Finite Group Databasebeta

← C2×#23773203 #35155787

Subgroups — C2×#23773203 #35155787

Order 20224.

2098 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099119C211yesmaximal, characteristic
2C2×C4×Q8×D79C211yesmaximal, characteristic
3#23773203C2116yesmaximal, direct product factor
4C2×#19098871C211yesmaximal, characteristic, complemented
5C2×#19098870C211yesmaximal, characteristic, complemented
6C2×#19098867C211yesmaximal, characteristic, complemented
7C2×#19098857C211yesmaximal, characteristic, complemented
8C2×#19098856C211yesmaximal, characteristic, complemented
9C2×#19098847C211yesmaximal, characteristic, complemented
10C2×#19098846C211yesmaximal, characteristic, complemented
11C2×#19098604C211yesmaximal, characteristic
12C2×#19098602C211yesmaximal, characteristic
13C2×#19098585C211yesmaximal, characteristic
14C2×#19098570C211yesmaximal, characteristic
15C2×#19098570C211yesmaximal, characteristic
16C2×#479×C79C211yesmaximal, characteristic, complemented
17C22×Q8×D79C2211yescharacteristic
18C22×#11929607C2211yescharacteristic
19C22×#11929607C2211yescharacteristic
20#19099119—24no—
21#19099119C2218yes—
22C2×#14579160C2211yescharacteristic
23C2×#14579160C2211yescharacteristic
24C2×#14579153C2211yescharacteristic
25C2×#14579139—21no—
26C2×#14579139—21no—
27C2×Q8×Dic79C2211yescharacteristic
28C2×C4×Dic158—21no—
29C2×C4×Dic158C2211yescharacteristic
30C2×#14579126—21no—
31C2×#14579126—21no—
32C2×#14579126—21no—
33C2×#14579126C2211yescharacteristic
34C4×Q8×D79—24no—
35C4×Q8×D79C2218yes—
36C2×#14579119C2211yescharacteristic
37C2×#14579119C2211yescharacteristic
38C2×C4⋊C4×D79—21no—
39C2×C4⋊C4×D79C2211yescharacteristic
40C2×C42×D79—21no—
41C2×C42×D79C2211yescharacteristic
42#19098871C2218yescomplemented
43#19098870C2218yescomplemented
44#19098867C2218yescomplemented
45#19098857C2218yescomplemented
46#19098856C2218yescomplemented
47#19098847C2218yescomplemented
48#19098846C2218yescomplemented
49#19098604C2218yes—
50#19098602C2218yes—
51C2×#14579095C2211yescharacteristic
52C2×#14579094C2211yescharacteristic
53C2×#14579094C2211yescharacteristic
54C2×#14579093C2211yescharacteristic
55C2×#14579092C2211yescharacteristic
56C2×#14579092C2211yescharacteristic
57#19098585C2218yes—
58C2×C4⋊(C79⋊C8)C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×Dic79⋊C8C2211yescharacteristic
61#19098570C2218yes—
62#19098570C2218yes—
63C2×#14579086C2211yescharacteristic
64C2×#14579086C2211yescharacteristic
65C2×#14579085C2211yescharacteristic
66C2×#14579085C2211yescharacteristic
67C2×#14579084C2211yescharacteristic
68C2×#14579084C2211yescharacteristic
69C2×#125×C79C2211yescharacteristic
70C2×C4×Q8×C79C2211yescharacteristic
71#479×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×C4⋊C8×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C22×Dic158—21no—
80C22×Dic158C2311yescharacteristic
81C2×Q8×D79—22no—
82C2×Q8×D79—24no—
83C2×Q8×D79Q818yescomplemented
84C2×Q8×D79C2314yes—
85C22×C4×D79—21no—
86C22×C4×D79—21no—
87C22×C4×D79D411yescharacteristic
88C22×C4×D79D411yescharacteristic
89C22×C4×D79C2311yescharacteristic
90C2×#11929607—24no—
91C2×#11929607—24no—
92C2×#11929607C2314yes—
93C2×#11929607C2314yes—
94C22×C79⋊C8C2311yescharacteristic
95C22×C79⋊C8C2311yescharacteristic
96#14579160—22no—
97#14579160—22no—
98#14579160C2314yes—
99#14579160C2314yes—
100#14579153—22no—
101#14579153C2314yes—
102#14579139—28no—
103#14579139—28no—
104Q8×Dic79—22no—
105Q8×Dic79C2314yes—
106C4×Dic158—22no—
107C4×Dic158—28no—
108C4×Dic158C2314yes—
109#14579126—22no—
110#14579126—28no—
111#14579126—28no—
112#14579126—28no—
113#14579126C2314yes—
114#14579119—22no—
115#14579119—22no—
116#14579119C2314yes—
117#14579119C2314yes—
118C2×C4⋊Dic79—21no—
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⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C4⋊C4×D79—28no—
130C4⋊C4×D79—22no—
131C4⋊C4×D79C2314yes—
132C2×(C2×D79)⋊C4—21no—
133C2×(C2×D79)⋊C4—21no—
134C2×C4×Dic79—21no—
135C2×C4×Dic79—21no—
136C2×C4×Dic79—21no—
137C2×C4×Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79D411yescharacteristic
140C2×C4×Dic79D411yescharacteristic
141C2×C4×Dic79C2311yescharacteristic
142C42×D79—28no—
143C42×D79D414yes—
144C42×D79C2314yes—
145#14579095C2314yes—
146#14579094C2314yes—
147#14579094C2314yes—
148#14579093C2314yes—
149#14579092C2314yes—
150#14579092C2314yes—
151C4⋊(C79⋊C8)C2314yes—
152Dic79⋊C8C2314yes—
153Dic79⋊C8C2314yes—
154#14579086C2314yes—
155#14579086C2314yes—
156#14579085C2314yes—
157#14579085C2314yes—
158#14579084C2314yes—
159#14579084C2314yes—
160C22×Q8×C79C2311yescharacteristic
161C22×C8×C79C2311yescharacteristic
162C22×C8×C79C2311yescharacteristic
163#125×C79—22no—
164#125×C79C2314yes—
165C4×Q8×C79—22no—
166C4×Q8×C79C2314yes—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C42×C79—21no—
174C2×C42×C79C2311yescharacteristic
175#107×C79C2314yes—
176#106×C79C2314yes—
177C4⋊C8×C79C2314yes—
178#103×C79C2314yes—
179#103×C79C2314yes—
180C23×D79C2×D411yescharacteristic
181C2×Dic158—28no—
182C2×Dic158—24no—
183C2×Dic158—24no—
184C2×Dic158—24no—
185C2×Dic158—21no—
186C2×Dic158—22no—
187C2×Dic158—44no—
188C2×Dic158—44no—
189C2×Dic158C2×Q814yes—
190C2×Dic158C2412yes—
191Q8×D79—216no—
192Q8×D79—28no—
193Q8×D79C2×Q8116yescomplemented
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79C2×D411yescharacteristic
199C22×Dic79C2×D411yescharacteristic
200C22×Dic79C2×D411yescharacteristic
201C2×C4×D79—24no—
202C2×C4×D79—28no—
203C2×C4×D79—24no—
204C2×C4×D79—24no—
205C2×C4×D79—42no—
206C2×C4×D79—44no—
207C2×C4×D79C2×D414yes—
208C2×C4×D79C2×D414yes—
209C2×C4×D79C2×D412yes—
210C2×C4×D79C2×Q814yes—
211C2×C4×D79#4114yes—
212C2×C4×D79C2412yes—
213#11929607—28no—
214#11929607—28no—
215C2×C79⋊C8—22no—
216C2×C79⋊C8—22no—
217C2×C79⋊C8C2412yes—
218C2×C79⋊C8C2412yes—
219C4⋊Dic79—24no—
220C4⋊Dic79—21no—
221C4⋊Dic79—21no—
222C4⋊Dic79—21no—
223C4⋊Dic79C2412yes—
224C4⋊Dic79C2412yes—
225C4⋊Dic79C2412yes—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228Dic79⋊C4—24no—
229Dic79⋊C4—24no—
230Dic79⋊C4—24no—
231Dic79⋊C4—24no—
232Dic79⋊C4—24no—
233(C2×D79)⋊C4—24no—
234(C2×D79)⋊C4—24no—
235C4×Dic79—24no—
236C4×Dic79—24no—
237C4×Dic79—24no—
238C4×Dic79—24no—
239C4×Dic79—24no—
240C4×Dic79C2×D412yes—
241C4×Dic79C2×D414yes—
242C4×Dic79C2×D414yes—
243C4×Dic79C2412yes—
244C2×Q8×C79—21no—
245C2×Q8×C79—22no—
246C2×Q8×C79C2×Q814yes—
247C2×Q8×C79C2412yes—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79—21no—
251C22×C4×C79—21no—
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2411yescharacteristic
255C2×C8×C79—22no—
256C2×C8×C79—22no—
257C2×C8×C79C2412yes—
258C2×C8×C79C2412yes—
259C4⋊C4×C79—24no—
260C4⋊C4×C79—24no—
261C4⋊C4×C79—24no—
262C4⋊C4×C79—21no—
263C4⋊C4×C79—21no—
264C4⋊C4×C79—21no—
265C4⋊C4×C79C2412yes—
266C4⋊C4×C79C2412yes—
267C4⋊C4×C79C2412yes—
268C42×C79—24no—
269C42×C79C2×D412yes—
270C42×C79C2412yes—
271C23×C79C22×D411yescharacteristic
272C22×D79—22no—
273C22×D79—22no—
274C22×D79C22⋊Q814yes—
275C22×D79C22×D412yes—
276Q8×C79—24no—
277Q8×C79—22no—
278Q8×C79C22×Q814yes—
279C2×C4×C79—24no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—42no—
287C2×C4×C79—42no—
288C2×C4×C79—42no—
289C2×C4×C79C22×D412yes—
290C2×C4×C79C22×D412yes—
291C2×C4×C79C22×D411yescharacteristic
292C2×C4×C79C22×Q812yes—
293C2×C4×C79C2×#4112yes—
294C2×C4×C79C2511yescharacteristic
295C2×Dic79—24no—
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—42no—
302C2×Dic79—42no—
303C2×Dic79—42no—
304C2×Dic79C22⋊Q814yes—
305C2×Dic79#13714yes—
306C2×Dic79C22×D412yes—
307C2×Dic79C22×D412yes—
308C2×Dic79C22×D412yes—
309C4×D79—216no—
310C4×D79—28no—
311C4×D79—44no—
312C4×D79—48no—
313C4×D79C22⋊Q818yes—
314C4×D79C22×Q814yes—
315C4×D79C2×#4114yes—
316Dic158—24no—
317Dic158—22no—
318Dic158—216no—
319Dic158—48no—
320Dic158—48no—
321Dic158C22×Q814yes—
322C8×C79—22no—
323C8×C79—22no—
324C79⋊C8—22no—
325C79⋊C8—22no—
326C22×C79C2×C22⋊Q812yes—
327C22×C79C2×#13712yes—
328C22×C79#57512yes—
329C22×C79C23×D411yescharacteristic
330C2×D79—28no—
331C2×D79—22no—
332C2×D79—22no—
333C2×D79C2×C22⋊Q814yes—
334C4×C79—24no—
335C4×C79—22no—
336C4×C79—22no—
337C4×C79—42no—
338C4×C79—42no—
339C4×C79—42no—
340C4×C79C2×C22⋊Q812yes—
341C4×C79C23×Q811yescharacteristic
342C4×C79C22×#4111yescharacteristic
343Dic79—24no—
344Dic79—22no—
345Dic79—42no—
346Dic79—42no—
347Dic79—42no—
348Dic79C2×C22⋊Q814yes—
349Dic79C2×#13714yes—
350C2×#3078—791nomaximal, Sylow
351C2×C79#307814yescomplemented
352C2×C79C22×C22⋊Q811yescharacteristic
353C2×C79C22×#13711yescharacteristic
354C2×C79C2×#57511yescharacteristic
355D79—24no—
356C2×#533—791no—
357C22×C4×Q8—791no—
358#3078—7916no—
359C2×#479—791no—
360C2×#479—791no—
361C2×#479—791no—
362C2×#479D7911yescharacteristic, complemented
363C2×#477—791no—
364C2×#477—791no—
365C2×#475—791no—
366C2×#475—791no—
367C2×#428—791no—
368C2×#428—791no—
369C2×#423—791no—
370C2×#419—791no—
371C2×#419—791no—
372C79C2×#307811yescharacteristic, complemented, Sylow
373C23×Q8—791no—
374C22×M16—791no—
375C22×M16—791no—
376#533—798no—
377#533—1584no—
378C2×C4⋊Q8—791no—
379C2×C4⋊Q8—791no—
380C2×#125—791no—
381C2×#125C2×D7911yescharacteristic
382C2×C22⋊Q8—1581no—
383C2×C22⋊Q8—1581no—
384C2×C4×Q8—791no—
385C2×C4×Q8—798no—
386C2×C4×Q8—791no—
387C2×C4×Q8—791no—
388C2×C4×Q8—1581no—
389C2×C4×Q8—1581no—
390C2×C4×Q8—1581no—
391C2×C4×Q8—1581no—
392C2×C4×Q8—1584no—
393C2×C4×Q8C2×D7911yescharacteristic
394C2×#117—791no—
395C2×#117—791no—
396C22×C4⋊C4—791no—
397C22×C4⋊C4—1581no—
398C22×C42—791no—
399C22×C42—1581no—
400#479—798no—
401#479—798no—
402#479—798no—
403#479C2×D7918yescomplemented
404#477—798no—
405#477—798no—
406#475—798no—
407#475—798no—
408#428—798no—
409#428—798no—
410C2×#107—791no—
411C2×#107—791no—
412C2×#107—791no—
413C2×#107C2×D7911yescharacteristic
414C2×#106—791no—
415C2×#106—791no—
416C2×#106—791no—
417C2×#106C2×D7911yescharacteristic
418#423—798no—
419C2×C4⋊C8—791no—
420C2×C4⋊C8—791no—
421C2×C4⋊C8—791no—
422C2×C4⋊C8C2×D7911yescharacteristic
423#419—798no—
424#419—798no—
425C2×#103—791no—
426C2×#103—791no—
427C2×#103—791no—
428C2×#103—791no—
429C2×#103—791no—
430C2×#103—791no—
431C2×#103C2×D7911yescharacteristic
432C2×#103C2×D7911yescharacteristic
433C22×Q8—798no—
434C22×Q8—794no—
435C22×Q8—791no—
436C22×Q8—1581no—
437C22×Q8—1581no—
438C22×Q8—1581no—
439C22×Q8—1582no—
440C22×Q8—1584no—
441C22×Q8C22×D7911yescharacteristic
442C23×C4—791no—
443C23×C4—791no—
444C23×C4—791no—
445C23×C4—1581no—
446C23×C4—1581no—
447C2×M16—794no—
448C2×M16—794no—
449C2×M16—1584no—
450C2×M16—1584no—
451C22×C8—791no—
452C22×C8—791no—
453C22×C8C22×D7911yescharacteristic
454C22×C8C22×D7911yescharacteristic
455C4⋊Q8—794no—
456C4⋊Q8—794no—
457C4⋊Q8—1582no—
458C4⋊Q8—1582no—
459#125—22no—
460#125—794no—
461#125—1582no—
462#125C22×D7914yes—
463C22⋊Q8—1588no—
464C22⋊Q8—1588no—
465C4×Q8—22no—
466C4×Q8—794no—
467C4×Q8—794no—
468C4×Q8—794no—
469C4×Q8—1588no—
470C4×Q8—1588no—
471C4×Q8—1582no—
472C4×Q8—1588no—
473C4×Q8—1588no—
474C4×Q8—1582no—
475C4×Q8—1582no—
476C4×Q8C22×D7914yes—
477#117—794no—
478#117—794no—
479#117—1582no—
480#117—1582no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—791no—
485C2×C4⋊C4—791no—
486C2×C4⋊C4—791no—
487C2×C4⋊C4—794no—
488C2×C4⋊C4—1582no—
489C2×C4⋊C4—1588no—
490C2×C4⋊C4—1581no—
491C2×C4⋊C4—1581no—
492C2×C4⋊C4—1581no—
493C2×C4⋊C4—1581no—
494C2×C4⋊C4—1581no—
495C2×C4⋊C4—1581no—
496C2×C4⋊C4—1581no—
497C2×C4⋊C4—1581no—
498C2×C4⋊C4C22×D7911yescharacteristic
499C2×C4⋊C4C22×D7911yescharacteristic
500C2×C4⋊C4C22×D7911yescharacteristic
501C2×C22⋊C4—1581no—
502C2×C22⋊C4—1581no—
503C2×C42—21no—
504C2×C42—791no—
505C2×C42—791no—
506C2×C42—791no—
507C2×C42—794no—
508C2×C42—794no—
509C2×C42—1588no—
510C2×C42—1581no—
511C2×C42—1581no—
512C2×C42—1581no—
513C2×C42—1581no—
514C2×C42—1581no—
515C2×C42C22×D7911yescharacteristic
516#107—794no—
517#107—794no—
518#107—794no—
519#107C22×D7914yes—
520#106—794no—
521#106—794no—
522#106—794no—
523#106C22×D7914yes—
524C4⋊C8—794no—
525C4⋊C8—794no—
526C4⋊C8—794no—
527C4⋊C8C22×D7914yes—
528#103—794no—
529#103—794no—
530#103—794no—
531#103—794no—
532#103—794no—
533#103—794no—
534#103C22×D7914yes—
535#103C22×D7914yes—
536C24—791no—
537C2×Q8—22no—
538C2×Q8—21no—
539C2×Q8—3164no—
540C2×Q8—3164no—
541C2×Q8—7916no—
542C2×Q8—794no—
543C2×Q8—792no—
544C2×Q8—1584no—
545C2×Q8—1584no—
546C2×Q8—1584no—
547C2×Q8—1588no—
548C2×Q8—15816no—
549C2×Q8—1588no—
550C2×Q8—1582no—
551C2×Q8—1581no—
552C2×Q8Q8×D7914yes—
553C2×Q8C23×D7912yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—3162no—
559C22×C4—3164no—
560C22×C4—794no—
561C22×C4—791no—
562C22×C4—791no—
563C22×C4—794no—
564C22×C4—794no—
565C22×C4—792no—
566C22×C4—792no—
567C22×C4—791no—
568C22×C4—794no—
569C22×C4—1584no—
570C22×C4—1584no—
571C22×C4—1584no—
572C22×C4—1588no—
573C22×C4—1581no—
574C22×C4—1581no—
575C22×C4—1581no—
576C22×C4—1581no—
577C22×C4D4×D7911yescharacteristic
578C22×C4D4×D7911yescharacteristic
579C22×C4C23×D7911yescharacteristic
580M16—1588no—
581M16—1588no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—792no—
585C2×C8—792no—
586C2×C8—1582no—
587C2×C8—1582no—
588C2×C8C23×D7912yes—
589C2×C8C23×D7912yes—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—792no—
597C4⋊C4—792no—
598C4⋊C4—792no—
599C4⋊C4—1584no—
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—1581no—
609C4⋊C4—1581no—
610C4⋊C4C23×D7912yes—
611C4⋊C4C23×D7912yes—
612C4⋊C4C23×D7912yes—
613C22⋊C4—1584no—
614C22⋊C4—1584no—
615C42—24no—
616C42—792no—
617C42—794no—
618C42—794no—
619C42—792no—
620C42—1584no—
621C42—1584no—
622C42—1584no—
623C42—1584no—
624C42—1584no—
625C42D4×D7912yes—
626C42C23×D7912yes—
627C23—794no—
628C23—792no—
629C23—1582no—
630C23—1582no—
631C23C2×D4×D7911yescharacteristic
632Q8—24no—
633Q8—22no—
634Q8—3168no—
635Q8—3168no—
636Q8—794no—
637Q8—15816no—
638Q8—1584no—
639Q8—1582no—
640Q8C2×Q8×D7914yes—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—3164no—
652C2×C4—3168no—
653C2×C4—3162no—
654C2×C4—3162no—
655C2×C4—3162no—
656C2×C4—794no—
657C2×C4—794no—
658C2×C4—792no—
659C2×C4—792no—
660C2×C4—798no—
661C2×C4—794no—
662C2×C4—794no—
663C2×C4—792no—
664C2×C4—1588no—
665C2×C4—15816no—
666C2×C4—1582no—
667C2×C4—1582no—
668C2×C4—1582no—
669C2×C4—1584no—
670C2×C4—1582no—
671C2×C4—1582no—
672C2×C4C2×D4×D7912yes—
673C2×C4C2×D4×D7912yes—
674C2×C4C2×D4×D7911yescharacteristic
675C2×C4C2×Q8×D7912yes—
676C2×C4#41×D7912yes—
677C2×C4C24×D7911yescharacteristic
678C8—22no—
679C8—22no—
680C8—1582no—
681C8—1582no—
682C22—794no—
683C22—1588no—
684C22—1582no—
685C22—1582no—
686C22C22⋊Q8×D7912yes—
687C22#137×D7912yes—
688C22#1909936012yes—
689C22C22×D4×D7911yescharacteristic
690C4—22no—
691C4—22no—
692C4—24no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—3162no—
697C4—3162no—
698C4—3162no—
699C4—794no—
700C4—794no—
701C4—1582no—
702C4—1584no—
703C4C22⋊Q8×D7912yes—
704C4C22×Q8×D7911yescharacteristic
705C4C2×#41×D7911yescharacteristic
706C2—1584no—
707C2#2377320314yesdirect product factor
708C2C2×C22⋊Q8×D7911yescharacteristic
709C2C2×#137×D7911yescharacteristic
710C2C2×#1909936011yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#479×C79C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
hypercenterC2×#479D79
hypocenterC79C2×#3078
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. #23773203C2direct (N × H)
4. C2×#19098871C2semidirect
5. C2×#19098870C2semidirect
6. C2×#19098867C2semidirect
7. C2×#19098857C2semidirect
8. C2×#19098856C2semidirect
9. C2×#19098847C2semidirect
10. C2×#19098846C2semidirect
16. C2×#479×C79C2semidirect
42. #19098871C22semidirect
43. #19098870C22semidirect
44. #19098867C22semidirect
45. #19098857C22semidirect
46. #19098856C22semidirect
47. #19098847C22semidirect
48. #19098846C22semidirect
71. #479×C79C22semidirect
83. C2×Q8×D79Q8semidirect
193. Q8×D79C2×Q8semidirect
351. C2×C79#3078semidirect
362. C2×#479D79semidirect
372. C79C2×#3078semidirect
403. #479C2×D79semidirect
707. C2#23773203direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991192
C2×C4×Q8×D792
#237732032
C2×#190988712
C2×#190988702
C2×#190988672
C2×#190988572
C2×#190988562
C2×#190988472
C2×#190988462
C2×#190986042
C2×#190986022
C2×#190985852
C2×#190985702
C2×#479×C792
C2×#307879