Finite Group Databasebeta

← C2×#23774297 #35158972

Subgroups — C2×#23774297 #35158972

Order 20224.

2250 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099141C211yesmaximal, characteristic, complemented
2#23774297C2116yesmaximal, direct product factor
3C2×#19098898C211yesmaximal, characteristic, complemented
4C2×#19098896C211yesmaximal, characteristic, complemented
5C2×#19098876C211yesmaximal, characteristic, complemented
6C2×#19098874C211yesmaximal, characteristic, complemented
7C2×#19098811C211yesmaximal, characteristic, complemented
8C2×#19098807C211yesmaximal, characteristic, complemented
9C2×#19098802C211yesmaximal, characteristic, complemented
10C2×#19098797C211yesmaximal, characteristic, complemented
11C2×#19098725C211yesmaximal, characteristic, complemented
12C2×#19098723C211yesmaximal, characteristic, complemented
13C2×#19098708C211yesmaximal, characteristic, complemented
14C2×#19098706C211yesmaximal, characteristic, complemented
15C2×#19098530C211yesmaximal, characteristic, complemented
16C2×#537×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C22×#11929614C2211yescharacteristic
19C22×#11929612C2211yescharacteristic
20C22×#11929611C2211yescharacteristic
21C22×#11929609C2211yescharacteristic
22C22×#11929608C2211yescharacteristic
23C23×C79⋊C8C2211yescharacteristic
24#19099141—24no—
25#19099141C2218yescomplemented
26C2×#14579140C2211yescharacteristic
27C2×#14579140C2211yescharacteristic
28C2×#14579137—21no—
29C2×#14579135C2211yescharacteristic
30C2×#14579135C2211yescharacteristic
31C2×#14579133—21no—
32C2×#14579133—21no—
33C2×#14579132—21no—
34C22×C4⋊Dic79C2211yescharacteristic
35#19098898C2218yescomplemented
36#19098896C2218yescomplemented
37#19098876C2218yescomplemented
38#19098874C2218yescomplemented
39#19098811C2218yescomplemented
40#19098807C2218yescomplemented
41#19098802C2218yescomplemented
42#19098797C2218yescomplemented
43#19098725C2218yescomplemented
44#19098723C2218yescomplemented
45#19098708C2218yescomplemented
46#19098706C2218yescomplemented
47C2×#14579094C2211yescharacteristic
48C2×#14579094C2211yescharacteristic
49C2×#14579094C2211yescharacteristic
50C2×#14579094C2211yescharacteristic
51C2×#14579085C2211yescharacteristic
52C2×#14579085C2211yescharacteristic
53C2×#14579084C2211yescharacteristic
54C2×#14579084C2211yescharacteristic
55C2×#14579082C2211yescharacteristic
56C2×#14579082C2211yescharacteristic
57C2×#14579081C2211yescharacteristic
58C2×#14579081C2211yescharacteristic
59#19098530C2218yescomplemented
60C2×C22⋊(C79⋊C8)C2211yescharacteristic
61C2×C22⋊(C79⋊C8)C2211yescharacteristic
62C2×C22⋊(C79⋊C8)C2211yescharacteristic
63C2×C22⋊(C79⋊C8)C2211yescharacteristic
64C22×#41×C79C2211yescharacteristic
65C22×#41×C79C2211yescharacteristic
66#537×C79—24no—
67#537×C79C2218yescomplemented
68C2×C22⋊Q8×C79—21no—
69C2×C22⋊Q8×C79C2211yescharacteristic
70C2×C22⋊Q8×C79C2211yescharacteristic
71C2×#121×C79—21no—
72C2×#121×C79—21no—
73C2×#121×C79—21no—
74C2×#121×C79C2211yescharacteristic
75C2×#121×C79C2211yescharacteristic
76C22×C4⋊C4×C79C2211yescharacteristic
77C2×#11929624—22no—
78C2×#11929624—42no—
79C2×#11929624—42no—
80C2×#11929624C2314yes—
81C22×Dic158C2311yescharacteristic
82C22×D316C2311yescharacteristic
83C22×C22⋊D79—21no—
84C22×C22⋊D79—21no—
85C22×C22⋊D79—21no—
86C23×Dic79—21no—
87C22×C4×D79—21no—
88C2×#11929614—42no—
89C2×#11929614C2314yes—
90C2×#11929612—42no—
91C2×#11929612C2314yes—
92C2×#11929611—42no—
93C2×#11929611C2314yes—
94C2×#11929609—42no—
95C2×#11929609C2314yes—
96C2×#11929608—42no—
97C2×#11929608C2314yes—
98C22×C79⋊C8—42no—
99C22×C79⋊C8C2311yescharacteristic
100C22×C79⋊C8C2311yescharacteristic
101C22×C79⋊C8C2311yescharacteristic
102C22×C79⋊C8C2311yescharacteristic
103C22×C79⋊C8C2314yes—
104#14579140—22no—
105#14579140—22no—
106#14579140C2314yes—
107#14579140C2314yes—
108#14579137—28no—
109#14579135—22no—
110#14579135—22no—
111#14579135C2314yes—
112#14579135C2314yes—
113#14579133—28no—
114#14579133—28no—
115#14579132—28no—
116C2×C4⋊Dic79—22no—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79C2314yes—
119C2×C4⋊Dic79C2311yescharacteristic
120C2×C4⋊Dic79C2311yescharacteristic
121C2×Dic79⋊C4—21no—
122C2×Dic79⋊C4—21no—
123C2×C22⋊Dic79—21no—
124C2×C22⋊Dic79—21no—
125C2×(C2×D79)⋊C4—21no—
126C2×(C2×D79)⋊C4—21no—
127#14579094C2314yes—
128#14579094C2314yes—
129#14579094C2314yes—
130#14579094C2314yes—
131#14579085C2314yes—
132#14579085C2314yes—
133#14579084C2314yes—
134#14579084C2314yes—
135#14579082C2314yes—
136#14579082C2314yes—
137#14579081C2314yes—
138#14579081C2314yes—
139C22⋊(C79⋊C8)C2314yes—
140C22⋊(C79⋊C8)C2314yes—
141C22⋊(C79⋊C8)C2314yes—
142C22⋊(C79⋊C8)C2314yes—
143C2×#41×C79—22no—
144C2×#41×C79—42no—
145C2×#41×C79—42no—
146C2×#41×C79—42no—
147C2×#41×C79—42no—
148C2×#41×C79D414yes—
149C2×#41×C79C2314yes—
150C2×#41×C79C2314yes—
151C22×Q8×C79D411yescharacteristic
152C22×Q8×C79C2311yescharacteristic
153C22×D4×C79—21no—
154C22×D4×C79—21no—
155C22×D4×C79—21no—
156C22×D4×C79D411yescharacteristic
157C22×D4×C79D411yescharacteristic
158C22×D4×C79D411yescharacteristic
159C22×D4×C79C2311yescharacteristic
160C23×C4×C79—21no—
161C23×C4×C79—21no—
162C23×C4×C79C2311yescharacteristic
163C23×C4×C79C2311yescharacteristic
164C23×C4×C79C2311yescharacteristic
165C22⋊Q8×C79—28no—
166C22⋊Q8×C79—22no—
167C22⋊Q8×C79—22no—
168C22⋊Q8×C79C2314yes—
169C22⋊Q8×C79C2314yes—
170#121×C79—28no—
171#121×C79—28no—
172#121×C79—28no—
173#121×C79—22no—
174#121×C79—22no—
175#121×C79C2314yes—
176#121×C79C2314yes—
177C2×C4⋊C4×C79—21no—
178C2×C4⋊C4×C79—22no—
179C2×C4⋊C4×C79—21no—
180C2×C4⋊C4×C79—21no—
181C2×C4⋊C4×C79C2314yes—
182C2×C4⋊C4×C79C2311yescharacteristic
183C2×C4⋊C4×C79C2311yescharacteristic
184C2×C22⋊C4×C79—21no—
185C2×C22⋊C4×C79—21no—
186C2×C22⋊C4×C79—21no—
187C2×C22⋊C4×C79—21no—
188C23×D79—21no—
189#11929624—44no—
190#11929624—44no—
191#11929624—48no—
192C2×Dic158—21no—
193C2×Dic158—22no—
194C2×Dic158—22no—
195C2×Dic158C2412yes—
196C2×D316—21no—
197C2×D316—22no—
198C2×D316—22no—
199C2×D316C2412yes—
200C2×C22⋊D79—24no—
201C2×C22⋊D79—24no—
202C2×C22⋊D79—24no—
203C2×C22⋊D79—44no—
204C2×C22⋊D79—82no—
205C2×C22⋊D79—82no—
206C22×Dic79—21no—
207C22×Dic79—21no—
208C22×Dic79—21no—
209C22×Dic79—24no—
210C22×Dic79—82no—
211C2×C4×D79—24no—
212C2×C4×D79—44no—
213#11929614—44no—
214#11929612—44no—
215#11929611—44no—
216#11929609—44no—
217#11929608—44no—
218C2×C79⋊C8—22no—
219C2×C79⋊C8—22no—
220C2×C79⋊C8—22no—
221C2×C79⋊C8—22no—
222C2×C79⋊C8—44no—
223C2×C79⋊C8C2412yes—
224C2×C79⋊C8C2412yes—
225C2×C79⋊C8C2412yes—
226C2×C79⋊C8C2412yes—
227C4⋊Dic79—24no—
228C4⋊Dic79—21no—
229C4⋊Dic79—21no—
230C4⋊Dic79C2412yes—
231C4⋊Dic79C2412yes—
232Dic79⋊C4—24no—
233Dic79⋊C4—24no—
234C22⋊Dic79—24no—
235C22⋊Dic79—24no—
236(C2×D79)⋊C4—24no—
237(C2×D79)⋊C4—24no—
238C24×C79—21no—
239C24×C79C2×D411yescharacteristic
240C24×C79C2×D411yescharacteristic
241C24×C79C2×D411yescharacteristic
242#41×C79—48no—
243#41×C79—44no—
244#41×C79—44no—
245#41×C79—44no—
246#41×C79—44no—
247#41×C79—48no—
248C2×Q8×C79—21no—
249C2×Q8×C79—22no—
250C2×Q8×C79—22no—
251C2×Q8×C79—42no—
252C2×Q8×C79C2×D414yes—
253C2×Q8×C79C2412yes—
254C2×D4×C79—24no—
255C2×D4×C79—24no—
256C2×D4×C79—24no—
257C2×D4×C79—21no—
258C2×D4×C79—22no—
259C2×D4×C79—22no—
260C2×D4×C79—42no—
261C2×D4×C79—42no—
262C2×D4×C79—42no—
263C2×D4×C79—44no—
264C2×D4×C79—82no—
265C2×D4×C79—82no—
266C2×D4×C79C2×D414yes—
267C2×D4×C79C2×D414yes—
268C2×D4×C79C2×D414yes—
269C2×D4×C79C2412yes—
270C22×C4×C79—22no—
271C22×C4×C79—22no—
272C22×C4×C79—22no—
273C22×C4×C79—22no—
274C22×C4×C79—22no—
275C22×C4×C79—22no—
276C22×C4×C79—21no—
277C22×C4×C79—21no—
278C22×C4×C79—21no—
279C22×C4×C79—24no—
280C22×C4×C79—24no—
281C22×C4×C79—44no—
282C22×C4×C79—82no—
283C22×C4×C79C2×D412yes—
284C22×C4×C79C2×D411yescharacteristic
285C22×C4×C79C2×D411yescharacteristic
286C22×C4×C79C2×D411yescharacteristic
287C22×C4×C79C2×D412yes—
288C22×C4×C79C2×D412yes—
289C22×C4×C79C2412yes—
290C22×C4×C79C2412yes—
291C22×C4×C79C2412yes—
292C22×C4×C79C2411yescharacteristic
293C4⋊C4×C79—24no—
294C4⋊C4×C79—21no—
295C4⋊C4×C79—21no—
296C4⋊C4×C79—24no—
297C4⋊C4×C79—24no—
298C4⋊C4×C79C2412yes—
299C4⋊C4×C79C2412yes—
300C22⋊C4×C79—24no—
301C22⋊C4×C79—24no—
302C22⋊C4×C79—24no—
303C22⋊C4×C79—24no—
304C23×C79—22no—
305C23×C79—22no—
306C23×C79—22no—
307C23×C79—22no—
308C23×C79—22no—
309C23×C79—22no—
310C23×C79—22no—
311C23×C79—22no—
312C23×C79—22no—
313C23×C79—22no—
314C23×C79—42no—
315C23×C79—42no—
316C23×C79—42no—
317C23×C79C22×D412yes—
318C23×C79C22×D412yes—
319C23×C79C22×D412yes—
320C23×C79C22×D411yescharacteristic
321C22×D79—22no—
322C22×D79—42no—
323C22×D79—42no—
324C22×D79—42no—
325Q8×C79—22no—
326Q8×C79—22no—
327Q8×C79—44no—
328Q8×C79—42no—
329D4×C79—22no—
330D4×C79—22no—
331D4×C79—44no—
332D4×C79—44no—
333D4×C79—44no—
334D4×C79—48no—
335D4×C79—42no—
336D4×C79—84no—
337D4×C79—84no—
338C2×C4×C79—22no—
339C2×C4×C79—22no—
340C2×C4×C79—22no—
341C2×C4×C79—24no—
342C2×C4×C79—24no—
343C2×C4×C79—24no—
344C2×C4×C79—22no—
345C2×C4×C79—22no—
346C2×C4×C79—22no—
347C2×C4×C79—22no—
348C2×C4×C79—22no—
349C2×C4×C79—22no—
350C2×C4×C79—22no—
351C2×C4×C79—22no—
352C2×C4×C79—22no—
353C2×C4×C79—48no—
354C2×C4×C79—42no—
355C2×C4×C79—42no—
356C2×C4×C79—42no—
357C2×C4×C79—84no—
358C2×C4×C79C22×D412yes—
359C2×C4×C79C22×D412yes—
360C2×C4×C79C22×D412yes—
361C2×C4×C79C22×D411yescharacteristic
362C2×C4×C79H(5,𝔽2)12yes—
363C2×C4×C79H(5,𝔽2)12yes—
364C2×C4×C79C2511yescharacteristic
365C22⋊D79—48no—
366C22⋊D79—84no—
367C22⋊D79—84no—
368C2×Dic79—22no—
369C2×Dic79—22no—
370C2×Dic79—22no—
371C2×Dic79—42no—
372C2×Dic79—42no—
373C2×Dic79—42no—
374C2×Dic79—84no—
375D316—22no—
376D316—22no—
377D316—42no—
378C4×D79—48no—
379Dic158—22no—
380Dic158—22no—
381Dic158—42no—
382C79⋊C8—22no—
383C79⋊C8—22no—
384C79⋊C8—22no—
385C79⋊C8—22no—
386C22×C79—22no—
387C22×C79—22no—
388C22×C79—22no—
389C22×C79—22no—
390C22×C79—22no—
391C22×C79—22no—
392C22×C79—22no—
393C22×C79—22no—
394C22×C79—22no—
395C22×C79—44no—
396C22×C79—44no—
397C22×C79—44no—
398C22×C79—42no—
399C22×C79—42no—
400C22×C79—42no—
401C22×C79—84no—
402C22×C79#53412yes—
403C22×C79#57612yes—
404C22×C79#57812yes—
405C22×C79C23×D411yescharacteristic
406C2×D79—42no—
407C2×D79—42no—
408C2×D79—42no—
409C2×D79—84no—
410C4×C79—22no—
411C4×C79—22no—
412C4×C79—22no—
413C4×C79—42no—
414C4×C79—42no—
415C4×C79—42no—
416C4×C79#53412yes—
417C4×C79C2×H(5,𝔽2)11yescharacteristic
418C4×C79C2×H(5,𝔽2)11yescharacteristic
419Dic79—42no—
420Dic79—42no—
421Dic79—42no—
422C2×#3203—791nomaximal, Sylow
423C2×C79—42no—
424C2×C79—42no—
425C2×C79—42no—
426C2×C79—82no—
427C2×C79#320314yescomplemented
428C2×C79C2×#53411yescharacteristic
429C2×C79C2×#57611yescharacteristic
430C2×C79C2×#57811yescharacteristic
431D79—82no—
432C2×#537—791no—
433C2×#537D7911yescharacteristic, complemented
434#3203—7916no—
435C2×#484—791no—
436C2×#484—791no—
437C2×#480—791no—
438C2×#480—791no—
439C2×#468—791no—
440C2×#468—791no—
441C2×#467—791no—
442C2×#466—791no—
443C2×#452—791no—
444C2×#452—791no—
445C2×#449—791no—
446C2×#449—791no—
447C2×#408—791no—
448C79C2×#320311yescharacteristic, complemented, Sylow
449C22×#41—791no—
450C22×#41C2×D7911yescharacteristic
451C22×#41C2×D7911yescharacteristic
452C22×Q16—791no—
453C22×SD16—791no—
454C22×SD16—791no—
455C22×D8—791no—
456C22×M16—791no—
457C23×C8—791no—
458#537—24no—
459#537—798no—
460#537—1584no—
461#537C2×D7918yescomplemented
462C2×C22⋊Q8—21no—
463C2×C22⋊Q8—791no—
464C2×C22⋊Q8—791no—
465C2×C22⋊Q8—1581no—
466C2×C22⋊Q8C2×D7911yescharacteristic
467C2×C22⋊Q8C2×D7911yescharacteristic
468C2×#121—21no—
469C2×#121—21no—
470C2×#121—21no—
471C2×#121—791no—
472C2×#121—791no—
473C2×#121—1581no—
474C2×#121—1581no—
475C2×#121—1581no—
476C2×#121C2×D7911yescharacteristic
477C2×#121C2×D7911yescharacteristic
478C22×C4⋊C4—791no—
479C22×C4⋊C4C2×D7911yescharacteristic
480#484—798no—
481#484—798no—
482#480—798no—
483#480—798no—
484#468—798no—
485#468—798no—
486#467—798no—
487#466—798no—
488#452—798no—
489#452—798no—
490#449—798no—
491#449—798no—
492C2×#107—791no—
493C2×#107—791no—
494C2×#107—791no—
495C2×#107—791no—
496C2×#103—791no—
497C2×#103—791no—
498C2×#103—791no—
499C2×#103—791no—
500C2×#102—791no—
501C2×#102—791no—
502C2×#102—791no—
503C2×#102—791no—
504#408—798no—
505C2×C22⋊C8—791no—
506C2×C22⋊C8—791no—
507C2×C22⋊C8—791no—
508C2×C22⋊C8—791no—
509C2×#41—22no—
510C2×#41—42no—
511C2×#41—42no—
512C2×#41—42no—
513C2×#41—42no—
514C2×#41—3162no—
515C2×#41—3162no—
516C2×#41—794no—
517C2×#41—1582no—
518C2×#41C22⋊D7914yes—
519C2×#41C22×D7914yes—
520C2×#41C22×D7914yes—
521C22×Q8—791no—
522C22×Q8C22⋊D7911yescharacteristic
523C22×Q8C22×D7911yescharacteristic
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—791no—
528C22×D4—1581no—
529C22×D4—1581no—
530C22×D4—1581no—
531C22×D4C22⋊D7911yescharacteristic
532C22×D4C22⋊D7911yescharacteristic
533C22×D4C22⋊D7911yescharacteristic
534C22×D4C22×D7911yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—1581no—
538C23×C4—1581no—
539C23×C4C22×D7911yescharacteristic
540C23×C4C22×D7911yescharacteristic
541C23×C4C22×D7911yescharacteristic
542C2×Q16—3162no—
543C2×Q16—794no—
544C2×SD16—3162no—
545C2×SD16—3162no—
546C2×SD16—794no—
547C2×SD16—794no—
548C2×D8—3162no—
549C2×D8—794no—
550C2×M16—3162no—
551C2×M16—794no—
552C22×C8—3162no—
553C22×C8—794no—
554C22×C8—791no—
555C22×C8—791no—
556C22×C8—791no—
557C22×C8—791no—
558C22⋊Q8—28no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—794no—
562C22⋊Q8—794no—
563C22⋊Q8—1588no—
564C22⋊Q8—1582no—
565C22⋊Q8—1582no—
566C22⋊Q8C22×D7914yes—
567C22⋊Q8C22×D7914yes—
568#121—28no—
569#121—28no—
570#121—28no—
571#121—22no—
572#121—22no—
573#121—794no—
574#121—794no—
575#121—1588no—
576#121—1588no—
577#121—1588no—
578#121—1582no—
579#121—1582no—
580#121C22×D7914yes—
581#121C22×D7914yes—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—791no—
587C2×C4⋊C4—791no—
588C2×C4⋊C4—794no—
589C2×C4⋊C4—1581no—
590C2×C4⋊C4—1582no—
591C2×C4⋊C4—1581no—
592C2×C4⋊C4—1581no—
593C2×C4⋊C4C22×D7911yescharacteristic
594C2×C4⋊C4C22×D7911yescharacteristic
595C2×C4⋊C4C22×D7914yes—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—1581no—
601C2×C22⋊C4—1581no—
602C2×C22⋊C4—1581no—
603C2×C22⋊C4—1581no—
604#107—794no—
605#107—794no—
606#107—794no—
607#107—794no—
608#103—794no—
609#103—794no—
610#103—794no—
611#103—794no—
612#102—794no—
613#102—794no—
614#102—794no—
615#102—794no—
616C22⋊C8—794no—
617C22⋊C8—794no—
618C22⋊C8—794no—
619C22⋊C8—794no—
620C24—21no—
621C24—1581no—
622C24C2×C22⋊D7911yescharacteristic
623C24C2×C22⋊D7911yescharacteristic
624C24C2×C22⋊D7911yescharacteristic
625#41—48no—
626#41—44no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—48no—
631#41—3168no—
632#41—3164no—
633#41—3164no—
634C2×Q8—21no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—42no—
638C2×Q8—792no—
639C2×Q8—1582no—
640C2×Q8—1582no—
641C2×Q8—1581no—
642C2×Q8C2×C22⋊D7914yes—
643C2×Q8C23×D7912yes—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—44no—
654C2×D4—82no—
655C2×D4—82no—
656C2×D4—3164no—
657C2×D4—792no—
658C2×D4—6322no—
659C2×D4—6322no—
660C2×D4—1584no—
661C2×D4—1584no—
662C2×D4—1584no—
663C2×D4—1582no—
664C2×D4—1582no—
665C2×D4—1581no—
666C2×D4C2×C22⋊D7914yes—
667C2×D4C2×C22⋊D7914yes—
668C2×D4C2×C22⋊D7914yes—
669C2×D4C23×D7912yes—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—44no—
682C22×C4—82no—
683C22×C4—3164no—
684C22×C4—6322no—
685C22×C4—1581no—
686C22×C4—1581no—
687C22×C4—1581no—
688C22×C4—1584no—
689C22×C4—1584no—
690C22×C4C2×C22⋊D7912yes—
691C22×C4C2×C22⋊D7912yes—
692C22×C4C2×C22⋊D7912yes—
693C22×C4C2×C22⋊D7911yescharacteristic
694C22×C4C2×C22⋊D7911yescharacteristic
695C22×C4C2×C22⋊D7911yescharacteristic
696C22×C4C23×D7912yes—
697C22×C4C23×D7912yes—
698C22×C4C23×D7912yes—
699C22×C4C23×D7911yescharacteristic
700Q16—3164no—
701SD16—3164no—
702SD16—3164no—
703D8—3164no—
704M16—3164no—
705C2×C8—3164no—
706C2×C8—792no—
707C2×C8—792no—
708C2×C8—792no—
709C2×C8—792no—
710C2×C8—1582no—
711C2×C8—1582no—
712C2×C8—1582no—
713C2×C8—1582no—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—24no—
718C4⋊C4—24no—
719C4⋊C4—792no—
720C4⋊C4—792no—
721C4⋊C4—1584no—
722C4⋊C4—1584no—
723C4⋊C4—1584no—
724C4⋊C4—1581no—
725C4⋊C4—1581no—
726C4⋊C4C23×D7912yes—
727C4⋊C4C23×D7912yes—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—1584no—
733C22⋊C4—1584no—
734C22⋊C4—1584no—
735C22⋊C4—1584no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—3162no—
750C23—3162no—
751C23—3162no—
752C23—1582no—
753C23C22×C22⋊D7912yes—
754C23C22×C22⋊D7912yes—
755C23C22×C22⋊D7912yes—
756C23C22×C22⋊D7911yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—44no—
760Q8—42no—
761Q8—3162no—
762Q8—1582no—
763Q8—1582no—
764D4—22no—
765D4—22no—
766D4—44no—
767D4—44no—
768D4—44no—
769D4—48no—
770D4—42no—
771D4—84no—
772D4—84no—
773D4—3168no—
774D4—3162no—
775D4—6324no—
776D4—6324no—
777D4—1582no—
778D4—1582no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—48no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—84no—
799C2×C4—3168no—
800C2×C4—3162no—
801C2×C4—3162no—
802C2×C4—3162no—
803C2×C4—6324no—
804C2×C4—1582no—
805C2×C4—1582no—
806C2×C4—1582no—
807C2×C4C22×C22⋊D7912yes—
808C2×C4C22×C22⋊D7912yes—
809C2×C4C22×C22⋊D7912yes—
810C2×C4C22×C22⋊D7911yescharacteristic
811C2×C4#1457920612yes—
812C2×C4#1457920612yes—
813C2×C4C24×D7911yescharacteristic
814C8—1582no—
815C8—1582no—
816C8—1582no—
817C8—1582no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—84no—
834C22—3162no—
835C22—3162no—
836C22—3162no—
837C22—6324no—
838C22#1909912212yes—
839C22#1909936612yes—
840C22#1909937812yes—
841C22C23×C22⋊D7911yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—3162no—
849C4—3162no—
850C4—3162no—
851C4#1909912212yes—
852C4C2×#1457920611yescharacteristic
853C4C2×#1457920611yescharacteristic
854C2—42no—
855C2—42no—
856C2—42no—
857C2—82no—
858C2—6322no—
859C2#2377429714yesdirect product factor
860C2C2×#1909912211yescharacteristic
861C2C2×#1909936611yescharacteristic
862C2C2×#1909937811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#537×C79C2
socleC23×C79C22×D4
hypercenterC2×#537D79
hypocenterC79C2×#3203
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#19099141C2semidirect
2. #23774297C2direct (N × H)
3. C2×#19098898C2semidirect
4. C2×#19098896C2semidirect
5. C2×#19098876C2semidirect
6. C2×#19098874C2semidirect
7. C2×#19098811C2semidirect
8. C2×#19098807C2semidirect
9. C2×#19098802C2semidirect
10. C2×#19098797C2semidirect
11. C2×#19098725C2semidirect
12. C2×#19098723C2semidirect
13. C2×#19098708C2semidirect
14. C2×#19098706C2semidirect
15. C2×#19098530C2semidirect
16. C2×#537×C79C2semidirect
25. #19099141C22semidirect
35. #19098898C22semidirect
36. #19098896C22semidirect
37. #19098876C22semidirect
38. #19098874C22semidirect
39. #19098811C22semidirect
40. #19098807C22semidirect
41. #19098802C22semidirect
42. #19098797C22semidirect
43. #19098725C22semidirect
44. #19098723C22semidirect
45. #19098708C22semidirect
46. #19098706C22semidirect
59. #19098530C22semidirect
67. #537×C79C22semidirect
427. C2×C79#3203semidirect
433. C2×#537D79semidirect
448. C79C2×#3203semidirect
461. #537C2×D79semidirect
859. C2#23774297direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991412
#237742972
C2×#190988982
C2×#190988962
C2×#190988762
C2×#190988742
C2×#190988112
C2×#190988072
C2×#190988022
C2×#190987972
C2×#190987252
C2×#190987232
C2×#190987082
C2×#190987062
C2×#190985302
C2×#537×C792
C2×#320379