Finite Group Databasebeta

← C2×#23776354 #35168806

Subgroups — C2×#23776354 #35168806

Order 20224.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099273C211yesmaximal, characteristic, complemented
2#23776354C2116yesmaximal, direct product factor
3C2×#19098973C211yesmaximal, characteristic, complemented
4C2×#19098969C211yesmaximal, characteristic, complemented
5C2×#19098962C211yesmaximal, characteristic, complemented
6C2×#19098863C211yesmaximal, characteristic, complemented
7C2×#19098863C211yesmaximal, characteristic, complemented
8C2×#19098860C211yesmaximal, characteristic, complemented
9C2×#19098860C211yesmaximal, characteristic, complemented
10C2×#19098843C211yesmaximal, characteristic, complemented
11C2×#19098840C211yesmaximal, characteristic, complemented
12C2×#19098694C211yesmaximal, characteristic, complemented
13C2×#19098673C211yesmaximal, characteristic
14C2×#19098673C211yesmaximal, characteristic
15C2×C4×#11929609C211yesmaximal, characteristic
16C2×#554×C79C211yesmaximal, characteristic, complemented
17C22×#11929609C2211yescharacteristic
18#19099273—24no—
19#19099273C2218yescomplemented
20C2×#14579161C2211yescharacteristic
21C2×#14579153C2211yescharacteristic
22C2×#14579153C2211yescharacteristic
23C2×#14579139—21no—
24C2×#14579139—21no—
25C2×#14579137—21no—
26C2×C4×D316C2211yescharacteristic
27C2×C4×D316C2211yescharacteristic
28C2×C4×D316C2211yescharacteristic
29C2×C4⋊C4×D79—21no—
30#19098973C2218yescomplemented
31#19098969C2218yescomplemented
32#19098962C2218yescomplemented
33#19098863C2218yescomplemented
34#19098863C2218yescomplemented
35#19098860C2218yescomplemented
36#19098860C2218yescomplemented
37#19098843C2218yescomplemented
38#19098840C2218yescomplemented
39#19098694C2218yescomplemented
40#19098673C2218yes—
41#19098673C2218yes—
42C4×#11929609C2218yes—
43C2×#14579094C2211yescharacteristic
44C2×#14579094C2211yescharacteristic
45C2×#14579094C2211yescharacteristic
46C2×#14579094C2211yescharacteristic
47C2×#14579094C2211yescharacteristic
48C2×#14579092C2211yescharacteristic
49C2×#14579092C2211yescharacteristic
50C2×#14579092C2211yescharacteristic
51C2×#14579092C2211yescharacteristic
52C2×C4⋊(C79⋊C8)C2211yescharacteristic
53C2×C4⋊(C79⋊C8)C2211yescharacteristic
54C2×C4⋊(C79⋊C8)C2211yescharacteristic
55C2×#14579082C2211yescharacteristic
56C2×#14579082C2211yescharacteristic
57C2×#14579082C2211yescharacteristic
58C2×#14579081C2211yescharacteristic
59C2×#14579081C2211yescharacteristic
60C2×#14579081C2211yescharacteristic
61C2×#14579072C2211yescharacteristic
62C2×#14579072C2211yescharacteristic
63C2×C4×C79⋊C8C2211yescharacteristic
64#554×C79—24no—
65#554×C79C2218yescomplemented
66C2×C4⋊Q8×C79C2211yescharacteristic
67C2×#125×C79C2211yescharacteristic
68C2×#125×C79C2211yescharacteristic
69C2×C22⋊Q8×C79—21no—
70C2×C22⋊Q8×C79—21no—
71C2×C22⋊Q8×C79—21no—
72C2×C4×Q8×C79C2211yescharacteristic
73C2×C4×D4×C79C2211yescharacteristic
74C2×C4×D4×C79C2211yescharacteristic
75C2×C4×D4×C79C2211yescharacteristic
76C22×C4⋊C4×C79—21no—
77C22×Dic158—21no—
78C22×D316C2311yescharacteristic
79C22×C4×D79—21no—
80C22×C4×D79—21no—
81C22×C4×D79—21no—
82C2×#11929609Q818yescomplemented
83C2×#11929609C2314yes—
84C22×C79⋊C8C2311yescharacteristic
85C22×C79⋊C8C2311yescharacteristic
86C22×C79⋊C8C2311yescharacteristic
87C22×C79⋊C8C2311yescharacteristic
88#14579161—22no—
89#14579161C2314yes—
90#14579153—22no—
91#14579153—22no—
92#14579153C2314yes—
93#14579153C2314yes—
94#14579139—28no—
95#14579139—28no—
96#14579137—28no—
97C4×D316—22no—
98C4×D316—22no—
99C4×D316—22no—
100C4×D316C2314yes—
101C4×D316C2314yes—
102C4×D316C2314yes—
103C2×C4⋊Dic79—21no—
104C2×C4⋊Dic79C2311yescharacteristic
105C2×C4⋊Dic79C2311yescharacteristic
106C2×C4⋊Dic79C2311yescharacteristic
107C2×Dic79⋊C4—21no—
108C2×Dic79⋊C4—21no—
109C2×Dic79⋊C4—21no—
110C2×Dic79⋊C4—21no—
111C4⋊C4×D79—28no—
112C2×(C2×D79)⋊C4—21no—
113C2×(C2×D79)⋊C4—21no—
114C2×(C2×D79)⋊C4—21no—
115#14579094C2314yes—
116#14579094C2314yes—
117#14579094C2314yes—
118#14579094C2314yes—
119#14579094C2314yes—
120#14579092C2314yes—
121#14579092C2314yes—
122#14579092C2314yes—
123#14579092C2314yes—
124C4⋊(C79⋊C8)C2314yes—
125C4⋊(C79⋊C8)C2314yes—
126C4⋊(C79⋊C8)C2314yes—
127#14579082C2314yes—
128#14579082C2314yes—
129#14579082C2314yes—
130#14579081C2314yes—
131#14579081C2314yes—
132#14579081C2314yes—
133#14579072C2314yes—
134#14579072C2314yes—
135C4×C79⋊C8C2314yes—
136C22×Q8×C79—21no—
137C22×Q8×C79D411yescharacteristic
138C22×D4×C79C2311yescharacteristic
139C23×C4×C79—21no—
140C23×C4×C79—21no—
141C23×C4×C79—21no—
142C4⋊Q8×C79—22no—
143C4⋊Q8×C79C2314yes—
144#125×C79—22no—
145#125×C79—22no—
146#125×C79C2314yes—
147#125×C79C2314yes—
148C22⋊Q8×C79—28no—
149C22⋊Q8×C79—28no—
150C22⋊Q8×C79—28no—
151C4×Q8×C79D414yes—
152C4×Q8×C79C2314yes—
153C4×D4×C79—22no—
154C4×D4×C79—22no—
155C4×D4×C79—22no—
156C4×D4×C79C2314yes—
157C4×D4×C79C2314yes—
158C4×D4×C79C2314yes—
159C2×C4⋊C4×C79—21no—
160C2×C4⋊C4×C79—21no—
161C2×C4⋊C4×C79—21no—
162C2×C4⋊C4×C79—21no—
163C2×C4⋊C4×C79—21no—
164C2×C4⋊C4×C79—28no—
165C2×C4⋊C4×C79D411yescharacteristic
166C2×C4⋊C4×C79D411yescharacteristic
167C2×C4⋊C4×C79D411yescharacteristic
168C2×C4⋊C4×C79C2311yescharacteristic
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C22⋊C4×C79—21no—
172C2×C22⋊C4×C79—21no—
173C2×C22⋊C4×C79—21no—
174C2×C42×C79C2311yescharacteristic
175C2×C42×C79C2311yescharacteristic
176C2×C42×C79C2311yescharacteristic
177C23×D79—21no—
178C2×Dic158—24no—
179C2×Dic158—82no—
180C2×D316—21no—
181C2×D316—22no—
182C2×D316C2×Q814yes—
183C2×D316C2412yes—
184C22×Dic79—21no—
185C22×Dic79—21no—
186C22×Dic79—21no—
187C2×C4×D79—24no—
188C2×C4×D79—24no—
189C2×C4×D79—24no—
190C2×C4×D79—44no—
191C2×C4×D79—82no—
192C2×C4×D79—82no—
193#11929609C2×Q8116yescomplemented
194C2×C79⋊C8—22no—
195C2×C79⋊C8—22no—
196C2×C79⋊C8—22no—
197C2×C79⋊C8C2×Q814yes—
198C2×C79⋊C8C2412yes—
199C2×C79⋊C8C2412yes—
200C2×C79⋊C8C2412yes—
201C2×C79⋊C8C2412yes—
202C4⋊Dic79—24no—
203C4⋊Dic79—21no—
204C4⋊Dic79—21no—
205C4⋊Dic79—21no—
206C4⋊Dic79C2412yes—
207C4⋊Dic79C2412yes—
208C4⋊Dic79C2412yes—
209Dic79⋊C4—24no—
210Dic79⋊C4—24no—
211Dic79⋊C4—24no—
212Dic79⋊C4—24no—
213(C2×D79)⋊C4—24no—
214(C2×D79)⋊C4—24no—
215(C2×D79)⋊C4—24no—
216C24×C79—21no—
217C2×Q8×C79—24no—
218C2×Q8×C79—42no—
219C2×Q8×C79—82no—
220C2×Q8×C79C2×D414yes—
221C2×D4×C79—21no—
222C2×D4×C79—22no—
223C2×D4×C79C2×Q814yes—
224C2×D4×C79C2412yes—
225C22×C4×C79—21no—
226C22×C4×C79—21no—
227C22×C4×C79—21no—
228C22×C4×C79—24no—
229C22×C4×C79—24no—
230C22×C4×C79—24no—
231C22×C4×C79—44no—
232C22×C4×C79—82no—
233C22×C4×C79—82no—
234C22×C4×C79C2×D411yescharacteristic
235C22×C4×C79C2×D411yescharacteristic
236C22×C4×C79C2×D411yescharacteristic
237C22×C4×C79C2×D411yescharacteristic
238C22×C4×C79C2×D411yescharacteristic
239C22×C4×C79C2×D411yescharacteristic
240C22×C4×C79C2411yescharacteristic
241C4⋊C4×C79—24no—
242C4⋊C4×C79—24no—
243C4⋊C4×C79—24no—
244C4⋊C4×C79—24no—
245C4⋊C4×C79—24no—
246C4⋊C4×C79—21no—
247C4⋊C4×C79—21no—
248C4⋊C4×C79—21no—
249C4⋊C4×C79C2×D414yes—
250C4⋊C4×C79C2×D414yes—
251C4⋊C4×C79C2×D414yes—
252C4⋊C4×C79C2412yes—
253C4⋊C4×C79C2412yes—
254C4⋊C4×C79C2412yes—
255C22⋊C4×C79—24no—
256C22⋊C4×C79—24no—
257C22⋊C4×C79—24no—
258C42×C79C2×D412yes—
259C42×C79C2×D412yes—
260C42×C79C2×D412yes—
261C42×C79C2412yes—
262C42×C79C2412yes—
263C42×C79C2412yes—
264C23×C79—24no—
265C23×C79—22no—
266C23×C79—42no—
267C23×C79—42no—
268C23×C79C22×D411yescharacteristic
269C22×D79—24no—
270C22×D79—22no—
271C22×D79—42no—
272C22×D79—42no—
273Q8×C79—44no—
274Q8×C79—84no—
275D4×C79—24no—
276D4×C79—22no—
277D4×C79C22×Q814yes—
278C2×C4×C79—22no—
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—22no—
286C2×C4×C79—22no—
287C2×C4×C79—48no—
288C2×C4×C79—42no—
289C2×C4×C79—42no—
290C2×C4×C79—42no—
291C2×C4×C79—84no—
292C2×C4×C79—84no—
293C2×C4×C79C22×D412yes—
294C2×C4×C79C22×D412yes—
295C2×C4×C79C22×D412yes—
296C2×C4×C79C22×D412yes—
297C2×C4×C79C22×D412yes—
298C2×C4×C79C22×D412yes—
299C2×C4×C79C22×D411yescharacteristic
300C2×C4×C79C22×Q812yes—
301C2×C4×C792−1+412yes—
302C2×C4×C79C2511yescharacteristic
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—42no—
307C2×Dic79—42no—
308C2×Dic79—42no—
309D316—24no—
310D316—22no—
311D316C22×Q814yes—
312C4×D79—48no—
313C4×D79—84no—
314C4×D79—84no—
315Dic158—84no—
316C79⋊C8—22no—
317C79⋊C8—22no—
318C79⋊C8—22no—
319C79⋊C8C22×Q814yes—
320C22×C79—24no—
321C22×C79—48no—
322C22×C79—42no—
323C22×C79—42no—
324C22×C79D4×Q812yes—
325C22×C79#57512yes—
326C22×C79#57612yes—
327C22×C79C23×D411yescharacteristic
328C2×D79—24no—
329C2×D79—48no—
330C2×D79—42no—
331C2×D79—42no—
332C4×C79—22no—
333C4×C79—22no—
334C4×C79—22no—
335C4×C79—22no—
336C4×C79—22no—
337C4×C79—22no—
338C4×C79—42no—
339C4×C79—42no—
340C4×C79—42no—
341C4×C79D4×Q812yes—
342C4×C79C23×Q811yescharacteristic
343C4×C79C2×2−1+411yescharacteristic
344Dic79—42no—
345Dic79—42no—
346Dic79—42no—
347C2×#3389—791nomaximal, Sylow
348C2×C79—44no—
349C2×C79#338914yescomplemented
350C2×C79C2×D4×Q811yescharacteristic
351C2×C79C2×#57511yescharacteristic
352C2×C79C2×#57611yescharacteristic
353D79—44no—
354C2×#554—791no—
355C2×#554D7911yescharacteristic, complemented
356#3389—7916no—
357C2×#501—791no—
358C2×#501—791no—
359C2×#499—791no—
360C2×#478—791no—
361C2×#478—791no—
362C2×#478—791no—
363C2×#478—791no—
364C2×#474—791no—
365C2×#474—791no—
366C2×#446—791no—
367C2×#442—791no—
368C2×#442—791no—
369C2×C4×D8—791no—
370C79C2×#338911yescharacteristic, complemented, Sylow
371C22×D8—791no—
372#554—24no—
373#554—798no—
374#554—1584no—
375#554C2×D7918yescomplemented
376C2×C4⋊Q8—791no—
377C2×C4⋊Q8C2×D7911yescharacteristic
378C2×#125—791no—
379C2×#125—791no—
380C2×#125C2×D7911yescharacteristic
381C2×#125C2×D7911yescharacteristic
382C2×C22⋊Q8—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8—1581no—
386C2×C22⋊Q8—1581no—
387C2×C22⋊Q8—1581no—
388C2×C4×Q8C2×D7911yescharacteristic
389C2×C4×D4—791no—
390C2×C4×D4—791no—
391C2×C4×D4—791no—
392C2×C4×D4C2×D7911yescharacteristic
393C2×C4×D4C2×D7911yescharacteristic
394C2×C4×D4C2×D7911yescharacteristic
395C22×C4⋊C4—21no—
396C22×C4⋊C4—1581no—
397#501—798no—
398#501—798no—
399#499—798no—
400#478—798no—
401#478—798no—
402#478—798no—
403#478—798no—
404#474—798no—
405#474—798no—
406#446—798no—
407#442—798no—
408#442—798no—
409C4×D8—798no—
410C2×#107—791no—
411C2×#107—791no—
412C2×#107—791no—
413C2×#107—791no—
414C2×#107—791no—
415C2×#106—791no—
416C2×#106—791no—
417C2×#106—791no—
418C2×#106—791no—
419C2×C4⋊C8—791no—
420C2×C4⋊C8—791no—
421C2×C4⋊C8—791no—
422C2×#102—791no—
423C2×#102—791no—
424C2×#102—791no—
425C2×#102—791no—
426C2×#102—791no—
427C2×#102—791no—
428C2×#97—791no—
429C2×#97—791no—
430C2×C4×C8—791no—
431C22×Q8—21no—
432C22×Q8—1581no—
433C22×Q8C22⋊D7911yescharacteristic
434C22×D4—791no—
435C22×D4C22×D7911yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—1581no—
440C23×C4—1581no—
441C23×C4—1581no—
442C2×D8—798no—
443C2×D8—794no—
444C22×C8—791no—
445C22×C8—791no—
446C22×C8—791no—
447C22×C8—791no—
448C4⋊Q8—22no—
449C4⋊Q8—794no—
450C4⋊Q8—1582no—
451C4⋊Q8C22×D7914yes—
452#125—22no—
453#125—22no—
454#125—794no—
455#125—794no—
456#125—1582no—
457#125—1582no—
458#125C22×D7914yes—
459#125C22×D7914yes—
460C22⋊Q8—28no—
461C22⋊Q8—28no—
462C22⋊Q8—28no—
463C22⋊Q8—1588no—
464C22⋊Q8—1588no—
465C22⋊Q8—1588no—
466C4×Q8C22⋊D7914yes—
467C4×Q8C22×D7914yes—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—794no—
472C4×D4—794no—
473C4×D4—794no—
474C4×D4—1582no—
475C4×D4—1582no—
476C4×D4—1582no—
477C4×D4C22×D7914yes—
478C4×D4C22×D7914yes—
479C4×D4C22×D7914yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—28no—
486C2×C4⋊C4—791no—
487C2×C4⋊C4—791no—
488C2×C4⋊C4—791no—
489C2×C4⋊C4—1581no—
490C2×C4⋊C4—1581no—
491C2×C4⋊C4—1581no—
492C2×C4⋊C4—1581no—
493C2×C4⋊C4—1581no—
494C2×C4⋊C4—1588no—
495C2×C4⋊C4C22⋊D7911yescharacteristic
496C2×C4⋊C4C22⋊D7911yescharacteristic
497C2×C4⋊C4C22⋊D7911yescharacteristic
498C2×C4⋊C4C22×D7911yescharacteristic
499C2×C4⋊C4C22×D7911yescharacteristic
500C2×C4⋊C4C22×D7911yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1581no—
505C2×C22⋊C4—1581no—
506C2×C22⋊C4—1581no—
507C2×C42C22×D7911yescharacteristic
508C2×C42C22×D7911yescharacteristic
509C2×C42C22×D7911yescharacteristic
510#107—794no—
511#107—794no—
512#107—794no—
513#107—794no—
514#107—794no—
515#106—794no—
516#106—794no—
517#106—794no—
518#106—794no—
519C4⋊C8—794no—
520C4⋊C8—794no—
521C4⋊C8—794no—
522#102—794no—
523#102—794no—
524#102—794no—
525#102—794no—
526#102—794no—
527#102—794no—
528#97—794no—
529#97—794no—
530C4×C8—794no—
531C24—21no—
532C24—1581no—
533C2×Q8—24no—
534C2×Q8—42no—
535C2×Q8—82no—
536C2×Q8—6322no—
537C2×Q8—1584no—
538C2×Q8C2×C22⋊D7914yes—
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—794no—
542C2×D4—792no—
543C2×D4—1582no—
544C2×D4—1581no—
545C2×D4Q8×D7914yes—
546C2×D4C23×D7912yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—44no—
554C22×C4—82no—
555C22×C4—82no—
556C22×C4—3164no—
557C22×C4—6322no—
558C22×C4—6322no—
559C22×C4—1581no—
560C22×C4—1581no—
561C22×C4—1581no—
562C22×C4—1584no—
563C22×C4—1584no—
564C22×C4—1584no—
565C22×C4C2×C22⋊D7911yescharacteristic
566C22×C4C2×C22⋊D7911yescharacteristic
567C22×C4C2×C22⋊D7911yescharacteristic
568C22×C4C2×C22⋊D7911yescharacteristic
569C22×C4C2×C22⋊D7911yescharacteristic
570C22×C4C2×C22⋊D7911yescharacteristic
571C22×C4C23×D7911yescharacteristic
572D8—7916no—
573C2×C8—794no—
574C2×C8—792no—
575C2×C8—792no—
576C2×C8—792no—
577C2×C8—792no—
578C2×C8—1582no—
579C2×C8—1582no—
580C2×C8—1582no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—792no—
590C4⋊C4—792no—
591C4⋊C4—792no—
592C4⋊C4—1584no—
593C4⋊C4—1584no—
594C4⋊C4—1584no—
595C4⋊C4—1584no—
596C4⋊C4—1581no—
597C4⋊C4—1581no—
598C4⋊C4—1581no—
599C4⋊C4—1584no—
600C4⋊C4C2×C22⋊D7914yes—
601C4⋊C4C2×C22⋊D7914yes—
602C4⋊C4C2×C22⋊D7914yes—
603C4⋊C4C23×D7912yes—
604C4⋊C4C23×D7912yes—
605C4⋊C4C23×D7912yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—1584no—
610C22⋊C4—1584no—
611C22⋊C4—1584no—
612C42C2×C22⋊D7912yes—
613C42C2×C22⋊D7912yes—
614C42C2×C22⋊D7912yes—
615C42C23×D7912yes—
616C42C23×D7912yes—
617C42C23×D7912yes—
618C23—24no—
619C23—22no—
620C23—42no—
621C23—42no—
622C23—3162no—
623C23—3162no—
624C23—1584no—
625C23—1582no—
626C23C22×C22⋊D7911yescharacteristic
627Q8—44no—
628Q8—84no—
629Q8—6324no—
630D4—22no—
631D4—24no—
632D4—794no—
633D4—1582no—
634D4—1584no—
635D4C2×Q8×D7914yes—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—48no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—3168no—
652C2×C4—3162no—
653C2×C4—3162no—
654C2×C4—3162no—
655C2×C4—6324no—
656C2×C4—6324no—
657C2×C4—1582no—
658C2×C4—1582no—
659C2×C4—1582no—
660C2×C4C22×C22⋊D7912yes—
661C2×C4C22×C22⋊D7912yes—
662C2×C4C22×C22⋊D7912yes—
663C2×C4C22×C22⋊D7912yes—
664C2×C4C22×C22⋊D7912yes—
665C2×C4C22×C22⋊D7912yes—
666C2×C4C22×C22⋊D7911yescharacteristic
667C2×C4C2×Q8×D7912yes—
668C2×C4#1457920912yes—
669C2×C4C24×D7911yescharacteristic
670C8—794no—
671C8—1582no—
672C8—1582no—
673C8—1582no—
674C22—24no—
675C22—42no—
676C22—48no—
677C22—42no—
678C22—3162no—
679C22—3168no—
680C22—3162no—
681C22—1584no—
682C22Q8×C22⋊D7912yes—
683C22#1909936112yes—
684C22#1909936612yes—
685C22C23×C22⋊D7911yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—22no—
691C4—22no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—3162no—
696C4—3162no—
697C4—3162no—
698C4Q8×C22⋊D7912yes—
699C4C22×Q8×D7911yescharacteristic
700C4C2×#1457920911yescharacteristic
701C2—44no—
702C2—3164no—
703C2#2377635414yesdirect product factor
704C2C2×Q8×C22⋊D7911yescharacteristic
705C2C2×#1909936111yescharacteristic
706C2C2×#1909936611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#554×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929609C22
hypercenterC2×#554D79
hypocenterC79C2×#3389
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#19099273C2semidirect
2. #23776354C2direct (N × H)
3. C2×#19098973C2semidirect
4. C2×#19098969C2semidirect
5. C2×#19098962C2semidirect
6. C2×#19098863C2semidirect
7. C2×#19098863C2semidirect
8. C2×#19098860C2semidirect
9. C2×#19098860C2semidirect
10. C2×#19098843C2semidirect
11. C2×#19098840C2semidirect
12. C2×#19098694C2semidirect
16. C2×#554×C79C2semidirect
19. #19099273C22semidirect
30. #19098973C22semidirect
31. #19098969C22semidirect
32. #19098962C22semidirect
33. #19098863C22semidirect
34. #19098863C22semidirect
35. #19098860C22semidirect
36. #19098860C22semidirect
37. #19098843C22semidirect
38. #19098840C22semidirect
39. #19098694C22semidirect
65. #554×C79C22semidirect
82. C2×#11929609Q8semidirect
193. #11929609C2×Q8semidirect
349. C2×C79#3389semidirect
355. C2×#554D79semidirect
370. C79C2×#3389semidirect
375. #554C2×D79semidirect
703. C2#23776354direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992732
#237763542
C2×#190989732
C2×#190989692
C2×#190989622
C2×#190988632
C2×#190988602
C2×#190988432
C2×#190988402
C2×#190986942
C2×#190986732
C2×C4×#119296092
C2×#554×C792
C2×#338979