Finite Group Databasebeta

← C2×#23776010 #35167002

Subgroups — C2×#23776010 #35167002

Order 20224.

1866 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×#19099284C211yesmaximal, characteristic
2C2×#19099271C211yesmaximal, characteristic
3#23776010C2116yesmaximal, direct product factor
4C2×#19098960C211yesmaximal, characteristic, complemented
5C2×#19098903C211yesmaximal, characteristic, complemented
6C2×#19098901C211yesmaximal, characteristic, complemented
7C2×#19098892C211yesmaximal, characteristic, complemented
8C2×#19098891C211yesmaximal, characteristic, complemented
9C2×#19098856C211yesmaximal, characteristic, complemented
10C2×#19098846C211yesmaximal, characteristic, complemented
11C2×#19098818C211yesmaximal, characteristic, complemented
12C2×Q16×Dic79C211yesmaximal, characteristic, complemented
13C2×#19098639C211yesmaximal, characteristic
14C2×#19098605C211yesmaximal, characteristic, complemented
15C2×#19098602C211yesmaximal, characteristic, complemented
16C2×#470×C79C211yesmaximal, characteristic, complemented
17C22×#11929607C2211yescharacteristic
18#19099284—24no—
19#19099284C2218yes—
20#19099271—24no—
21#19099271C2218yes—
22C2×#14579160C2211yescharacteristic
23C2×#14579160C2211yescharacteristic
24C2×#14579156—21no—
25C2×#14579154—21no—
26C2×#14579151—21no—
27C2×#14579147—21no—
28C2×#14579141—21no—
29C2×#14579138—21no—
30C2×#14579137C2211yescharacteristic
31C2×#14579137C2211yescharacteristic
32C2×Q8×Dic79C2211yescharacteristic
33C2×Q8×Dic79C2211yescharacteristic
34C2×#14579126—21no—
35C2×C4×C22⋊D79C2211yescharacteristic
36C2×(C22⋊D79)⋊C4—21no—
37C2×#14579120C2211yescharacteristic
38C2×#14579119C2211yescharacteristic
39C22×C4⋊Dic79C2211yescharacteristic
40C2×C4⋊C4×D79C2211yescharacteristic
41#19098960C2218yescomplemented
42#19098903C2218yescomplemented
43#19098901C2218yescomplemented
44#19098892C2218yescomplemented
45#19098891C2218yescomplemented
46#19098856C2218yescomplemented
47#19098846C2218yescomplemented
48#19098818C2218yescomplemented
49Q16×Dic79C2218yescomplemented
50#19098639C2218yes—
51#19098605C2218yescomplemented
52#19098602C2218yescomplemented
53C2×#14579095C2211yescharacteristic
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579093C2211yescharacteristic
58C2×#14579092C2211yescharacteristic
59C2×#14579092C2211yescharacteristic
60C2×#14579092C2211yescharacteristic
61C2×Dic79⋊C8C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579085C2211yescharacteristic
65C2×#14579085C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×Q16×C79C2211yescharacteristic
70C22×M16×C79C2211yescharacteristic
71C2×C22⋊Q8×C79C2211yescharacteristic
72C2×C22⋊Q8×C79C2211yescharacteristic
73#470×C79C2218yescomplemented
74C2×#106×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C22×C22⋊D79D411yescharacteristic
80C23×Dic79—21no—
81C22×C4×D79—21no—
82C22×C4×D79C2311yescharacteristic
83C2×#11929607—24no—
84C2×#11929607C2314yes—
85C22×C79⋊C8C2311yescharacteristic
86C22×C79⋊C8C2311yescharacteristic
87#14579160—22no—
88#14579160—22no—
89#14579160C2314yes—
90#14579160C2314yes—
91#14579156—28no—
92#14579154—28no—
93#14579151—28no—
94#14579147—28no—
95#14579141—28no—
96#14579138—28no—
97#14579137—22no—
98#14579137—22no—
99#14579137C2314yes—
100#14579137C2314yes—
101Q8×Dic79—22no—
102Q8×Dic79—22no—
103Q8×Dic79C2314yes—
104Q8×Dic79C2314yes—
105#14579126—28no—
106C4×C22⋊D79D414yes—
107C4×C22⋊D79C2314yes—
108(C22⋊D79)⋊C4—28no—
109#14579120—22no—
110#14579120C2314yes—
111#14579119—22no—
112#14579119C2314yes—
113C2×C4⋊Dic79—22no—
114C2×C4⋊Dic79—21no—
115C2×C4⋊Dic79—21no—
116C2×C4⋊Dic79—21no—
117C2×C4⋊Dic79C2314yes—
118C2×C4⋊Dic79C2311yescharacteristic
119C2×C4⋊Dic79C2311yescharacteristic
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⋊C4D411yescharacteristic
128C4⋊C4×D79—22no—
129C4⋊C4×D79C2314yes—
130C2×C22⋊Dic79—21no—
131C2×C22⋊Dic79D411yescharacteristic
132C2×(C2×D79)⋊C4—21no—
133C2×(C2×D79)⋊C4—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4D411yescharacteristic
136C2×C4×Dic79—21no—
137C2×C4×Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79C2311yescharacteristic
141#14579095C2314yes—
142#14579095C2314yes—
143#14579094C2314yes—
144#14579093C2314yes—
145#14579093C2314yes—
146#14579092C2314yes—
147#14579092C2314yes—
148#14579092C2314yes—
149Dic79⋊C8C2314yes—
150#14579085C2314yes—
151#14579085C2314yes—
152#14579085C2314yes—
153#14579085C2314yes—
154C22⋊(C79⋊C8)C2314yes—
155(C2×D79)⋊C8C2314yes—
156C8×Dic79C2314yes—
157C22×Q8×C79C2311yescharacteristic
158C22×Q8×C79C2311yescharacteristic
159C23×C4×C79C2311yescharacteristic
160C2×Q16×C79—24no—
161C2×Q16×C79C2314yes—
162C2×M16×C79—24no—
163C2×M16×C79C2314yes—
164C22×C8×C79C2311yescharacteristic
165C22×C8×C79C2311yescharacteristic
166C22⋊Q8×C79—22no—
167C22⋊Q8×C79—22no—
168C22⋊Q8×C79C2314yes—
169C22⋊Q8×C79C2314yes—
170C2×C4⋊C4×C79—21no—
171C2×C4⋊C4×C79—21no—
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176#106×C79C2314yes—
177#103×C79C2314yes—
178#103×C79C2314yes—
179C23×D79C2×D411yescharacteristic
180C2×Dic158—24no—
181C2×Dic158—24no—
182C2×Dic158—44no—
183C2×Dic158—82no—
184C2×C22⋊D79—24no—
185C2×C22⋊D79C2×D414yes—
186C22×Dic79—21no—
187C22×Dic79—21no—
188C22×Dic79—21no—
189C22×Dic79—21no—
190C22×Dic79—24no—
191C22×Dic79—82no—
192C22×Dic79C2×D411yescharacteristic
193C22×Dic79C2×D411yescharacteristic
194C22×Dic79C2×D411yescharacteristic
195C2×C4×D79—24no—
196C2×C4×D79—22no—
197C2×C4×D79—22no—
198C2×C4×D79—82no—
199C2×C4×D79C2×D412yes—
200C2×C4×D79C2412yes—
201#11929607—28no—
202C2×C79⋊C8—22no—
203C2×C79⋊C8—22no—
204C2×C79⋊C8C2412yes—
205C2×C79⋊C8C2412yes—
206C4⋊Dic79—24no—
207C4⋊Dic79—24no—
208C4⋊Dic79—21no—
209C4⋊Dic79—21no—
210C4⋊Dic79—24no—
211C4⋊Dic79—21no—
212C4⋊Dic79—21no—
213C4⋊Dic79C2412yes—
214C4⋊Dic79C2412yes—
215C4⋊Dic79C2412yes—
216C4⋊Dic79C2412yes—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4C2×D414yes—
223C22⋊Dic79—24no—
224C22⋊Dic79C2×D414yes—
225(C2×D79)⋊C4—24no—
226(C2×D79)⋊C4—24no—
227(C2×D79)⋊C4—24no—
228(C2×D79)⋊C4C2×D414yes—
229C4×Dic79—24no—
230C4×Dic79—24no—
231C4×Dic79—24no—
232C4×Dic79—24no—
233C4×Dic79C2×D412yes—
234C4×Dic79C2412yes—
235C24×C79C2×D411yescharacteristic
236C2×Q8×C79—21no—
237C2×Q8×C79—21no—
238C2×Q8×C79—22no—
239C2×Q8×C79—22no—
240C2×Q8×C79—22no—
241C2×Q8×C79—22no—
242C2×Q8×C79C2412yes—
243C2×Q8×C79C2412yes—
244C22×C4×C79—22no—
245C22×C4×C79—22no—
246C22×C4×C79—21no—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79C2×D411yescharacteristic
251C22×C4×C79C2×D412yes—
252C22×C4×C79C2412yes—
253C22×C4×C79C2411yescharacteristic
254Q16×C79—28no—
255M16×C79—28no—
256C2×C8×C79—22no—
257C2×C8×C79#4114yes—
258C2×C8×C79C2412yes—
259C2×C8×C79C2412yes—
260C4⋊C4×C79—24no—
261C4⋊C4×C79—24no—
262C4⋊C4×C79—21no—
263C4⋊C4×C79—21no—
264C4⋊C4×C79C2412yes—
265C4⋊C4×C79C2412yes—
266C22⋊C4×C79—24no—
267C22⋊C4×C79—24no—
268C23×C79—22no—
269C23×C79—22no—
270C23×C79—22no—
271C23×C79C22×D412yes—
272C23×C79C22×D411yescharacteristic
273C22×D79—22no—
274C22×D79—22no—
275C22×D79—22no—
276C22×D79C22×D412yes—
277Q8×C79—22no—
278Q8×C79—22no—
279Q8×C79—22no—
280Q8×C79—22no—
281Q8×C79—42no—
282Q8×C79—42no—
283C2×C4×C79—22no—
284C2×C4×C79—24no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—42no—
292C2×C4×C79—42no—
293C2×C4×C79—42no—
294C2×C4×C79—42no—
295C2×C4×C79C22×D412yes—
296C2×C4×C79C22×D411yescharacteristic
297C2×C4×C79C2×#4112yes—
298C2×C4×C792−1+412yes—
299C2×C4×C79C2511yescharacteristic
300C22⋊D79—28no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—42no—
308C2×Dic79—42no—
309C2×Dic79—42no—
310C2×Dic79—42no—
311C2×Dic79—84no—
312C2×Dic79#13714yes—
313C2×Dic79C22×D412yes—
314C2×Dic79C22×D412yes—
315C2×Dic79C22×D412yes—
316C4×D79—24no—
317C4×D79—22no—
318C4×D79—22no—
319C4×D79—84no—
320Dic158—48no—
321Dic158—84no—
322C8×C79—22no—
323C8×C79C2×#4114yes—
324C79⋊C8—22no—
325C79⋊C8—22no—
326C22×C79—22no—
327C22×C79—22no—
328C22×C79—22no—
329C22×C79—44no—
330C22×C79#54712yes—
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—42no—
349Dic79—42no—
350Dic79—42no—
351Dic79—42no—
352Dic79C2×#13714yes—
353C2×#3356—791nomaximal, Sylow
354C2×C79—42no—
355C2×C79#335614yescomplemented
356C2×C79C2×#54711yescharacteristic
357C2×C79C22×#13711yescharacteristic
358C2×C79C2×#57711yescharacteristic
359D79—42no—
360C2×#556—791no—
361C2×#554—791no—
362#3356—7916no—
363C2×#498—791no—
364C2×#485—791no—
365C2×#485—791no—
366C2×#483—791no—
367C2×#483—791no—
368C2×#477—791no—
369C2×#475—791no—
370C2×#470—791no—
371C2×#470D7911yescharacteristic, complemented
372C2×C4×Q16—791no—
373C2×#436—791no—
374C2×#428—791no—
375C2×#428—791no—
376C79C2×#335611yescharacteristic, complemented, Sylow
377C22×Q16C2×D7911yescharacteristic
378C22×M16—791no—
379C22×M16C2×D7911yescharacteristic
380#556—798no—
381#556—1584no—
382#554—798no—
383#554—1584no—
384C2×C4⋊Q8—791no—
385C2×C4⋊Q8—791no—
386C2×#126—1581no—
387C2×#126—1581no—
388C2×#125—1581no—
389C2×#124—1581no—
390C2×C22⋊Q8—791no—
391C2×C22⋊Q8—791no—
392C2×C22⋊Q8—1581no—
393C2×C22⋊Q8—1581no—
394C2×C22⋊Q8C2×D7911yescharacteristic
395C2×C22⋊Q8C2×D7911yescharacteristic
396C2×C4×Q8—791no—
397C2×C4×Q8—791no—
398C2×C4×Q8—1581no—
399C2×C4×D4—791no—
400C2×C4×D4—1581no—
401C2×#117—791no—
402C2×#117—791no—
403C22×C4⋊C4—791no—
404C22×C4⋊C4—791no—
405#498—798no—
406#485—798no—
407#485—798no—
408#483—798no—
409#483—798no—
410#477—798no—
411#475—798no—
412#470—798no—
413#470C2×D7918yescomplemented
414C4×Q16—798no—
415#436—798no—
416#428—798no—
417#428—798no—
418C2×#107—791no—
419C2×#107—791no—
420C2×#107—791no—
421C2×#106—791no—
422C2×#106—791no—
423C2×#106—791no—
424C2×#106—791no—
425C2×#106—791no—
426C2×#106C2×D7911yescharacteristic
427C2×C4⋊C8—791no—
428C2×#103—791no—
429C2×#103—791no—
430C2×#103—791no—
431C2×#103—791no—
432C2×#103C2×D7911yescharacteristic
433C2×#103C2×D7911yescharacteristic
434C2×C22⋊C8—791no—
435C2×C22⋊C8—791no—
436C2×C4×C8—791no—
437C22×Q8—1581no—
438C22×Q8—1581no—
439C22×Q8C22×D7911yescharacteristic
440C22×Q8C22×D7911yescharacteristic
441C22×D4—791no—
442C23×C4—791no—
443C23×C4—1581no—
444C23×C4—1581no—
445C23×C4C22×D7911yescharacteristic
446C2×Q16—24no—
447C2×Q16C22×D7914yes—
448C2×M16—24no—
449C2×M16—794no—
450C2×M16—1584no—
451C2×M16C22×D7914yes—
452C22×C8—791no—
453C22×C8—791no—
454C22×C8C22×D7911yescharacteristic
455C22×C8C22×D7911yescharacteristic
456C4⋊Q8—794no—
457C4⋊Q8—794no—
458C4⋊Q8—1582no—
459C4⋊Q8—1582no—
460#126—1588no—
461#126—1588no—
462#125—1588no—
463#124—1588no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—794no—
467C22⋊Q8—794no—
468C22⋊Q8—1588no—
469C22⋊Q8—1588no—
470C22⋊Q8—1582no—
471C22⋊Q8—1582no—
472C22⋊Q8C22×D7914yes—
473C22⋊Q8C22×D7914yes—
474C4×Q8—794no—
475C4×Q8—794no—
476C4×Q8—1582no—
477C4×Q8—1582no—
478C4×Q8—1588no—
479C4×D4—794no—
480C4×D4—794no—
481C4×D4—1588no—
482#117—794no—
483#117—794no—
484#117—1582no—
485#117—1582no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—791no—
489C2×C4⋊C4—791no—
490C2×C4⋊C4—791no—
491C2×C4⋊C4—794no—
492C2×C4⋊C4—791no—
493C2×C4⋊C4—791no—
494C2×C4⋊C4—794no—
495C2×C4⋊C4—1582no—
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⋊C4—1581no—
504C2×C4⋊C4—1582no—
505C2×C4⋊C4C22×D7911yescharacteristic
506C2×C4⋊C4C22×D7911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
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×C42—791no—
516C2×C42—1581no—
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#106—794no—
526#106—794no—
527#106—794no—
528#106C22×D7914yes—
529C4⋊C8—794no—
530#103—794no—
531#103—794no—
532#103—794no—
533#103—794no—
534#103C22×D7914yes—
535#103C22×D7914yes—
536C22⋊C8—794no—
537C22⋊C8—794no—
538C4×C8—794no—
539C24—791no—
540C24D4×D7911yescharacteristic
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—3164no—
548C2×Q8—6322no—
549C2×Q8—1584no—
550C2×Q8—1584no—
551C2×Q8C23×D7912yes—
552C2×Q8C23×D7912yes—
553C2×D4—794no—
554C2×D4—1584no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—791no—
562C22×C4—791no—
563C22×C4—791no—
564C22×C4—792no—
565C22×C4—792no—
566C22×C4—6322no—
567C22×C4—6322no—
568C22×C4—1584no—
569C22×C4—1581no—
570C22×C4—1581no—
571C22×C4—1581no—
572C22×C4—1581no—
573C22×C4—1584no—
574C22×C4—1582no—
575C22×C4—1582no—
576C22×C4D4×D7912yes—
577C22×C4D4×D7911yescharacteristic
578C22×C4C23×D7912yes—
579C22×C4C23×D7911yescharacteristic
580Q16—28no—
581M16—28no—
582M16—1588no—
583C2×C8—22no—
584C2×C8—792no—
585C2×C8—792no—
586C2×C8—1582no—
587C2×C8—1582no—
588C2×C8#1192962314yes—
589C2×C8C23×D7912yes—
590C2×C8C23×D7912yes—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—794no—
596C4⋊C4—792no—
597C4⋊C4—792no—
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—1581no—
608C4⋊C4—1584no—
609C4⋊C4—1581no—
610C4⋊C4—1581no—
611C4⋊C4—1581no—
612C4⋊C4C23×D7912yes—
613C4⋊C4C23×D7912yes—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—794no—
617C22⋊C4—794no—
618C22⋊C4—1584no—
619C22⋊C4—1584no—
620C22⋊C4—1584no—
621C22⋊C4—1584no—
622C42—792no—
623C42—792no—
624C42—1584no—
625C42—1584no—
626C42—1584no—
627C42—1584no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—792no—
632C23—1582no—
633C23—1582no—
634C23—1582no—
635C23C2×D4×D7912yes—
636C23C2×D4×D7911yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—42no—
642Q8—42no—
643Q8—3168no—
644Q8—6324no—
645D4—1588no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—3162no—
659C2×C4—3162no—
660C2×C4—3162no—
661C2×C4—3162no—
662C2×C4—794no—
663C2×C4—792no—
664C2×C4—792no—
665C2×C4—792no—
666C2×C4—6324no—
667C2×C4—6324no—
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×#1192962312yes—
680C2×C4#1457920812yes—
681C2×C4C24×D7911yescharacteristic
682C8—22no—
683C8—1582no—
684C8—1582no—
685C8C2×#1192962314yes—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—44no—
690C22—3164no—
691C22—1582no—
692C22—1582no—
693C22—1582no—
694C22#1909921312yes—
695C22#137×D7912yes—
696C22#1909937212yes—
697C22C22×D4×D7911yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—3162no—
704C4—3162no—
705C4—3162no—
706C4—3162no—
707C4—794no—
708C4—1582no—
709C4—1582no—
710C4#1909921312yes—
711C4C22×#1192962311yescharacteristic
712C4C2×#1457920811yescharacteristic
713C2—42no—
714C2—3162no—
715C2#2377601014yesdirect product factor
716C2C2×#1909921311yescharacteristic
717C2C2×#137×D7911yescharacteristic
718C2C2×#1909937211yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#470×C79C2
socleC23×C79C22×D4
prime radicalC22×C22⋊D79D4
hypercenterC2×#470D79
hypocenterC79C2×#3356
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
3. #23776010C2direct (N × H)
4. C2×#19098960C2semidirect
5. C2×#19098903C2semidirect
6. C2×#19098901C2semidirect
7. C2×#19098892C2semidirect
8. C2×#19098891C2semidirect
9. C2×#19098856C2semidirect
10. C2×#19098846C2semidirect
11. C2×#19098818C2semidirect
12. C2×Q16×Dic79C2semidirect
14. C2×#19098605C2semidirect
15. C2×#19098602C2semidirect
16. C2×#470×C79C2semidirect
41. #19098960C22semidirect
42. #19098903C22semidirect
43. #19098901C22semidirect
44. #19098892C22semidirect
45. #19098891C22semidirect
46. #19098856C22semidirect
47. #19098846C22semidirect
48. #19098818C22semidirect
49. Q16×Dic79C22semidirect
51. #19098605C22semidirect
52. #19098602C22semidirect
73. #470×C79C22semidirect
355. C2×C79#3356semidirect
371. C2×#470D79semidirect
376. C79C2×#3356semidirect
413. #470C2×D79semidirect
715. C2#23776010direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992842
C2×#190992712
#237760102
C2×#190989602
C2×#190989032
C2×#190989012
C2×#190988922
C2×#190988912
C2×#190988562
C2×#190988462
C2×#190988182
C2×Q16×Dic792
C2×#190986392
C2×#190986052
C2×#190986022
C2×#470×C792
C2×#335679