Finite Group Databasebeta

← C2×#23775851 #35166812

Subgroups — C2×#23775851 #35166812

Order 20224.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099268C211yesmaximal, characteristic
2C2×#19099248C211yesmaximal, characteristic
3#23775851C2116yesmaximal, direct product factor
4C2×#19098970C211yesmaximal, characteristic, complemented
5C2×#19098898C211yesmaximal, characteristic, complemented
6C2×#19098907C211yesmaximal, characteristic, complemented
7C2×#19098895C211yesmaximal, characteristic, complemented
8C2×#19098893C211yesmaximal, characteristic, complemented
9C2×#19098873C211yesmaximal, characteristic, complemented
10C2×#19098847C211yesmaximal, characteristic, complemented
11C2×#19098822C211yesmaximal, characteristic, complemented
12C2×#19098804C211yesmaximal, characteristic, complemented
13C2×#19098669C211yesmaximal, characteristic, complemented
14C2×#19098634C211yesmaximal, characteristic
15C2×#19098602C211yesmaximal, characteristic, complemented
16C22×#106×C79C211yesmaximal, characteristic, complemented
17C22×Dic316C2211yescharacteristic
18C22×#11929607C2211yescharacteristic
19#19099268—24no—
20#19099268C2218yes—
21#19099248—24no—
22#19099248C2218yes—
23C2×#14579160C2211yescharacteristic
24C2×#14579156—21no—
25C2×#14579152C2211yescharacteristic
26C2×#14579151—21no—
27C2×#14579151—21no—
28C2×#14579144—21no—
29C2×#14579141C2211yescharacteristic
30C2×#14579141C2211yescharacteristic
31C2×#14579140—21no—
32C2×#14579140C2211yescharacteristic
33C2×#14579140C2211yescharacteristic
34C2×#14579139—21no—
35C2×#14579126C2211yescharacteristic
36C2×#14579126C2211yescharacteristic
37C2×C4×C22⋊D79—21no—
38C2×C4×C22⋊D79C2211yescharacteristic
39C2×#14579120—21no—
40C2×#14579119C2211yescharacteristic
41C2×C4⋊C4×D79C2211yescharacteristic
42#19098970C2218yescomplemented
43#19098907C2218yescomplemented
44#19098898C2218yescomplemented
45#19098895C2218yescomplemented
46#19098893C2218yescomplemented
47#19098873C2218yescomplemented
48#19098847C2218yescomplemented
49#19098822C2218yescomplemented
50#19098804C2218yescomplemented
51#19098669C2218yescomplemented
52#19098634C2218yes—
53#19098602C2218yescomplemented
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×#14579092C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579086C2211yescharacteristic
62C2×#14579084C2211yescharacteristic
63C2×#14579084C2211yescharacteristic
64C2×#14579084C2211yescharacteristic
65C2×#14579084C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×#14579071C2211yescharacteristic
69C23×C8×C79C2211yescharacteristic
70C22×C4⋊C4×C79C2211yescharacteristic
71C22×C4⋊C4×C79C2211yescharacteristic
72C2×#106×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×#106×C79C2211yescharacteristic
75C2×#106×C79C2211yescharacteristic
76C2×#106×C79C2218yescomplemented
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C22×Dic158C2311yescharacteristic
80C22×C22⋊D79D411yescharacteristic
81C22×C4×D79—21no—
82C22×C4×D79C2311yescharacteristic
83C2×Dic316—24no—
84C2×Dic316C2314yes—
85C2×#11929607—24no—
86C2×#11929607C2314yes—
87C22×C79⋊C8C2311yescharacteristic
88C22×C79⋊C8C2311yescharacteristic
89#14579160—22no—
90#14579160C2314yes—
91#14579156—28no—
92#14579152—22no—
93#14579152C2314yes—
94#14579151—28no—
95#14579151—28no—
96#14579144—28no—
97#14579141—22no—
98#14579141—22no—
99#14579141C2314yes—
100#14579141C2314yes—
101#14579140—22no—
102#14579140—22no—
103#14579140—28no—
104#14579140C2314yes—
105#14579140C2314yes—
106#14579139—28no—
107#14579126—22no—
108#14579126—22no—
109#14579126C2314yes—
110#14579126C2314yes—
111C4×C22⋊D79—28no—
112C4×C22⋊D79D414yes—
113C4×C22⋊D79C2314yes—
114#14579120—28no—
115#14579119—22no—
116#14579119C2314yes—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79C2311yescharacteristic
121C2×C4⋊Dic79C2311yescharacteristic
122C2×Dic79⋊C4—21no—
123C2×Dic79⋊C4—21no—
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4D411yescharacteristic
130C4⋊C4×D79—22no—
131C4⋊C4×D79C2314yes—
132C2×C22⋊Dic79—21no—
133C2×C22⋊Dic79—21no—
134C2×C22⋊Dic79D411yescharacteristic
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4D411yescharacteristic
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79C2311yescharacteristic
143#14579095C2314yes—
144#14579094C2314yes—
145#14579094C2314yes—
146#14579092C2314yes—
147#14579092C2314yes—
148Dic79⋊C8C2314yes—
149#14579086C2314yes—
150#14579086C2314yes—
151#14579084C2314yes—
152#14579084C2314yes—
153#14579084C2314yes—
154#14579084C2314yes—
155C22⋊(C79⋊C8)C2314yes—
156(C2×D79)⋊C8C2314yes—
157#14579071C2314yes—
158C23×C4×C79—21no—
159C23×C4×C79—21no—
160C23×C4×C79C2311yescharacteristic
161C22×C8×C79—24no—
162C22×C8×C79C2311yescharacteristic
163C22×C8×C79C2314yes—
164C22×C8×C79C2311yescharacteristic
165C2×C4⋊C4×C79—22no—
166C2×C4⋊C4×C79—22no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2314yes—
174C2×C4⋊C4×C79C2314yes—
175#106×C79C2314yes—
176#106×C79C2314yes—
177#106×C79C2314yes—
178#106×C79C2314yes—
179C23×D79C2×D411yescharacteristic
180C2×Dic158—24no—
181C2×Dic158—21no—
182C2×Dic158—21no—
183C2×Dic158—22no—
184C2×Dic158—22no—
185C2×Dic158—22no—
186C2×Dic158—22no—
187C2×Dic158—82no—
188C2×Dic158C2412yes—
189C2×Dic158C2412yes—
190C2×C22⋊D79—24no—
191C2×C22⋊D79C2×D414yes—
192C22×Dic79—21no—
193C22×Dic79—21no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79C2×D411yescharacteristic
197C22×Dic79C2×D411yescharacteristic
198C22×Dic79C2×D411yescharacteristic
199C2×C4×D79—24no—
200C2×C4×D79—22no—
201C2×C4×D79—22no—
202C2×C4×D79—82no—
203C2×C4×D79C2×D412yes—
204C2×C4×D79C2412yes—
205Dic316—28no—
206#11929607—28no—
207C2×C79⋊C8—22no—
208C2×C79⋊C8—22no—
209C2×C79⋊C8C2412yes—
210C2×C79⋊C8C2412yes—
211C4⋊Dic79—24no—
212C4⋊Dic79—24no—
213C4⋊Dic79—24no—
214C4⋊Dic79—21no—
215C4⋊Dic79—21no—
216C4⋊Dic79C2412yes—
217C4⋊Dic79C2412yes—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4C2×D414yes—
226C22⋊Dic79—24no—
227C22⋊Dic79—24no—
228C22⋊Dic79C2×D414yes—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4—24no—
232(C2×D79)⋊C4C2×D414yes—
233C4×Dic79—24no—
234C4×Dic79—24no—
235C4×Dic79—24no—
236C4×Dic79C2×D412yes—
237C4×Dic79C2412yes—
238C24×C79C2×D411yescharacteristic
239C22×C4×C79—22no—
240C22×C4×C79—22no—
241C22×C4×C79—21no—
242C22×C4×C79—21no—
243C22×C4×C79—21no—
244C22×C4×C79—21no—
245C22×C4×C79—24no—
246C22×C4×C79—24no—
247C22×C4×C79—44no—
248C22×C4×C79—82no—
249C22×C4×C79C2×D411yescharacteristic
250C22×C4×C79C2×D412yes—
251C22×C4×C79C2412yes—
252C22×C4×C79C2411yescharacteristic
253C2×C8×C79—28no—
254C2×C8×C79—22no—
255C2×C8×C79#4114yes—
256C2×C8×C79C2412yes—
257C2×C8×C79C2412yes—
258C4⋊C4×C79—21no—
259C4⋊C4×C79—21no—
260C4⋊C4×C79—24no—
261C4⋊C4×C79—21no—
262C4⋊C4×C79—21no—
263C4⋊C4×C79—24no—
264C4⋊C4×C79C2412yes—
265C4⋊C4×C79C2412yes—
266C4⋊C4×C79C2412yes—
267C4⋊C4×C79C2412yes—
268C23×C79—22no—
269C23×C79—22no—
270C23×C79#13714yes—
271C23×C79C22×D412yes—
272C23×C79C22×D411yescharacteristic
273C22×D79—22no—
274C22×D79—22no—
275C22×D79—22no—
276C22×D79C22×D412yes—
277C2×C4×C79—22no—
278C2×C4×C79—24no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—48no—
286C2×C4×C79—42no—
287C2×C4×C79—42no—
288C2×C4×C79—42no—
289C2×C4×C79—42no—
290C2×C4×C79—84no—
291C2×C4×C79C22×D412yes—
292C2×C4×C79C22×D411yescharacteristic
293C2×C4×C79C2×#4112yes—
294C2×C4×C792−1+412yes—
295C2×C4×C79C2511yescharacteristic
296C22⋊D79—28no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—42no—
305C2×Dic79—42no—
306C2×Dic79—42no—
307C2×Dic79—42no—
308C2×Dic79C22×D412yes—
309C2×Dic79C22×D412yes—
310C2×Dic79C22×D412yes—
311C4×D79—24no—
312C4×D79—22no—
313C4×D79—22no—
314C4×D79—84no—
315Dic158—22no—
316Dic158—22no—
317Dic158—22no—
318Dic158—22no—
319Dic158—42no—
320Dic158—42no—
321Dic158—84no—
322C8×C79—22no—
323C8×C79C2×#4114yes—
324C79⋊C8—22no—
325C79⋊C8—22no—
326C22×C79—28no—
327C22×C79—22no—
328C22×C79—22no—
329C22×C79#54712yes—
330C22×C79C2×#13714yes—
331C22×C79C2×#13712yes—
332C22×C79#57712yes—
333C22×C79C23×D411yescharacteristic
334C2×D79—22no—
335C2×D79—22no—
336C2×D79—22no—
337C2×D79—44no—
338C4×C79—22no—
339C4×C79—42no—
340C4×C79—42no—
341C4×C79—42no—
342C4×C79—42no—
343C4×C79#54712yes—
344C4×C79C22×#4111yescharacteristic
345C4×C79C2×2−1+411yescharacteristic
346Dic79—22no—
347Dic79—22no—
348Dic79—22no—
349Dic79—42no—
350Dic79—42no—
351Dic79—42no—
352Dic79—42no—
353C2×#3344—791nomaximal, Sylow
354C2×C79—24no—
355C2×C79#334414yescomplemented
356C2×C79C2×#54711yescharacteristic
357C2×C79C22×#13711yescharacteristic
358C2×C79C2×#57711yescharacteristic
359D79—42no—
360C2×#554—791no—
361C2×#552—791no—
362#3344—7916no—
363C2×#501—791no—
364C2×#484—791no—
365C2×#485—791no—
366C2×#483—791no—
367C2×#483—791no—
368C2×#479—791no—
369C2×#475—791no—
370C2×#470—791no—
371C2×#467—791no—
372C2×#441—791no—
373C2×#435—791no—
374C2×#428—791no—
375C22×#106D7911yescharacteristic, complemented
376C79C2×#334411yescharacteristic, complemented, Sylow
377C22×Q16—791no—
378C22×M16—791no—
379C23×C8C2×D7911yescharacteristic
380#554—798no—
381#554—1584no—
382#552—798no—
383#552—1584no—
384C2×C4⋊Q8—791no—
385C2×#126—1581no—
386C2×#125—791no—
387C2×#125—1581no—
388C2×#125—1581no—
389C2×#123—1581no—
390C2×C22⋊Q8—791no—
391C2×C22⋊Q8—791no—
392C2×C22⋊Q8—791no—
393C2×C22⋊Q8—791no—
394C2×C22⋊Q8—1581no—
395C2×C22⋊Q8—1581no—
396C2×C4×Q8—791no—
397C2×C4×Q8—791no—
398C2×C4×D4—791no—
399C2×C4×D4—1581no—
400C2×#117—791no—
401C2×#117—1581no—
402C22×C4⋊C4—791no—
403C22×C4⋊C4C2×D7911yescharacteristic
404C22×C4⋊C4C2×D7911yescharacteristic
405#501—798no—
406#485—798no—
407#484—798no—
408#483—798no—
409#483—798no—
410#479—798no—
411#475—798no—
412#470—798no—
413#467—798no—
414#441—798no—
415#435—798no—
416#428—798no—
417C2×#107—791no—
418C2×#107—791no—
419C2×#107—791no—
420C2×#106—791no—
421C2×#106—791no—
422C2×#106C2×D7911yescharacteristic
423C2×#106C2×D7911yescharacteristic
424C2×#106C2×D7911yescharacteristic
425C2×#106C2×D7911yescharacteristic
426C2×#106C2×D7918yescomplemented
427C2×C4⋊C8—791no—
428C2×#103—791no—
429C2×#103—791no—
430C2×#103—791no—
431C2×#103—791no—
432C2×#103—791no—
433C2×#103—791no—
434C2×C22⋊C8—791no—
435C2×C22⋊C8—791no—
436C2×#97—791no—
437C22×Q8—791no—
438C22×Q8—791no—
439C22×Q8—1581no—
440C22×D4—791no—
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—791no—
444C23×C4—1581no—
445C23×C4C22×D7911yescharacteristic
446C2×Q16—794no—
447C2×Q16—1584no—
448C2×M16—794no—
449C2×M16—1584no—
450C22×C8—24no—
451C22×C8—791no—
452C22×C8—791no—
453C22×C8C22×D7911yescharacteristic
454C22×C8C22×D7914yes—
455C22×C8C22×D7911yescharacteristic
456C4⋊Q8—794no—
457C4⋊Q8—1582no—
458#126—1588no—
459#125—794no—
460#125—1582no—
461#125—1588no—
462#125—1588no—
463#123—1588no—
464C22⋊Q8—794no—
465C22⋊Q8—794no—
466C22⋊Q8—794no—
467C22⋊Q8—794no—
468C22⋊Q8—1588no—
469C22⋊Q8—1588no—
470C22⋊Q8—1582no—
471C22⋊Q8—1582no—
472C22⋊Q8—1582no—
473C22⋊Q8—1582no—
474C4×Q8—794no—
475C4×Q8—794no—
476C4×Q8—1582no—
477C4×Q8—1582no—
478C4×D4—794no—
479C4×D4—794no—
480C4×D4—1588no—
481#117—794no—
482#117—1588no—
483#117—1582no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—791no—
489C2×C4⋊C4—791no—
490C2×C4⋊C4—791no—
491C2×C4⋊C4—794no—
492C2×C4⋊C4—1582no—
493C2×C4⋊C4—1581no—
494C2×C4⋊C4—1581no—
495C2×C4⋊C4—1581no—
496C2×C4⋊C4—1581no—
497C2×C4⋊C4—1581no—
498C2×C4⋊C4—1581no—
499C2×C4⋊C4—1581no—
500C2×C4⋊C4—1581no—
501C2×C4⋊C4—1581no—
502C2×C4⋊C4—1581no—
503C2×C4⋊C4C22×D7911yescharacteristic
504C2×C4⋊C4C22×D7911yescharacteristic
505C2×C4⋊C4C22×D7911yescharacteristic
506C2×C4⋊C4C22×D7911yescharacteristic
507C2×C4⋊C4C22×D7914yes—
508C2×C4⋊C4C22×D7914yes—
509C2×C22⋊C4—791no—
510C2×C22⋊C4—791no—
511C2×C22⋊C4—1581no—
512C2×C22⋊C4—1581no—
513C2×C22⋊C4—1581no—
514C2×C22⋊C4—1581no—
515C2×C22⋊C4—1581no—
516C2×C42—791no—
517C2×C42—1581no—
518C2×C42—1581no—
519C2×C42—1581no—
520#107—794no—
521#107—794no—
522#107—794no—
523#106—794no—
524#106—794no—
525#106C22×D7914yes—
526#106C22×D7914yes—
527#106C22×D7914yes—
528#106C22×D7914yes—
529C4⋊C8—794no—
530#103—794no—
531#103—794no—
532#103—794no—
533#103—794no—
534#103—794no—
535#103—794no—
536C22⋊C8—794no—
537C22⋊C8—794no—
538#97—794no—
539C24—791no—
540C24D4×D7911yescharacteristic
541C2×Q8—792no—
542C2×Q8—792no—
543C2×Q8—6322no—
544C2×Q8—1584no—
545C2×Q8—1582no—
546C2×Q8—1582no—
547C2×Q8—1582no—
548C2×Q8—1582no—
549C2×Q8—1581no—
550C2×Q8—1581no—
551C2×D4—794no—
552C2×D4—1584no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—44no—
562C22×C4—82no—
563C22×C4—791no—
564C22×C4—791no—
565C22×C4—791no—
566C22×C4—792no—
567C22×C4—792no—
568C22×C4—6322no—
569C22×C4—1584no—
570C22×C4—1581no—
571C22×C4—1581no—
572C22×C4—1581no—
573C22×C4—1581no—
574C22×C4—1582no—
575C22×C4—1582no—
576C22×C4D4×D7912yes—
577C22×C4D4×D7911yescharacteristic
578C22×C4C23×D7912yes—
579C22×C4C23×D7911yescharacteristic
580Q16—1588no—
581M16—1588no—
582C2×C8—22no—
583C2×C8—28no—
584C2×C8—792no—
585C2×C8—792no—
586C2×C8—1582no—
587C2×C8—1582no—
588C2×C8#1192962414yes—
589C2×C8C23×D7912yes—
590C2×C8C23×D7912yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—24no—
597C4⋊C4—794no—
598C4⋊C4—792no—
599C4⋊C4—792no—
600C4⋊C4—1584no—
601C4⋊C4—1584no—
602C4⋊C4—1584no—
603C4⋊C4—1584no—
604C4⋊C4—1584no—
605C4⋊C4—1584no—
606C4⋊C4—1584no—
607C4⋊C4—1584no—
608C4⋊C4—1584no—
609C4⋊C4—1584no—
610C4⋊C4—1581no—
611C4⋊C4—1581no—
612C4⋊C4C23×D7912yes—
613C4⋊C4C23×D7912yes—
614C4⋊C4C23×D7912yes—
615C4⋊C4C23×D7912yes—
616C22⋊C4—794no—
617C22⋊C4—794no—
618C22⋊C4—1584no—
619C22⋊C4—1584no—
620C22⋊C4—1584no—
621C22⋊C4—1584no—
622C22⋊C4—1584no—
623C42—792no—
624C42—792no—
625C42—1584no—
626C42—1584no—
627C42—1584no—
628C23—22no—
629C23—22no—
630C23—792no—
631C23—1582no—
632C23—1582no—
633C23—1582no—
634C23#1457919014yes—
635C23C2×D4×D7912yes—
636C23C2×D4×D7911yescharacteristic
637Q8—3162no—
638Q8—3162no—
639Q8—6324no—
640Q8—1582no—
641Q8—1582no—
642Q8—1582no—
643Q8—1582no—
644D4—1588no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—48no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—84no—
659C2×C4—3162no—
660C2×C4—3162no—
661C2×C4—3162no—
662C2×C4—3162no—
663C2×C4—792no—
664C2×C4—792no—
665C2×C4—792no—
666C2×C4—6324no—
667C2×C4—1582no—
668C2×C4—1582no—
669C2×C4—1582no—
670C2×C4—1582no—
671C2×C4—1582no—
672C2×C4—1582no—
673C2×C4—1582no—
674C2×C4—1582no—
675C2×C4—1584no—
676C2×C4—1582no—
677C2×C4C2×D4×D7912yes—
678C2×C4C2×D4×D7911yescharacteristic
679C2×C4C2×#1192962412yes—
680C2×C4#1457920912yes—
681C2×C4C24×D7911yescharacteristic
682C8—22no—
683C8—1582no—
684C8—1582no—
685C8C2×#1192962414yes—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—3164no—
690C22—1582no—
691C22—1582no—
692C22—1582no—
693C22#1909921412yes—
694C22C2×#1457919014yes—
695C22C2×#1457919012yes—
696C22#1909936912yes—
697C22C22×D4×D7911yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—3162no—
704C4—3162no—
705C4—3162no—
706C4—3162no—
707C4—1582no—
708C4—1582no—
709C4—1582no—
710C4#1909921412yes—
711C4C22×#1192962411yescharacteristic
712C4C2×#1457920911yescharacteristic
713C2—24no—
714C2—3162no—
715C2#2377585114yesdirect product factor
716C2C2×#1909921411yescharacteristic
717C2C22×#1457919011yescharacteristic
718C2C2×#1909936911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC22×#106×C79C2
socleC23×C79C22×D4
prime radicalC22×C22⋊D79D4
hypercenterC22×#106D79
hypocenterC79C2×#3344
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
3. #23775851C2direct (N × H)
4. C2×#19098970C2semidirect
5. C2×#19098898C2semidirect
6. C2×#19098907C2semidirect
7. C2×#19098895C2semidirect
8. C2×#19098893C2semidirect
9. C2×#19098873C2semidirect
10. C2×#19098847C2semidirect
11. C2×#19098822C2semidirect
12. C2×#19098804C2semidirect
13. C2×#19098669C2semidirect
15. C2×#19098602C2semidirect
16. C22×#106×C79C2semidirect
42. #19098970C22semidirect
43. #19098907C22semidirect
44. #19098898C22semidirect
45. #19098895C22semidirect
46. #19098893C22semidirect
47. #19098873C22semidirect
48. #19098847C22semidirect
49. #19098822C22semidirect
50. #19098804C22semidirect
51. #19098669C22semidirect
53. #19098602C22semidirect
76. C2×#106×C79C22semidirect
355. C2×C79#3344semidirect
375. C22×#106D79semidirect
376. C79C2×#3344semidirect
426. C2×#106C2×D79semidirect
715. C2#23775851direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992682
C2×#190992482
#237758512
C2×#190989702
C2×#190988982
C2×#190989072
C2×#190988952
C2×#190988932
C2×#190988732
C2×#190988472
C2×#190988222
C2×#190988042
C2×#190986692
C2×#190986342
C2×#190986022
C22×#106×C792
C2×#334479