Finite Group Databasebeta

← C2×#23777191 #35196737

Subgroups — C2×#23777191 #35196737

Order 20224.

11534 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579209C211yesmaximal, characteristic, complemented
2C22×#14579207C211yesmaximal, characteristic, complemented
3#23777191C2132yesmaximal, direct product factor
4C2×#19099225C211yesmaximal, characteristic, complemented
5C2×#19099224C211yesmaximal, characteristic, complemented
6C2×#19099220C211yesmaximal, characteristic, complemented
7C2×#19099210C213yesmaximal, complemented
8C2×#19099209C213yesmaximal, complemented
9C2×#19099206C213yesmaximal, complemented
10C2×#19099204C213yesmaximal, complemented
11C2×#19099136C213yesmaximal, complemented
12C2×#19099129C213yesmaximal, complemented
13C2×#19099110C213yesmaximal, complemented
14C2×#124×D79C213yesmaximal, complemented
15C2×C4×#11929625C211yesmaximal, characteristic, complemented
16C2×#548×C79C211yesmaximal, characteristic, complemented
17C2×#14579209—216no—
18C2×#14579209C22116yescomplemented
19C2×#14579207—216no—
20C2×#14579207C22116yescomplemented
21C22×#11929625C2211yescharacteristic
22C22×#11929625C2211yescharacteristic
23C22×#11929625C2213yescomplemented
24C22×#11929624C2213yes—
25C22×#11929624C2213yescomplemented
26C22×#11929624C2213yescomplemented
27C22×Q8×D79C2211yescharacteristic, complemented
28C22×Q8×D79C2213yescomplemented
29C23×D316C2213yes—
30C22×D4×D79C2213yes—
31C22×D4×D79C2213yes—
32#19099225C22116yescomplemented
33#19099224C22116yescomplemented
34#19099220C22116yescomplemented
35#19099210C22148yescomplemented
36#19099209C22148yescomplemented
37#19099206C22148yescomplemented
38#19099204C22148yescomplemented
39#19099136C22148yescomplemented
40#19099129C22148yescomplemented
41#19099110C22148yescomplemented
42C2×#14579160C2213yescomplemented
43C2×#14579157C2213yescomplemented
44C2×#14579150C2213yescomplemented
45C2×#14579149C2213yescomplemented
46C2×#14579148C2213yescomplemented
47C2×#14579147C2213yescomplemented
48C2×#14579147C2216yescomplemented
49C2×#14579147C2211yescharacteristic, complemented
50#124×D79C22148yescomplemented
51C2×#14579146C2216yescomplemented
52C2×#14579143C2216yescomplemented
53C2×#14579141C2213yescomplemented
54C2×#14579140C2213yescomplemented
55C2×#14579137C2213yescomplemented
56C2×#14579136C2213yescomplemented
57C2×#14579136C2213yescomplemented
58C2×#14579135C2213yescomplemented
59C2×#14579134C2213yescomplemented
60C2×#14579134C2213yescomplemented
61C2×#14579132C2213yescomplemented
62C2×#14579132C2213yescomplemented
63C2×#14579131C2216yescomplemented
64C2×#14579129C2216yescomplemented
65C4×#11929625C22116yescomplemented
66C2×Q8×Dic79C2211yescharacteristic, complemented
67C2×C4×D316C2213yescomplemented
68C2×C4×D316C2213yescomplemented
69C2×#14579123C2213yescomplemented
70C2×C4×C22⋊D79C2213yescomplemented
71C2×C4×C22⋊D79C2213yescomplemented
72C2×#14579119C2213yescomplemented
73C2×C22⋊C4×D79C2216yescomplemented
74C2×C22⋊C4×D79C2216yescomplemented
75C2×C42×D79C2213yescomplemented
76C22×#41×C79C2211yescharacteristic
77C23×Q8×C79C2211yescharacteristic, complemented
78#548×C79C22116yescomplemented
79C2×#124×C79C2213yescomplemented
80C2×C22⋊Q8×C79C2213yescomplemented
81C2×#121×C79C2213yescomplemented
82C2×C4×Q8×C79C2211yescharacteristic, complemented
83C2×C4×D4×C79C2213yescomplemented
84C24×D79C2316yes—
85#14579209—2128no—
86#14579207—2128no—
87C2×#11929625—28no—
88C2×#11929625—224no—
89C2×#11929625D4116yescomplemented
90C2×#11929625C2318yes—
91C2×#11929625C2318yes—
92C2×#11929625C23124yescomplemented
93C2×#11929624—224no—
94C2×#11929624—224no—
95C2×#11929624—224no—
96C2×#11929624C23124yes—
97C2×#11929624C23124yescomplemented
98C2×#11929624C23124yescomplemented
99C22×Dic158C2313yes—
100C22×Dic158C2313yes—
101C22×Dic158C2311yescharacteristic
102C2×Q8×D79—28no—
103C2×Q8×D79—224no—
104C2×Q8×D79C23124yescomplemented
105C2×Q8×D79C2318yescomplemented
106C22×D316—224no—
107C22×D316C23124yes—
108C22×D316C2313yes—
109C22×D316C2313yes—
110C22×D316C2313yes—
111C22×D316C2313yes—
112C22×D316C2313yes—
113C22×C22⋊D79C2313yes—
114C22×C22⋊D79C2313yes—
115C22×C22⋊D79C2313yes—
116C22×C22⋊D79C2311yescharacteristic
117C22×C22⋊D79C2313yes—
118C22×C22⋊D79C2313yes—
119C2×D4×D79—224no—
120C2×D4×D79—224no—
121C2×D4×D79C23124yes—
122C2×D4×D79C23124yes—
123C22×C4×D79C2316yes—
124C22×C4×D79C2313yes—
125C22×C4×D79C2313yes—
126C22×C4×D79C2313yes—
127C22×C4×D79C2313yes—
128C22×C4×D79C2313yes—
129#14579160C23124yescomplemented
130#14579157C23124yescomplemented
131#14579150C23124yescomplemented
132#14579149C23124yescomplemented
133#14579148C23124yescomplemented
134#14579147C23148yescomplemented
135#14579147C23124yescomplemented
136#14579147C2318yescomplemented
137#14579146C23148yescomplemented
138#14579143C23148yescomplemented
139#14579141C23124yescomplemented
140#14579140C23124yescomplemented
141#14579137C23124yescomplemented
142#14579136C23124yescomplemented
143#14579136C23124yescomplemented
144#14579135C23124yescomplemented
145#14579134C23124yescomplemented
146#14579134C23124yescomplemented
147#14579132C23124yescomplemented
148#14579132C23124yescomplemented
149#14579131C23148yescomplemented
150#14579129C23148yescomplemented
151Q8×Dic79C2318yescomplemented
152C4×D316C23124yescomplemented
153C4×D316C23124yescomplemented
154#14579123C23124yescomplemented
155C4×C22⋊D79C23124yescomplemented
156C4×C22⋊D79C23124yescomplemented
157#14579119C23124yescomplemented
158C2×C4⋊Dic79C2313yes—
159C2×C4⋊Dic79C2313yes—
160C2×Dic79⋊C4C2313yes—
161C2×Dic79⋊C4C2313yes—
162C2×C22⋊Dic79C2313yes—
163C2×C22⋊Dic79C2316yes—
164C2×C22⋊Dic79C2311yescharacteristic
165C2×(C2×D79)⋊C4C2313yes—
166C2×(C2×D79)⋊C4C2313yes—
167C2×(C2×D79)⋊C4C2316yes—
168C2×(C2×D79)⋊C4C2316yes—
169C2×(C2×D79)⋊C4C2316yes—
170C2×(C2×D79)⋊C4C2311yescharacteristic
171C2×(C2×D79)⋊C4C2311yescharacteristic
172C22⋊C4×D79C23148yescomplemented
173C22⋊C4×D79C23148yescomplemented
174C2×C4×Dic79C2311yescharacteristic
175C2×C4×Dic79C2313yes—
176C2×C4×Dic79C2313yes—
177C42×D79C23124yescomplemented
178C2×#41×C79—28no—
179C2×#41×C79C2318yes—
180C22×Q8×C79—28no—
181C22×Q8×C79C2313yes—
182C22×Q8×C79C2311yescharacteristic
183C22×Q8×C79C2318yescomplemented
184C22×D4×C79C2313yes—
185C22×D4×C79C2313yes—
186C23×C4×C79C2313yes—
187C23×C4×C79C2313yes—
188#124×C79C23124yescomplemented
189C22⋊Q8×C79C23124yescomplemented
190#121×C79C23124yescomplemented
191C4×Q8×C79C2318yescomplemented
192C4×D4×C79C23124yescomplemented
193C2×C4⋊C4×C79C2313yes—
194C2×C4⋊C4×C79C2313yes—
195C2×C22⋊C4×C79C2311yescharacteristic
196C2×C22⋊C4×C79C2313yes—
197C2×C22⋊C4×C79C2316yes—
198C2×C42×C79C2313yes—
199C23×D79—224no—
200C23×D79—412no—
201C23×D79—412no—
202C23×D79C2413yes—
203C23×D79C2411yescharacteristic
204C23×D79C2413yes—
205C23×D79C24124yes—
206#11929625—296no—
207#11929625—232no—
208#11929625C2×D4164yescomplemented
209#11929624—296no—
210#11929624—296no—
211#11929624—296no—
212C2×Dic158—212no—
213C2×Dic158—24no—
214C2×Dic158—212no—
215C2×Dic158C24112yes—
216C2×Dic158C24112yes—
217C2×Dic158C2414yes—
218Q8×D79—296no—
219Q8×D79—232no—
220C2×D316—296no—
221C2×D316—212no—
222C2×D316—212no—
223C2×D316—212no—
224C2×D316—46no—
225C2×D316C2×D4124yes—
226C2×D316C24112yes—
227C2×D316C24112yes—
228C2×D316C24112yes—
229C2×D316C24112yes—
230C2×D316C24112yes—
231C2×C22⋊D79—24no—
232C2×C22⋊D79—212no—
233C2×C22⋊D79—212no—
234C2×C22⋊D79—212no—
235C2×C22⋊D79—46no—
236C2×C22⋊D79—46no—
237C2×C22⋊D79C24112yes—
238C2×C22⋊D79C24112yes—
239C2×C22⋊D79C24112yes—
240C2×C22⋊D79C2414yes—
241C2×C22⋊D79C24112yes—
242C2×C22⋊D79C24112yes—
243D4×D79—296no—
244D4×D79—296no—
245C22×Dic79C2413yes—
246C22×Dic79C2411yescharacteristic
247C22×Dic79C2411yescharacteristic
248C22×Dic79C2413yes—
249C22×Dic79C2411yescharacteristic
250C2×C4×D79—224no—
251C2×C4×D79—212no—
252C2×C4×D79—212no—
253C2×C4×D79—46no—
254C2×C4×D79—46no—
255C2×C4×D79C2×D4124yes—
256C2×C4×D79C24124yes—
257C2×C4×D79C24112yes—
258C2×C4×D79C24112yes—
259C2×C4×D79C24112yes—
260C2×C4×D79C24112yes—
261C2×C4×D79C24112yes—
262C4⋊Dic79C24112yes—
263C4⋊Dic79C24112yes—
264Dic79⋊C4C24112yes—
265Dic79⋊C4C24112yes—
266C22⋊Dic79C24112yes—
267C22⋊Dic79C24124yes—
268C22⋊Dic79C2414yes—
269(C2×D79)⋊C4C24112yes—
270(C2×D79)⋊C4C24112yes—
271(C2×D79)⋊C4C24124yes—
272(C2×D79)⋊C4C24124yes—
273(C2×D79)⋊C4C24124yes—
274(C2×D79)⋊C4C2414yes—
275(C2×D79)⋊C4C2414yes—
276C4×Dic79C2414yes—
277C4×Dic79C24112yes—
278C4×Dic79C24112yes—
279C24×C79C2413yes—
280C24×C79C2411yescharacteristic
281#41×C79—232no—
282C2×Q8×C79—232no—
283C2×Q8×C79—212no—
284C2×Q8×C79C2×D418yes—
285C2×Q8×C79C24112yes—
286C2×Q8×C79C2414yes—
287C2×D4×C79—212no—
288C2×D4×C79—46no—
289C2×D4×C79C24112yes—
290C2×D4×C79C24112yes—
291C22×C4×C79—212no—
292C22×C4×C79—212no—
293C22×C4×C79C2413yes—
294C22×C4×C79C2411yescharacteristic
295C22×C4×C79C24112yes—
296C22×C4×C79C24112yes—
297C22×C4×C79C2411yescharacteristic
298C22×C4×C79C2413yes—
299C22×C4×C79C2413yes—
300C4⋊C4×C79C24112yes—
301C4⋊C4×C79C24112yes—
302C22⋊C4×C79C2414yes—
303C22⋊C4×C79C24112yes—
304C22⋊C4×C79C24124yes—
305C42×C79C24112yes—
306C23×C79—22no—
307C23×C79—26no—
308C23×C79—22no—
309C23×C79—26no—
310C23×C79—26no—
311C23×C79—22no—
312C23×C79C2516yes—
313C23×C79C2512yes—
314C23×C79C2511yescharacteristic
315C22×D79—26no—
316C22×D79—26no—
317C22×D79—22no—
318C22×D79—26no—
319C22×D79—22no—
320C22×D79—26no—
321C22×D79—22no—
322C22×D79—26no—
323C22×D79—248no—
324C22×D79—424no—
325C22×D79—424no—
326C22×D79—848no—
327C22×D79C22×D4112yes—
328C22×D79C2516yes—
329C22×D79C2512yes—
330C22×D79C2516yes—
331Q8×C79—224no—
332Q8×C79C22×D4116yes—
333D4×C79—224no—
334D4×C79—412no—
335C2×C4×C79—26no—
336C2×C4×C79—22no—
337C2×C4×C79—22no—
338C2×C4×C79—26no—
339C2×C4×C79—224no—
340C2×C4×C79—224no—
341C2×C4×C79C22×D4112yes—
342C2×C4×C79C2516yes—
343C2×C4×C79C2512yes—
344C2×C4×C79C2516yes—
345C2×C4×C79C2512yes—
346C2×C4×C79C2516yes—
347C22⋊D79—224no—
348C22⋊D79—224no—
349C22⋊D79—224no—
350C22⋊D79—28no—
351C22⋊D79—412no—
352C22⋊D79—412no—
353C2×Dic79—22no—
354C2×Dic79—26no—
355C2×Dic79—22no—
356C2×Dic79—26no—
357C2×Dic79C22×D414yes—
358C2×Dic79C2512yes—
359C2×Dic79C2516yes—
360C2×Dic79C2516yes—
361C2×Dic79C2512yes—
362C2×Dic79C2512yes—
363D316—224no—
364D316—224no—
365D316—224no—
366D316—412no—
367D316C22×D4148yes—
368C4×D79—248no—
369C4×D79—224no—
370C4×D79—224no—
371C4×D79—412no—
372C4×D79—412no—
373C4×D79C22×D4148yes—
374Dic158—224no—
375Dic158—224no—
376Dic158—28no—
377C22×C79—22no—
378C22×C79—26no—
379C22×C79—22no—
380C22×C79—26no—
381C22×C79—22no—
382C22×C79—26no—
383C22×C79—412no—
384C22×C79—44no—
385C22×C79C23×D412yes—
386C22×C79#58512yes—
387C22×C79#58512yes—
388C22×C79C2611yescharacteristic
389C2×D79—26no—
390C2×D79—26no—
391C2×D79—224no—
392C2×D79—26no—
393C2×D79—22no—
394C2×D79—22no—
395C2×D79—26no—
396C2×D79—26no—
397C2×D79—22no—
398C2×D79—44no—
399C2×D79—412no—
400C2×D79—848no—
401C2×D79C23×D4112yes—
402C4×C79—22no—
403C4×C79—26no—
404C4×C79—26no—
405C4×C79—22no—
406C4×C79C23×D4112yes—
407Dic79—22no—
408Dic79—26no—
409Dic79—26no—
410Dic79—22no—
411Dic79C23×D414yes—
412C2×#3500—791nomaximal, Sylow
413C2×C79—46no—
414C2×C79—42no—
415C2×C79#350014yescomplemented
416C2×C79C24×D411yescharacteristic
417C2×C79C2×#58511yescharacteristic
418C2×C79C2×#58511yescharacteristic
419D79—212no—
420D79—42no—
421D79—46no—
422C22×2−1+4—791no—
423C22×H(5,𝔽2)—791no—
424#3500—7932no—
425C2×#548—791no—
426C2×#548—791no—
427C2×#548—791no—
428C2×#548D7911yescharacteristic, complemented
429C2×#546—793no—
430C2×#546—793no—
431C2×#546—793no—
432C2×#546—793no—
433C2×#536—793no—
434C2×#535—793no—
435C2×#532—793no—
436C22×#124—793no—
437C2×C4×#41—791no—
438C79C2×#350011yescharacteristic, complemented, Sylow
439C2×2−1+4—7916no—
440C2×2−1+4—15816no—
441C2×H(5,𝔽2)—7916no—
442C2×H(5,𝔽2)—15816no—
443C22×#41—791no—
444C22×#41—791no—
445C22×#41—793no—
446C22×#41—793no—
447C22×#41—793no—
448C22×#41—793no—
449C22×#41C2×D7911yescharacteristic
450C23×Q8—793no—
451C23×Q8—791no—
452C23×Q8C2×D7911yescharacteristic, complemented
453C23×D4—793no—
454C23×D4—793no—
455C23×D4—793no—
456#548—7916no—
457#548—7916no—
458#548—7916no—
459#548C2×D79116yescomplemented
460#546—7948no—
461#546—7948no—
462#546—7948no—
463#546—7948no—
464#536—7948no—
465#535—7948no—
466#532—7948no—
467C2×C4⋊Q8—793no—
468C2×#127—793no—
469C2×#124—793no—
470C2×#124—793no—
471C2×#124—7948no—
472C2×#124—793no—
473C2×#124—796no—
474C2×#124—791no—
475C2×#124—793no—
476C2×#124C2×D7913yescomplemented
477C2×#123—796no—
478C2×#123—796no—
479C2×C22⋊Q8—793no—
480C2×C22⋊Q8—793no—
481C2×C22⋊Q8—793no—
482C2×C22⋊Q8C2×D7913yescomplemented
483C2×#121—793no—
484C2×#121—793no—
485C2×#121—793no—
486C2×#121—793no—
487C2×#121—793no—
488C2×#121—793no—
489C2×#121—793no—
490C2×#121C2×D7913yescomplemented
491C2×#120—796no—
492C2×#120—796no—
493C4×#41—7916no—
494C2×C4×Q8—791no—
495C2×C4×Q8C2×D7911yescharacteristic, complemented
496C2×C4×D4—793no—
497C2×C4×D4—793no—
498C2×C4×D4—793no—
499C2×C4×D4—793no—
500C2×C4×D4—793no—
501C2×C4×D4C2×D7913yescomplemented
502C2×#117—793no—
503C22×C22⋊C4—796no—
504C22×C22⋊C4—796no—
505C22×C42—793no—
506C25—796no—
5072−1+4—158128no—
508H(5,𝔽2)—158128no—
509C2×#41—28no—
510C2×#41—7916no—
511C2×#41—798no—
512C2×#41—798no—
513C2×#41—7924no—
514C2×#41—7924no—
515C2×#41—7924no—
516C2×#41—7924no—
517C2×#41—15824no—
518C2×#41—15824no—
519C2×#41—15824no—
520C2×#41—15824no—
521C2×#41—1588no—
522C2×#41C22×D7918yes—
523C22×Q8—28no—
524C22×Q8—7924no—
525C22×Q8—798no—
526C22×Q8—793no—
527C22×Q8—793no—
528C22×Q8—791no—
529C22×Q8—15824no—
530C22×Q8—1588no—
531C22×Q8C22×D7913yes—
532C22×Q8C22×D7911yescharacteristic
533C22×Q8C22×D7918yescomplemented
534C22×D4—793no—
535C22×D4—793no—
536C22×D4—793no—
537C22×D4—793no—
538C22×D4—793no—
539C22×D4—791no—
540C22×D4—7924no—
541C22×D4—7924no—
542C22×D4—793no—
543C22×D4—793no—
544C22×D4—793no—
545C22×D4—793no—
546C22×D4—793no—
547C22×D4—7924no—
548C22×D4—15824no—
549C22×D4—15824no—
550C22×D4—15824no—
551C22×D4C22×D7913yes—
552C22×D4C22×D7913yes—
553C23×C4—793no—
554C23×C4—793no—
555C23×C4—793no—
556C23×C4—796no—
557C23×C4—793no—
558C23×C4—793no—
559C23×C4C22×D7913yes—
560C23×C4C22×D7913yes—
561C4⋊Q8—7924no—
562#127—7924no—
563#124—7924no—
564#124—7924no—
565#124—7924no—
566#124—7948no—
567#124—798no—
568#124—7924no—
569#124C22×D79124yescomplemented
570#123—7948no—
571#123—7948no—
572C22⋊Q8—7924no—
573C22⋊Q8—7924no—
574C22⋊Q8—7924no—
575C22⋊Q8C22×D79124yescomplemented
576#121—7924no—
577#121—7924no—
578#121—7924no—
579#121—7924no—
580#121—7924no—
581#121—7924no—
582#121—7924no—
583#121C22×D79124yescomplemented
584#120—7948no—
585#120—7948no—
586C4×Q8—798no—
587C4×Q8C22×D7918yescomplemented
588C4×D4—7924no—
589C4×D4—7924no—
590C4×D4—7924no—
591C4×D4—7924no—
592C4×D4—7924no—
593C4×D4C22×D79124yescomplemented
594#117—7924no—
595C2×C4⋊C4—793no—
596C2×C4⋊C4—793no—
597C2×C4⋊C4—793no—
598C2×C4⋊C4—793no—
599C2×C4⋊C4C22×D7913yes—
600C2×C4⋊C4C22×D7913yes—
601C2×C22⋊C4—793no—
602C2×C22⋊C4—796no—
603C2×C22⋊C4—791no—
604C2×C22⋊C4—793no—
605C2×C22⋊C4—793no—
606C2×C22⋊C4—796no—
607C2×C22⋊C4—796no—
608C2×C22⋊C4—796no—
609C2×C22⋊C4—791no—
610C2×C22⋊C4—791no—
611C2×C22⋊C4—7948no—
612C2×C22⋊C4—7948no—
613C2×C22⋊C4C22×D7913yes—
614C2×C22⋊C4C22×D7916yes—
615C2×C22⋊C4C22×D7911yescharacteristic
616C2×C42—793no—
617C2×C42—793no—
618C2×C42—791no—
619C2×C42—7924no—
620C2×C42C22×D7913yes—
621C24—31612no—
622C24—31612no—
623C24—7924no—
624C24—793no—
625C24—793no—
626C24—791no—
627C24—15824no—
628C24C23×D7913yes—
629C24C23×D7911yescharacteristic
630#41—232no—
631#41—7964no—
632#41—15896no—
633#41—15896no—
634#41—15896no—
635#41—15896no—
636#41—15832no—
637C2×Q8—232no—
638C2×Q8—212no—
639C2×Q8—7912no—
640C2×Q8—7912no—
641C2×Q8—794no—
642C2×Q8—15812no—
643C2×Q8—1584no—
644C2×Q8—15896no—
645C2×Q8—15832no—
646C2×Q8—15812no—
647C2×Q8D4×D7918yes—
648C2×Q8C23×D79112yes—
649C2×Q8C23×D7914yes—
650C2×D4—212no—
651C2×D4—46no—
652C2×D4—3166no—
653C2×D4—3166no—
654C2×D4—3166no—
655C2×D4—7912no—
656C2×D4—7912no—
657C2×D4—7912no—
658C2×D4—7912no—
659C2×D4—7912no—
660C2×D4—794no—
661C2×D4—7912no—
662C2×D4—7912no—
663C2×D4—7912no—
664C2×D4—7912no—
665C2×D4—7912no—
666C2×D4—7924no—
667C2×D4—15896no—
668C2×D4—15812no—
669C2×D4—15812no—
670C2×D4—15896no—
671C2×D4—15812no—
672C2×D4—1584no—
673C2×D4—15896no—
674C2×D4—15812no—
675C2×D4—15812no—
676C2×D4—15812no—
677C2×D4C23×D79112yes—
678C2×D4C23×D79112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—3166no—
682C22×C4—3166no—
683C22×C4—7912no—
684C22×C4—7912no—
685C22×C4—791no—
686C22×C4—7912no—
687C22×C4—7924no—
688C22×C4—791no—
689C22×C4—793no—
690C22×C4—793no—
691C22×C4—791no—
692C22×C4—7924no—
693C22×C4—7912no—
694C22×C4—7912no—
695C22×C4—15824no—
696C22×C4—15812no—
697C22×C4—15812no—
698C22×C4C23×D79112yes—
699C22×C4C23×D79112yes—
700C22×C4C23×D7911yescharacteristic
701C22×C4C23×D7913yes—
702C22×C4C23×D7913yes—
703C22×C4C23×D7911yescharacteristic
704C22×C4C23×D7913yes—
705C4⋊C4—7912no—
706C4⋊C4—7912no—
707C4⋊C4—7912no—
708C4⋊C4—7912no—
709C4⋊C4C23×D79112yes—
710C4⋊C4C23×D79112yes—
711C22⋊C4—7912no—
712C22⋊C4—7924no—
713C22⋊C4—794no—
714C22⋊C4—7912no—
715C22⋊C4—7912no—
716C22⋊C4—7924no—
717C22⋊C4—7924no—
718C22⋊C4—7924no—
719C22⋊C4—794no—
720C22⋊C4—794no—
721C22⋊C4C23×D79112yes—
722C22⋊C4C23×D79124yes—
723C22⋊C4C23×D7914yes—
724C42—794no—
725C42—7912no—
726C42—7912no—
727C42C23×D79112yes—
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—31624no—
735C23—31624no—
736C23—796no—
737C23—7912no—
738C23—796no—
739C23—792no—
740C23—63248no—
741C23—15848no—
742C23—1582no—
743C23—1586no—
744C23—1582no—
745C23—1586no—
746C23—1582no—
747C23—1586no—
748C23—1586no—
749C23—1586no—
750C23C24×D7916yes—
751C23C24×D7912yes—
752C23C24×D7911yescharacteristic
753Q8—224no—
754Q8—15824no—
755Q8—1588no—
756Q8—15824no—
757Q8C2×D4×D79116yes—
758D4—224no—
759D4—412no—
760D4—31612no—
761D4—31612no—
762D4—31612no—
763D4—7948no—
764D4—15824no—
765D4—15824no—
766D4—15824no—
767D4—1588no—
768D4—15824no—
769D4—15824no—
770D4—15824no—
771C2×C4—26no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—26no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—31612no—
778C2×C4—31612no—
779C2×C4—792no—
780C2×C4—794no—
781C2×C4—7948no—
782C2×C4—792no—
783C2×C4—796no—
784C2×C4—796no—
785C2×C4—792no—
786C2×C4—15848no—
787C2×C4—1582no—
788C2×C4—1586no—
789C2×C4—1582no—
790C2×C4—1586no—
791C2×C4—15824no—
792C2×C4—15824no—
793C2×C4C2×D4×D79112yes—
794C2×C4C24×D7912yes—
795C2×C4C24×D7916yes—
796C2×C4C24×D7916yes—
797C2×C4C24×D7912yes—
798C2×C4C24×D7916yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—412no—
806C22—44no—
807C22—31612no—
808C22—3164no—
809C22—7912no—
810C22—63248no—
811C22—1582no—
812C22—1586no—
813C22—1582no—
814C22—1586no—
815C22—1582no—
816C22—1586no—
817C22—1586no—
818C22—1586no—
819C22—15824no—
820C22C22×D4×D7912yes—
821C22#1909939912yes—
822C22#1909940012yes—
823C22C25×D7911yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—794no—
829C4—1582no—
830C4—1586no—
831C4—1582no—
832C4—1586no—
833C4C22×D4×D79112yes—
834C2—46no—
835C2—42no—
836C2—3166no—
837C2—3162no—
838C2—15812no—
839C2#2377719114yesdirect product factor
840C2C23×D4×D7911yescharacteristic
841C2C2×#1909939911yescharacteristic
842C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#548×C79C2
socleC23×C79C25
hypercenterC2×#548D79
hypocenterC79C2×#3500
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14579209C2semidirect
2. C22×#14579207C2semidirect
3. #23777191C2direct (N × H)
4. C2×#19099225C2semidirect
5. C2×#19099224C2semidirect
6. C2×#19099220C2semidirect
7. C2×#19099210C2semidirect
8. C2×#19099209C2semidirect
9. C2×#19099206C2semidirect
10. C2×#19099204C2semidirect
11. C2×#19099136C2semidirect
12. C2×#19099129C2semidirect
13. C2×#19099110C2semidirect
14. C2×#124×D79C2semidirect
15. C2×C4×#11929625C2semidirect
16. C2×#548×C79C2semidirect
18. C2×#14579209C22semidirect
20. C2×#14579207C22semidirect
23. C22×#11929625C22semidirect
25. C22×#11929624C22semidirect
26. C22×#11929624C22semidirect
27. C22×Q8×D79C22semidirect
28. C22×Q8×D79C22semidirect
32. #19099225C22semidirect
33. #19099224C22semidirect
34. #19099220C22semidirect
35. #19099210C22semidirect
36. #19099209C22semidirect
37. #19099206C22semidirect
38. #19099204C22semidirect
39. #19099136C22semidirect
40. #19099129C22semidirect
41. #19099110C22semidirect
42. C2×#14579160C22semidirect
43. C2×#14579157C22semidirect
44. C2×#14579150C22semidirect
45. C2×#14579149C22semidirect
46. C2×#14579148C22semidirect
47. C2×#14579147C22semidirect
48. C2×#14579147C22semidirect
49. C2×#14579147C22semidirect
50. #124×D79C22semidirect
51. C2×#14579146C22semidirect
52. C2×#14579143C22semidirect
53. C2×#14579141C22semidirect
54. C2×#14579140C22semidirect
55. C2×#14579137C22semidirect
56. C2×#14579136C22semidirect
57. C2×#14579136C22semidirect
58. C2×#14579135C22semidirect
59. C2×#14579134C22semidirect
60. C2×#14579134C22semidirect
61. C2×#14579132C22semidirect
62. C2×#14579132C22semidirect
63. C2×#14579131C22semidirect
64. C2×#14579129C22semidirect
65. C4×#11929625C22semidirect
66. C2×Q8×Dic79C22semidirect
67. C2×C4×D316C22semidirect
68. C2×C4×D316C22semidirect
69. C2×#14579123C22semidirect
70. C2×C4×C22⋊D79C22semidirect
71. C2×C4×C22⋊D79C22semidirect
72. C2×#14579119C22semidirect
73. C2×C22⋊C4×D79C22semidirect
74. C2×C22⋊C4×D79C22semidirect
75. C2×C42×D79C22semidirect
77. C23×Q8×C79C22semidirect
78. #548×C79C22semidirect
79. C2×#124×C79C22semidirect
80. C2×C22⋊Q8×C79C22semidirect
81. C2×#121×C79C22semidirect
82. C2×C4×Q8×C79C22semidirect
83. C2×C4×D4×C79C22semidirect
89. C2×#11929625D4semidirect
92. C2×#11929625C23semidirect
97. C2×#11929624C23semidirect
98. C2×#11929624C23semidirect
104. C2×Q8×D79C23semidirect
105. C2×Q8×D79C23semidirect
129. #14579160C23semidirect
130. #14579157C23semidirect
131. #14579150C23semidirect
132. #14579149C23semidirect
133. #14579148C23semidirect
134. #14579147C23semidirect
135. #14579147C23semidirect
136. #14579147C23semidirect
137. #14579146C23semidirect
138. #14579143C23semidirect
139. #14579141C23semidirect
140. #14579140C23semidirect
141. #14579137C23semidirect
142. #14579136C23semidirect
143. #14579136C23semidirect
144. #14579135C23semidirect
145. #14579134C23semidirect
146. #14579134C23semidirect
147. #14579132C23semidirect
148. #14579132C23semidirect
149. #14579131C23semidirect
150. #14579129C23semidirect
151. Q8×Dic79C23semidirect
152. C4×D316C23semidirect
153. C4×D316C23semidirect
154. #14579123C23semidirect
155. C4×C22⋊D79C23semidirect
156. C4×C22⋊D79C23semidirect
157. #14579119C23semidirect
172. C22⋊C4×D79C23semidirect
173. C22⋊C4×D79C23semidirect
177. C42×D79C23semidirect
183. C22×Q8×C79C23semidirect
188. #124×C79C23semidirect
189. C22⋊Q8×C79C23semidirect
190. #121×C79C23semidirect
191. C4×Q8×C79C23semidirect
192. C4×D4×C79C23semidirect
208. #11929625C2×D4semidirect
415. C2×C79#3500semidirect
428. C2×#548D79semidirect
438. C79C2×#3500semidirect
452. C23×Q8C2×D79semidirect
459. #548C2×D79semidirect
476. C2×#124C2×D79semidirect
482. C2×C22⋊Q8C2×D79semidirect
490. C2×#121C2×D79semidirect
495. C2×C4×Q8C2×D79semidirect
501. C2×C4×D4C2×D79semidirect
533. C22×Q8C22×D79semidirect
569. #124C22×D79semidirect
575. C22⋊Q8C22×D79semidirect
583. #121C22×D79semidirect
587. C4×Q8C22×D79semidirect
593. C4×D4C22×D79semidirect
839. C2#23777191direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145792092
C22×#145792072
#237771912
C2×#190992252
C2×#190992242
C2×#190992202
C2×#190992102
C2×#190992092
C2×#190992062
C2×#190992042
C2×#190991362
C2×#190991292
C2×#190991102
C2×#124×D792
C2×C4×#119296252
C2×#548×C792
C2×#350079