82no—
220C2×C4×D79C2×D412yes—
221C2×C4×D79C2×D412yes—
222C2×C4×D79#4114yes—
223C2×C4×D79#4114yes—
224C2×C4×D79C2412yes—
225C2×C4×D79C2412yes—
226#11929607—28no—
227C2×C79⋊C8—22no—
228C2×C79⋊C8—22no—
229C2×C79⋊C8C2412yes—
230C2×C79⋊C8C2412yes—
231C8×D79—28no—
232C4⋊Dic79—24no—
233C4⋊Dic79—21no—
234C4⋊Dic79—21no—
235C4⋊Dic79—24no—
236C4⋊Dic79—21no—
237C4⋊Dic79C2412yes—
238C4⋊Dic79C2412yes—
239C4⋊Dic79C2412yes—
240Dic79⋊C4—24no—
241Dic79⋊C4—24no—
242Dic79⋊C4—24no—
243Dic79⋊C4—24no—
244C22⋊Dic79—24no—
245(C2×D79)⋊C4—24no—
246(C2×D79)⋊C4—24no—
247(C2×D79)⋊C4—24no—
248(C2×D79)⋊C4—24no—
249(C2×D79)⋊C4—24no—
250C4×Dic79—24no—
251C4×Dic79—24no—
252C4×Dic79—24no—
253C24×C79C2×D411yescharacteristic
254C2×Q8×C79—21no—
255C2×Q8×C79—22no—
256C2×Q8×C79—22no—
257C2×Q8×C79C2412yes—
258C22×C4×C79—22no—
259C22×C4×C79—22no—
260C22×C4×C79—21no—
261C22×C4×C79—21no—
262C22×C4×C79—21no—
263C22×C4×C79—21no—
264C22×C4×C79C2×D411yescharacteristic
265C22×C4×C79C2×D412yes—
266C22×C4×C79C2412yes—
267C22×C4×C79C2411yescharacteristic
268C2×C8×C79—22no—
269C2×C8×C79—22no—
270C2×C8×C79C2412yes—
271C2×C8×C79C2412yes—
272C4⋊C4×C79—24no—
273C4⋊C4×C79—21no—
274C4⋊C4×C79—21no—
275C4⋊C4×C79—21no—
276C4⋊C4×C79C2412yes—
277C4⋊C4×C79C2412yes—
278C4⋊C4×C79C2412yes—
279C22⋊C4×C79—24no—
280C22⋊C4×C79—24no—
281C42×C79—24no—
282C23×C79—22no—
283C23×C79—22no—
284C23×C79—22no—
285C23×C79C22×D412yes—
286C23×C79C22×D411yescharacteristic
287C22×D79—22no—
288C22×D79—22no—
289C22×D79—22no—
290C22×D79—22no—
291C22×D79—22no—
292C22×D79#12314yes—
293C22×D79C22×D412yes—
294C22×D79C22×D412yes—
295Q8×C79—22no—
296Q8×C79—22no—
297Q8×C79—42no—
298C2×C4×C79—22no—
299C2×C4×C79—24no—
300C2×C4×C79—22no—
301C2×C4×C79—22no—
302C2×C4×C79—22no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—42no—
307C2×C4×C79—42no—
308C2×C4×C79—42no—
309C2×C4×C79—42no—
310C2×C4×C79C22×D412yes—
311C2×C4×C79C22×D411yescharacteristic
312C2×C4×C79C2×#4112yes—
313C2×C4×C79C2×#4112yes—
314C2×C4×C79C2511yescharacteristic
315C22⋊D79—28no—
316C22⋊D79—28no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—22no—
320C2×Dic79—22no—
321C2×Dic79—22no—
322C2×Dic79—42no—
323C2×Dic79—42no—
324C2×Dic79—42no—
325C2×Dic79—42no—
326C2×Dic79—84no—
327C2×Dic79#12314yes—
328C2×Dic79C22×D412yes—
329C2×Dic79C22×D412yes—
330D316—28no—
331C4×D79—24no—
332C4×D79—22no—
333C4×D79—22no—
334C4×D79—48no—
335C4×D79—84no—
336C4×D79—84no—
337C4×D79#12318yes—
338C4×D79C2×#4114yes—
339C4×D79C2×#4114yes—
340Dic158—28no—
341Dic158—22no—
342Dic158—22no—
343Dic158—42no—
344Dic158—48no—
345C8×C79—22no—
346C8×C79—22no—
347C79⋊C8—22no—
348C79⋊C8—22no—
349C22×C79—22no—
350C22×C79—22no—
351C22×C79—22no—
352C22×C79—44no—
353C22×C79C2×#12312yes—
354C22×C79#57712yes—
355C22×C79#57812yes—
356C22×C79C23×D411yescharacteristic
357C2×D79—28no—
358C2×D79—22no—
359C2×D79—22no—
360C2×D79—22no—
361C2×D79—22no—
362C2×D79—22no—
363C2×D79—44no—
364C2×D79C2×#12314yes—
365C4×C79—22no—
366C4×C79—42no—
367C4×C79—42no—
368C4×C79—42no—
369C4×C79—42no—
370C4×C79C2×#12312yes—
371C4×C79C22×#4111yescharacteristic
372C4×C79C22×#4111yescharacteristic
373Dic79—22no—
374Dic79—42no—
375Dic79—42no—
376Dic79—42no—
377Dic79—42no—
378Dic79C2×#12314yes—
379C2×#3097—791nomaximal, Sylow
380C2×C79—42no—
381C2×C79#309714yescomplemented
382C2×C79C22×#12311yescharacteristic
383C2×C79C2×#57711yescharacteristic
384C2×C79C2×#57811yescharacteristic
385D79—24no—
386D79—42no—
387C2×#536—791no—
388C2×#520—791no—
389#3097—7916no—
390C2×#484—791no—
391C2×#484—791no—
392C2×#485—791no—
393C2×#485—791no—
394C2×#485—791no—
395C2×#485D7911yescharacteristic, complemented
396C2×#483—791no—
397C2×#483—791no—
398C2×#428—791no—
399C2×#427—791no—
400C2×#419—791no—
401C22×#103—791no—
402C2×#408—791no—
403C79C2×#309711yescharacteristic, complemented, Sylow
404C22×#41—791no—
405C23×Q8—791no—
406C22×M16—791no—
407C23×C8—791no—
408#536—798no—
409#536—1584no—
410C2×C4⋊Q8—1581no—
411C2×#124—1581no—
412C2×#123—1581no—
413C2×#123—1581no—
414C2×C22⋊Q8—791no—
415C2×C22⋊Q8—791no—
416C2×C22⋊Q8—791no—
417C2×C22⋊Q8C2×D7911yescharacteristic
418#520—798no—
419#520—1584no—
420C2×C4×Q8—1581no—
421C2×C4×D4—1581no—
422C2×C4×D4—1581no—
423C2×C4×D4—1581no—
424C2×#117—791no—
425C2×#117—791no—
426C2×#117—791no—
427C2×#117C2×D7911yescharacteristic
428C22×C4⋊C4—791no—
429C22×C4⋊C4—791no—
430C22×C4⋊C4—791no—
431#485—798no—
432#485—798no—
433#485—798no—
434#485C2×D7918yescomplemented
435#484—798no—
436#484—798no—
437#483—798no—
438#483—798no—
439#428—798no—
440#427—798no—
441C2×#107—791no—
442C2×#107—791no—
443C2×#107—791no—
444C2×#107C2×D7911yescharacteristic
445C2×#106—791no—
446C2×#106—791no—
447C2×#106—791no—
448C2×#106C2×D7911yescharacteristic
449#419—798no—
450C2×#103—791no—
451C2×#103—791no—
452C2×#103—791no—
453C2×#103—791no—
454C2×#103—791no—
455C2×#103—791no—
456C2×#103—798no—
457C2×#103C2×D7911yescharacteristic
458C2×#103C2×D7911yescharacteristic
459#408—798no—
460C2×C22⋊C8—791no—
461C2×C22⋊C8—791no—
462C2×C22⋊C8—791no—
463C2×C22⋊C8C2×D7911yescharacteristic
464C2×#41—794no—
465C2×#41—794no—
466C2×#41—1584no—
467C2×#41—1584no—
468C22×Q8—791no—
469C22×Q8—794no—
470C22×Q8—791no—
471C22×Q8—1581no—
472C22×Q8—1584no—
473C22×Q8—1584no—
474C22×Q8—1582no—
475C22×Q8C22×D7911yescharacteristic
476C22×D4—791no—
477C22×D4—791no—
478C22×D4—791no—
479C23×C4—791no—
480C23×C4—791no—
481C23×C4—1581no—
482C23×C4—1581no—
483C23×C4—1581no—
484C23×C4—1581no—
485C23×C4C22×D7911yescharacteristic
486C2×M16—794no—
487C2×M16—1584no—
488C22×C8—791no—
489C22×C8—791no—
490C22×C8—794no—
491C22×C8—1584no—
492C22×C8C22×D7911yescharacteristic
493C22×C8C22×D7911yescharacteristic
494C4⋊Q8—1588no—
495#124—1588no—
496#123—1588no—
497#123—1588no—
498C22⋊Q8—22no—
499C22⋊Q8—794no—
500C22⋊Q8—794no—
501C22⋊Q8—794no—
502C22⋊Q8—1582no—
503C22⋊Q8—1582no—
504C22⋊Q8—1582no—
505C22⋊Q8C22×D7914yes—
506C4×Q8—1588no—
507C4×D4—1588no—
508C4×D4—1588no—
509C4×D4—1588no—
510#117—22no—
511#117—794no—
512#117—794no—
513#117—794no—
514#117—1582no—
515#117—1582no—
516#117—1582no—
517#117C22×D7914yes—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—791no—
520C2×C4⋊C4—791no—
521C2×C4⋊C4—794no—
522C2×C4⋊C4—791no—
523C2×C4⋊C4—794no—
524C2×C4⋊C4—794no—
525C2×C4⋊C4—1582no—
526C2×C4⋊C4—1582no—
527C2×C4⋊C4—1581no—
528C2×C4⋊C4—1581no—
529C2×C4⋊C4—1581no—
530C2×C4⋊C4—1581no—
531C2×C4⋊C4—1581no—
532C2×C4⋊C4—1582no—
533C2×C4⋊C4—1581no—
534C2×C4⋊C4C22×D7911yescharacteristic
535C2×C4⋊C4C22×D7911yescharacteristic
536C2×C4⋊C4C22×D7911yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—1581no—
540C2×C22⋊C4—1581no—
541C2×C22⋊C4—1581no—
542C2×C22⋊C4—1581no—
543C2×C22⋊C4—1581no—
544C2×C22⋊C4—1581no—
545C2×C42—21no—
546C2×C42—1581no—
547C2×C42—1581no—
548C2×C42—1581no—
549#107—794no—
550#107—794no—
551#107—794no—
552#107C22×D7914yes—
553#106—794no—
554#106—794no—
555#106—794no—
556#106C22×D7914yes—
557#103—794no—
558#103—794no—
559#103—794no—
560#103—794no—
561#103—794no—
562#103—794no—
563#103C22×D7914yes—
564#103C22×D7914yes—
565C22⋊C8—794no—
566C22⋊C8—794no—
567C22⋊C8—794no—
568C22⋊C8C22×D7914yes—
569C24—791no—
570C24—791no—
571C24D4×D7911yescharacteristic
572#41—15816no—
573#41—1588no—
574#41—1588no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—3164no—
579C2×Q8—3168no—
580C2×Q8—794no—
581C2×Q8—792no—
582C2×Q8—1584no—
583C2×Q8—1584no—
584C2×Q8—1588no—
585C2×Q8—1588no—
586C2×Q8—1582no—
587C2×Q8—1582no—
588C2×Q8—1581no—
589C2×Q8C23×D7912yes—
590C2×D4—794no—
591C2×D4—794no—
592C2×D4—794no—
593C2×D4—1584no—
594C2×D4—1584no—
595C2×D4—1584no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—3164no—
603C22×C4—791no—
604C22×C4—794no—
605C22×C4—794no—
606C22×C4—792no—
607C22×C4—792no—
608C22×C4—791no—
609C22×C4—792no—
610C22×C4—792no—
611C22×C4—6322no—
612C22×C4—6322no—
613C22×C4—6322no—
614C22×C4—1584no—
615C22×C4—1584no—
616C22×C4—1584no—
617C22×C4—1581no—
618C22×C4—1581no—
619C22×C4—1581no—
620C22×C4—1581no—
621C22×C4—1584no—
622C22×C4—1582no—
623C22×C4—1582no—
624C22×C4D4×D7912yes—
625C22×C4D4×D7911yescharacteristic
626C22×C4C23×D7912yes—
627C22×C4C23×D7911yescharacteristic
628M16—1588no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—792no—
632C2×C8—792no—
633C2×C8—1588no—
634C2×C8—1582no—
635C2×C8—1582no—
636C2×C8C23×D7912yes—
637C2×C8C23×D7912yes—
638C4⋊C4—24no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—792no—
643C4⋊C4—792no—
644C4⋊C4—792no—
645C4⋊C4—1584no—
646C4⋊C4—1584no—
647C4⋊C4—1584no—
648C4⋊C4—1584no—
649C4⋊C4—1584no—
650C4⋊C4—1581no—
651C4⋊C4—1581no—
652C4⋊C4—1584no—
653C4⋊C4—1581no—
654C4⋊C4C23×D7912yes—
655C4⋊C4C23×D7912yes—
656C4⋊C4C23×D7912yes—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—1584no—
660C22⋊C4—1584no—
661C22⋊C4—1584no—
662C22⋊C4—1584no—
663C22⋊C4—1584no—
664C22⋊C4—1584no—
665C42—24no—
666C42—1584no—
667C42—1584no—
668C42—1584no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—794no—
673C23—792no—
674C23—792no—
675C23—1582no—
676C23—1582no—
677C23—1582no—
678C23—1582no—
679C23—1582no—
680C23C2×D4×D7912yes—
681C23C2×D4×D7911yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—3168no—
686Q8—3162no—
687Q8—1588no—
688Q8—1582no—
689Q8—1582no—
690D4—1588no—
691D4—1588no—
692D4—1588no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—3168no—
706C2×C4—3162no—
707C2×C4—3162no—
708C2×C4—3162no—
709C2×C4—3162no—
710C2×C4—794no—
711C2×C4—792no—
712C2×C4—798no—
713C2×C4—794no—
714C2×C4—794no—
715C2×C4—792no—
716C2×C4—6324no—
717C2×C4—6324no—
718C2×C4—6324no—
719C2×C4—1582no—
720C2×C4—1582no—
721C2×C4—1582no—
722C2×C4—1582no—
723C2×C4—1582no—
724C2×C4—1584no—
725C2×C4—1582no—
726C2×C4—1582no—
727C2×C4C2×D4×D7912yes—
728C2×C4C2×D4×D7911yescharacteristic
729C2×C4#41×D7912yes—
730C2×C4#41×D7912yes—
731C2×C4C24×D7911yescharacteristic
732C8—22no—
733C8—22no—
734C8—1582no—
735C8—1582no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—44no—
740C22—3164no—
741C22—794no—
742C22—1582no—
743C22—1582no—
744C22—1582no—
745C22—1582no—
746C22—1582no—
747C22—1588no—
748C22#123×D7912yes—
749C22#1909937212yes—
750C22#1909937712yes—
751C22C22×D4×D7911yescharacteristic
752C4—22no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—3162no—
758C4—3162no—
759C4—3162no—
760C4—3162no—
761C4—794no—
762C4—1582no—
763C4#123×D7912yes—
764C4C2×#41×D7911yescharacteristic
765C4C2×#41×D7911yescharacteristic
766C2—42no—
767C2—3162no—
768C2—1584no—
769C2#2377336414yesdirect product factor
770C2C2×#123×D7911yescharacteristic
771C2C2×#1909937211yescharacteristic
772C2C2×#1909937711yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#485×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929624C22
hypercenterC2×#485D79
hypocenterC79C2×#3097
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #23773364C2direct (N × H)
4. C2×#19098899C2semidirect
5. C2×#19098897C2semidirect
6. C2×#19098906C2semidirect
7. C2×#19098904C2semidirect
8. C2×#19098903C2semidirect
9. C2×#19098895C2semidirect
10. C2×#19098891C2semidirect
11. C2×#19098602C2semidirect
12. C2×#19098600C2semidirect
13. C2×#19098570C2semidirect
14. C2×#103×D79C2semidirect
16. C2×#485×C79C2semidirect
42. #19098906C22semidirect
43. #19098904C22semidirect
44. #19098903C22semidirect
45. #19098899C22semidirect
46. #19098897C22semidirect
47. #19098895C22semidirect
48. #19098891C22semidirect
49. #19098602C22semidirect
50. #19098600C22semidirect
57. #19098570C22semidirect
64. #103×D79C22semidirect
71. #485×C79C22semidirect
381. C2×C79#3097semidirect
395. C2×#485D79semidirect
403. C79C2×#3097semidirect
434. #485C2×D79semidirect
769. C2#23773364direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991362
C2×#190990432
#237733642
C2×#190988992
C2×#190988972
C2×#190989062
C2×#190989042
C2×#190989032
C2×#190988952
C2×#190988912
C2×#190986022
C2×#190986002
C2×#190985702
C2×#103×D792
C2×#190985282
C2×#485×C792
C2×#309779