Finite Group Databasebeta

← C2×#23777179 #35196678

Subgroups — C2×#23777179 #35196678

Order 20224.

11126 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579208C212yesmaximal, complemented
2#23777179C2132yesmaximal, direct product factor
3C2×D4×Dic158C211yesmaximal, characteristic, complemented
4C2×#19099228C211yesmaximal, characteristic, complemented
5C2×#19099226C212yesmaximal, complemented
6C2×#19099217C211yesmaximal, characteristic, complemented
7C2×#19099214C212yesmaximal, complemented
8C2×#19099213C212yesmaximal, complemented
9C2×#19099212C212yesmaximal, complemented
10C2×#19099211C214yesmaximal, complemented
11C2×#19099136C212yesmaximal, complemented
12C2×#19099135C214yesmaximal, complemented
13C2×#19099110C211yesmaximal, characteristic, complemented
14C2×#19099108C212yesmaximal, complemented
15C22×#14579160C212yesmaximal, complemented
16C2×C4⋊Q8×D79C211yesmaximal, characteristic, complemented
17C2×C4×#11929623C211yesmaximal, characteristic, complemented
18C2×#547×C79C211yesmaximal, characteristic, complemented
19C2×#14579208—232no—
20C2×#14579208C22132yescomplemented
21C22×#11929624C2214yes—
22C22×#11929624C2212yes—
23C22×#11929623C2214yes—
24C22×#11929623C2212yes—
25C22×#11929623C2214yes—
26C22×#11929623C2211yescharacteristic
27C23×Dic158C2212yes—
28C23×Dic158C2214yes—
29C22×Q8×D79C2212yes—
30C22×Q8×D79C2212yes—
31D4×Dic158C22116yescomplemented
32#19099228C22116yescomplemented
33#19099226C22132yescomplemented
34#19099217C22116yescomplemented
35#19099214C22132yescomplemented
36#19099213C22132yescomplemented
37#19099212C22132yescomplemented
38#19099211C22164yescomplemented
39#19099136C22132yescomplemented
40#19099135C22164yescomplemented
41#19099110C22116yescomplemented
42#19099108C22132yescomplemented
43C2×#14579161C2211yescharacteristic
44C2×#14579160C2214yes—
45C2×#14579160C2212yes—
46C2×#14579160C2212yes—
47C2×#14579160C2212yes—
48C2×#14579160C2212yes—
49C2×#14579160C2211yescharacteristic
50C2×#14579160C2214yes—
51C2×#14579160C22132yescomplemented
52C2×#14579159C2212yes—
53C4⋊Q8×D79C22116yescomplemented
54C2×#14579157C2211yescharacteristic
55C2×#14579147C2214yes—
56C2×#14579147C2212yes—
57C2×#14579146C2214yes—
58C2×#14579145C2214yes—
59C2×#14579144C2214yes—
60C2×#14579143C2214yes—
61C2×#14579142C2214yes—
62C2×#14579141C2212yes—
63C2×#14579140C2212yes—
64C2×#14579139C2214yes—
65C2×#14579139C2214yes—
66C2×#14579138C2214yes—
67C2×#14579138C2214yes—
68C2×#14579137C2212yes—
69C2×#14579136C2211yescharacteristic
70C2×#14579135C2212yes—
71C2×#14579134C2212yes—
72C2×#14579133C2214yes—
73C2×#14579132C2211yescharacteristic
74C4×#11929623C22116yescomplemented
75C2×C4×Dic158C2211yescharacteristic
76C2×#14579126C2211yescharacteristic
77C2×C4×D316C2211yescharacteristic
78C2×D4×Dic79C2211yescharacteristic
79C2×D4×Dic79C2212yes—
80C2×#14579123C2212yes—
81C2×C4×C22⋊D79C2212yes—
82C2×C4×C22⋊D79C2212yes—
83C2×(C22⋊D79)⋊C4C2212yes—
84C2×(C22⋊D79)⋊C4C2214yes—
85C2×#14579119C2211yescharacteristic
86C2×#14579117C2212yes—
87C22×C4⋊Dic79C2212yes—
88C22×Dic79⋊C4C2214yes—
89C2×C4⋊C4×D79C2212yes—
90C2×C4⋊C4×D79C2212yes—
91C22×C4×Dic79C2212yes—
92C2×C42×D79C2211yescharacteristic
93C22×#41×C79C2212yes—
94#547×C79C22116yescomplemented
95C2×C4⋊Q8×C79C2211yescharacteristic
96C2×#123×C79C2214yes—
97C2×C22⋊Q8×C79C2212yes—
98C2×#121×C79C2212yes—
99C2×C4×D4×C79C2211yescharacteristic
100C2×C4×D4×C79C2211yescharacteristic
101C22×C4⋊C4×C79C2212yes—
102#14579208—2256no—
103C2×#11929624—232no—
104C2×#11929624—216no—
105C2×#11929624C23116yes—
106C2×#11929624C23132yes—
107C2×#11929623—216no—
108C2×#11929623—232no—
109C2×#11929623—232no—
110C2×#11929623D4116yescomplemented
111C2×#11929623C23132yes—
112C2×#11929623C23116yes—
113C2×#11929623C23132yes—
114C2×#11929623C2318yes—
115C22×Dic158—216no—
116C22×Dic158—232no—
117C22×Dic158C23116yes—
118C22×Dic158C23132yes—
119C22×Dic158C2314yes—
120C22×Dic158C2314yes—
121C22×Dic158C2312yes—
122C22×Dic158C2314yes—
123C22×Dic158C2312yes—
124C22×Dic158C2311yescharacteristic
125C2×Q8×D79—216no—
126C2×Q8×D79—216no—
127C2×Q8×D79C23116yes—
128C2×Q8×D79C23116yes—
129C22×D316C2311yescharacteristic
130C22×D316C2312yes—
131C22×C22⋊D79C2312yes—
132C22×C22⋊D79C2312yes—
133C22×C22⋊D79C2314yes—
134C22×C22⋊D79C2312yes—
135C22×C22⋊D79C2312yes—
136C23×Dic79C2312yes—
137C23×Dic79C2314yes—
138C23×Dic79C2314yes—
139C23×Dic79C2312yes—
140C22×C4×D79C2311yescharacteristic
141C22×C4×D79C2311yescharacteristic
142C22×C4×D79C2314yes—
143C22×C4×D79C2314yes—
144C22×C4×D79C2312yes—
145C22×C4×D79C2311yescharacteristic
146#14579161C2318yes—
147#14579160C23132yes—
148#14579160C23132yes—
149#14579160C23116yes—
150#14579160C23116yes—
151#14579160C23116yes—
152#14579160C23116yes—
153#14579160C2318yes—
154#14579159C23116yes—
155#14579157C2318yes—
156#14579147C23132yes—
157#14579147C23116yes—
158#14579146C23132yes—
159#14579145C23132yes—
160#14579144C23132yes—
161#14579143C23132yes—
162#14579142C23132yes—
163#14579141C23116yes—
164#14579140C23116yes—
165#14579139C23132yes—
166#14579139C23132yes—
167#14579138C23132yes—
168#14579138C23132yes—
169#14579137C23116yes—
170#14579136C2318yes—
171#14579135C23116yes—
172#14579134C23116yes—
173#14579133C23132yes—
174#14579132C2318yes—
175C4×Dic158C2318yes—
176#14579126C2318yes—
177C4×D316C2318yes—
178D4×Dic79C2318yes—
179D4×Dic79C23116yes—
180#14579123C23116yes—
181C4×C22⋊D79C23116yes—
182C4×C22⋊D79C23116yes—
183(C22⋊D79)⋊C4C23116yes—
184(C22⋊D79)⋊C4C23132yes—
185#14579119C2318yes—
186#14579117C23116yes—
187C2×C4⋊Dic79C23116yes—
188C2×C4⋊Dic79C2312yes—
189C2×C4⋊Dic79C2312yes—
190C2×C4⋊Dic79C2311yescharacteristic
191C2×C4⋊Dic79C2314yes—
192C2×C4⋊Dic79C2311yescharacteristic
193C2×Dic79⋊C4C23132yes—
194C2×Dic79⋊C4C2314yes—
195C2×Dic79⋊C4C2314yes—
196C2×Dic79⋊C4C2312yes—
197C2×Dic79⋊C4C2314yes—
198C2×Dic79⋊C4C2314yes—
199C2×Dic79⋊C4C2312yes—
200C2×Dic79⋊C4C2312yes—
201C4⋊C4×D79C23116yes—
202C4⋊C4×D79C23116yes—
203C2×C22⋊Dic79C2312yes—
204C2×C22⋊Dic79C2312yes—
205C2×C22⋊Dic79C2314yes—
206C2×(C2×D79)⋊C4C2312yes—
207C2×(C2×D79)⋊C4C2314yes—
208C2×(C2×D79)⋊C4C2312yes—
209C2×(C2×D79)⋊C4C2314yes—
210C2×(C2×D79)⋊C4C2312yes—
211C2×C4×Dic79C2311yescharacteristic
212C2×C4×Dic79C2311yescharacteristic
213C2×C4×Dic79C2311yescharacteristic
214C2×C4×Dic79C2312yes—
215C2×C4×Dic79C2312yes—
216C2×C4×Dic79C2312yes—
217C2×C4×Dic79C23116yes—
218C42×D79C2318yes—
219C2×#41×C79—216no—
220C2×#41×C79C23116yes—
221C22×Q8×C79C2312yes—
222C22×D4×C79C2311yescharacteristic
223C22×D4×C79C2314yes—
224C22×D4×C79C2311yescharacteristic
225C23×C4×C79C2312yes—
226C23×C4×C79C2314yes—
227C23×C4×C79C2312yes—
228C4⋊Q8×C79C2318yes—
229#123×C79C23132yes—
230C22⋊Q8×C79C23116yes—
231#121×C79C23116yes—
232C4×D4×C79C2318yes—
233C4×D4×C79C2318yes—
234C2×C4⋊C4×C79C23116yes—
235C2×C4⋊C4×C79C2311yescharacteristic
236C2×C4⋊C4×C79C2312yes—
237C2×C4⋊C4×C79C2314yes—
238C2×C4⋊C4×C79C2311yescharacteristic
239C2×C4⋊C4×C79C2312yes—
240C2×C22⋊C4×C79C2312yes—
241C2×C22⋊C4×C79C2312yes—
242C2×C22⋊C4×C79C2314yes—
243C2×C42×C79C2311yescharacteristic
244C23×D79C2412yes—
245C23×D79C2411yescharacteristic
246#11929624—264no—
247#11929624—2128no—
248#11929623—2128no—
249#11929623—264no—
250#11929623—2128no—
251#11929623C2×D4164yescomplemented
252C2×Dic158—216no—
253C2×Dic158—216no—
254C2×Dic158—216no—
255C2×Dic158—28no—
256C2×Dic158—2128no—
257C2×Dic158—264no—
258C2×Dic158—28no—
259C2×Dic158C2×D418yes—
260C2×Dic158C24116yes—
261C2×Dic158C2418yes—
262C2×Dic158C24116yes—
263C2×Dic158C24116yes—
264C2×Dic158C2418yes—
265C2×Dic158C2414yes—
266Q8×D79—264no—
267Q8×D79—264no—
268C2×D316—28no—
269C2×D316—24no—
270C2×D316C2418yes—
271C2×D316C2414yes—
272C2×C22⋊D79—28no—
273C2×C22⋊D79—28no—
274C2×C22⋊D79—216no—
275C2×C22⋊D79—28no—
276C2×C22⋊D79C2×D4116yes—
277C2×C22⋊D79C2418yes—
278C2×C22⋊D79C24116yes—
279C2×C22⋊D79C2418yes—
280C2×C22⋊D79C2418yes—
281C2×C22⋊D79C2418yes—
282C22×Dic79—216no—
283C22×Dic79—28no—
284C22×Dic79—216no—
285C22×Dic79C2×D4116yes—
286C22×Dic79C2412yes—
287C22×Dic79C2414yes—
288C22×Dic79C24116yes—
289C22×Dic79C24116yes—
290C22×Dic79C2412yes—
291C22×Dic79C2411yescharacteristic
292C22×Dic79C2418yes—
293C22×Dic79C2411yescharacteristic
294C22×Dic79C2412yes—
295C22×Dic79C2418yes—
296C22×Dic79C2411yescharacteristic
297C2×C4×D79—216no—
298C2×C4×D79—24no—
299C2×C4×D79—216no—
300C2×C4×D79—28no—
301C2×C4×D79—24no—
302C2×C4×D79C2×D418yes—
303C2×C4×D79C24116yes—
304C2×C4×D79C24116yes—
305C2×C4×D79C2418yes—
306C2×C4×D79C2414yes—
307C2×C4×D79C2414yes—
308C2×C4×D79C2414yes—
309C4⋊Dic79C2418yes—
310C4⋊Dic79C2418yes—
311C4⋊Dic79C2414yes—
312C4⋊Dic79C24116yes—
313C4⋊Dic79C2414yes—
314Dic79⋊C4C24116yes—
315Dic79⋊C4C24116yes—
316Dic79⋊C4C2418yes—
317Dic79⋊C4C24116yes—
318Dic79⋊C4C24116yes—
319Dic79⋊C4C2418yes—
320Dic79⋊C4C2418yes—
321C22⋊Dic79C2418yes—
322C22⋊Dic79C2418yes—
323C22⋊Dic79C24116yes—
324(C2×D79)⋊C4C2418yes—
325(C2×D79)⋊C4C24116yes—
326(C2×D79)⋊C4C2418yes—
327(C2×D79)⋊C4C24116yes—
328(C2×D79)⋊C4C2418yes—
329C4×Dic79C2414yes—
330C4×Dic79C2414yes—
331C4×Dic79C2414yes—
332C4×Dic79C2418yes—
333C4×Dic79C2418yes—
334C4×Dic79C2418yes—
335C24×C79C2412yes—
336C24×C79C2412yes—
337#41×C79—264no—
338C2×Q8×C79—28no—
339C2×Q8×C79C2418yes—
340C2×D4×C79—216no—
341C2×D4×C79—24no—
342C2×D4×C79C2×D418yes—
343C2×D4×C79C24116yes—
344C2×D4×C79C2414yes—
345C2×D4×C79C2414yes—
346C22×C4×C79—216no—
347C22×C4×C79—28no—
348C22×C4×C79—28no—
349C22×C4×C79C2412yes—
350C22×C4×C79C24116yes—
351C22×C4×C79C2418yes—
352C22×C4×C79C2414yes—
353C22×C4×C79C2411yescharacteristic
354C22×C4×C79C2412yes—
355C22×C4×C79C2418yes—
356C22×C4×C79C2411yescharacteristic
357C22×C4×C79C2411yescharacteristic
358C4⋊C4×C79C2414yes—
359C4⋊C4×C79C2418yes—
360C4⋊C4×C79C24116yes—
361C4⋊C4×C79C2414yes—
362C4⋊C4×C79C2418yes—
363C22⋊C4×C79C2418yes—
364C22⋊C4×C79C2418yes—
365C22⋊C4×C79C24116yes—
366C42×C79C2414yes—
367C23×C79—24no—
368C23×C79—24no—
369C23×C79—24no—
370C23×C79—24no—
371C23×C79—24no—
372C23×C79C22×D418yes—
373C23×C79C2514yes—
374C23×C79C2514yes—
375C23×C79C2511yescharacteristic
376C22×D79—22no—
377C22×D79—22no—
378C22×D79—24no—
379C22×D79—24no—
380C22×D79—24no—
381C22×D79C22×D414yes—
382C22×D79C2514yes—
383C22×D79C2512yes—
384Q8×C79—216no—
385D4×C79—232no—
386D4×C79—28no—
387D4×C79C22×D4116yes—
388C2×C4×C79—28no—
389C2×C4×C79—24no—
390C2×C4×C79—232no—
391C2×C4×C79—22no—
392C2×C4×C79—24no—
393C2×C4×C79—216no—
394C2×C4×C79—216no—
395C2×C4×C79C22×D414yes—
396C2×C4×C792−1+414yescomplemented
397C2×C4×C79C2514yes—
398C2×C4×C79C2512yes—
399C2×C4×C79C2518yes—
400C2×C4×C79C2514yes—
401C2×C4×C79C2512yes—
402C2×C4×C79C2512yes—
403C22⋊D79—232no—
404C22⋊D79—216no—
405C22⋊D79—216no—
406C22⋊D79—216no—
407C22⋊D79C22×D4132yes—
408C2×Dic79—28no—
409C2×Dic79—24no—
410C2×Dic79—232no—
411C2×Dic79—22no—
412C2×Dic79—24no—
413C2×Dic79—232no—
414C2×Dic79—216no—
415C2×Dic79C22×D418yes—
416C2×Dic79C22×D414yes—
417C2×Dic79C22×D4132yes—
418C2×Dic792−1+414yescomplemented
419C2×Dic79C2514yes—
420C2×Dic79C2512yes—
421C2×Dic79C2518yes—
422C2×Dic79C2514yes—
423C2×Dic79C2512yes—
424C2×Dic79C2514yes—
425C2×Dic79C2512yes—
426D316—216no—
427D316—28no—
428C4×D79—232no—
429C4×D79—216no—
430C4×D79—28no—
431C4×D79—232no—
432C4×D79—28no—
433C4×D79C22×D4116yes—
434Dic158—216no—
435Dic158—232no—
436Dic158—232no—
437Dic158—216no—
438Dic158—232no—
439Dic158C22×D4116yes—
440C22×C79—24no—
441C22×C79—24no—
442C22×C79—216no—
443C22×C79—24no—
444C22×C79—24no—
445C22×C79—24no—
446C22×C79—48no—
447C22×C79C23×D418yes—
448C22×C79C23×D412yes—
449C22×C79C2×2−1+412yes—
450C22×C79C2×2−1+412yes—
451C22×C79C2611yescharacteristic
452C2×D79—22no—
453C2×D79—22no—
454C2×D79—28no—
455C2×D79—24no—
456C2×D79—24no—
457C2×D79—24no—
458C2×D79—48no—
459C2×D79C23×D414yes—
460C4×C79—24no—
461C4×C79—28no—
462C4×C79—24no—
463C4×C79—22no—
464C4×C79C23×D414yes—
465C4×C79C2×2−1+414yescomplemented
466Dic79—28no—
467Dic79—24no—
468Dic79—22no—
469Dic79—24no—
470Dic79C23×D414yes—
471Dic79C23×D418yes—
472Dic79C2×2−1+414yescomplemented
473C2×#3499—791nomaximal, Sylow
474C2×C79—28no—
475C2×C79—44no—
476C2×C79#349914yescomplemented
477C2×C79C24×D411yescharacteristic
478C2×C79C22×2−1+411yescharacteristic
479C2×C79C22×2−1+411yescharacteristic
480D79—24no—
481D79—44no—
482C22×2−1+4—792no—
483#3499—7932no—
484C2×D4×Q8—791no—
485C2×D4×Q8—792no—
486C2×D4×Q8—791no—
487C2×#547—792no—
488C2×#547—794no—
489C2×#547—792no—
490C2×#547—791no—
491C2×#547—792no—
492C2×#547D7911yescharacteristic, complemented
493C2×#536—794no—
494C2×#536—792no—
495C2×#532—792no—
496C2×#532—791no—
497C22×C4⋊Q8—791no—
498C22×C4⋊Q8—792no—
499C2×C4×#41—791no—
500C79C2×#349911yescharacteristic, complemented, Sylow
501C2×2−1+4—7932no—
502C2×2−1+4—15832no—
503C22×#41—791no—
504C22×#41—794no—
505C22×#41—792no—
506C22×#41—794no—
507C22×#41—792no—
508C22×#41—794no—
509C22×#41C2×D7912yes—
510C23×Q8—792no—
511C23×Q8—792no—
512C23×Q8—794no—
513C23×Q8—792no—
514D4×Q8—7916no—
515D4×Q8—7932no—
516D4×Q8—7916no—
517#547—7932no—
518#547—7964no—
519#547—7932no—
520#547—7916no—
521#547—7932no—
522#547C2×D79116yescomplemented
523#536—7964no—
524#536—7932no—
525#532—7932no—
526#532—7916no—
527C2×C4⋊Q8—792no—
528C2×C4⋊Q8—7916no—
529C2×C4⋊Q8—792no—
530C2×C4⋊Q8—791no—
531C2×C4⋊Q8—792no—
532C2×C4⋊Q8—794no—
533C2×C4⋊Q8—794no—
534C2×C4⋊Q8—792no—
535C2×C4⋊Q8—792no—
536C2×C4⋊Q8—7932no—
537C2×C4⋊Q8—791no—
538C2×C4⋊Q8C2×D7911yescharacteristic
539C2×#127—791no—
540C2×#124—794no—
541C2×#124—792no—
542C2×#123—794no—
543C2×#123—794no—
544C2×#123—794no—
545C2×#123—794no—
546C2×#123—794no—
547C2×#123C2×D7914yes—
548C2×C22⋊Q8—792no—
549C2×C22⋊Q8—792no—
550C2×C22⋊Q8—794no—
551C2×C22⋊Q8—794no—
552C2×C22⋊Q8—792no—
553C2×C22⋊Q8—794no—
554C2×C22⋊Q8—794no—
555C2×C22⋊Q8C2×D7912yes—
556C2×#121—791no—
557C2×#121—794no—
558C2×#121—792no—
559C2×#121—791no—
560C2×#121—792no—
561C2×#121C2×D7912yes—
562C4×#41—7916no—
563C2×C4×Q8—791no—
564C2×C4×Q8—791no—
565C2×C4×D4—791no—
566C2×C4×D4—792no—
567C2×C4×D4—792no—
568C2×C4×D4—792no—
569C2×C4×D4—792no—
570C2×C4×D4—792no—
571C2×C4×D4—794no—
572C2×C4×D4—791no—
573C2×C4×D4C2×D7911yescharacteristic
574C2×C4×D4C2×D7911yescharacteristic
575C2×#117—791no—
576C2×#117—792no—
577C22×C4⋊C4—794no—
578C22×C4⋊C4—792no—
579C22×C4⋊C4—792no—
580C22×C4⋊C4—792no—
581C22×C4⋊C4C2×D7912yes—
582C22×C42—792no—
583C22×C42—791no—
5842−1+4—158256no—
585C2×#41—216no—
586C2×#41—7916no—
587C2×#41—798no—
588C2×#41—7932no—
589C2×#41—7916no—
590C2×#41—7932no—
591C2×#41—7916no—
592C2×#41—7932no—
593C2×#41—15816no—
594C2×#41—15832no—
595C2×#41—15832no—
596C2×#41—15832no—
597C2×#41—15816no—
598C2×#41C22×D79116yes—
599C22×Q8—7916no—
600C22×Q8—7916no—
601C22×Q8—791no—
602C22×Q8—794no—
603C22×Q8—794no—
604C22×Q8—792no—
605C22×Q8—794no—
606C22×Q8—792no—
607C22×Q8—7932no—
608C22×Q8—7916no—
609C22×Q8—15832no—
610C22×Q8—15816no—
611C22×Q8—15816no—
612C22×Q8—15816no—
613C22×Q8C22×D7912yes—
614C22×D4—792no—
615C22×D4—792no—
616C22×D4—792no—
617C22×D4—794no—
618C22×D4—792no—
619C22×D4—791no—
620C22×D4—792no—
621C22×D4C22×D7911yescharacteristic
622C22×D4C22×D7914yes—
623C22×D4C22×D7911yescharacteristic
624C23×C4—792no—
625C23×C4—791no—
626C23×C4—792no—
627C23×C4—794no—
628C23×C4—794no—
629C23×C4—791no—
630C23×C4—791no—
631C23×C4—794no—
632C23×C4—794no—
633C23×C4—792no—
634C23×C4C22×D7912yes—
635C23×C4C22×D7914yes—
636C23×C4C22×D7912yes—
637C4⋊Q8—7916no—
638C4⋊Q8—7916no—
639C4⋊Q8—798no—
640C4⋊Q8—7916no—
641C4⋊Q8—7932no—
642C4⋊Q8—7932no—
643C4⋊Q8—7916no—
644C4⋊Q8—7916no—
645C4⋊Q8—798no—
646C4⋊Q8C22×D7918yes—
647#127—798no—
648#124—7932no—
649#124—7916no—
650#123—7932no—
651#123—7932no—
652#123—7932no—
653#123—7932no—
654#123—7932no—
655#123C22×D79132yes—
656C22⋊Q8—7916no—
657C22⋊Q8—7916no—
658C22⋊Q8—7932no—
659C22⋊Q8—7932no—
660C22⋊Q8—7916no—
661C22⋊Q8—7932no—
662C22⋊Q8—7932no—
663C22⋊Q8C22×D79116yes—
664#121—798no—
665#121—7932no—
666#121—7916no—
667#121—798no—
668#121—7916no—
669#121C22×D79116yes—
670C4×Q8—798no—
671C4×Q8—798no—
672C4×D4—798no—
673C4×D4—7916no—
674C4×D4—7916no—
675C4×D4—7916no—
676C4×D4—7916no—
677C4×D4—7916no—
678C4×D4—7932no—
679C4×D4—798no—
680C4×D4C22×D7918yes—
681C4×D4C22×D7918yes—
682#117—798no—
683#117—7916no—
684C2×C4⋊C4—794no—
685C2×C4⋊C4—792no—
686C2×C4⋊C4—791no—
687C2×C4⋊C4—792no—
688C2×C4⋊C4—794no—
689C2×C4⋊C4—794no—
690C2×C4⋊C4—794no—
691C2×C4⋊C4—794no—
692C2×C4⋊C4—792no—
693C2×C4⋊C4—7932no—
694C2×C4⋊C4—7916no—
695C2×C4⋊C4—792no—
696C2×C4⋊C4—792no—
697C2×C4⋊C4—791no—
698C2×C4⋊C4—7916no—
699C2×C4⋊C4—7916no—
700C2×C4⋊C4C22×D7912yes—
701C2×C4⋊C4C22×D7912yes—
702C2×C4⋊C4C22×D7911yescharacteristic
703C2×C4⋊C4C22×D7914yes—
704C2×C4⋊C4C22×D79116yes—
705C2×C4⋊C4C22×D7911yescharacteristic
706C2×C22⋊C4—792no—
707C2×C22⋊C4—794no—
708C2×C22⋊C4—792no—
709C2×C22⋊C4—792no—
710C2×C22⋊C4—794no—
711C2×C22⋊C4—792no—
712C2×C22⋊C4—794no—
713C2×C22⋊C4—792no—
714C2×C22⋊C4C22×D7912yes—
715C2×C22⋊C4C22×D7914yes—
716C2×C22⋊C4C22×D7912yes—
717C2×C42—792no—
718C2×C42—791no—
719C2×C42—792no—
720C2×C42—791no—
721C2×C42—792no—
722C2×C42—7916no—
723C2×C42—791no—
724C2×C42—798no—
725C2×C42C22×D7911yescharacteristic
726C24—791no—
727C24—792no—
728C24C23×D7912yes—
729C24C23×D7912yes—
730#41—264no—
731#41—7964no—
732#41—15864no—
733#41—158128no—
734#41—158128no—
735#41—158128no—
736#41—15864no—
737C2×Q8—28no—
738C2×Q8—794no—
739C2×Q8—7916no—
740C2×Q8—7916no—
741C2×Q8—798no—
742C2×Q8—7916no—
743C2×Q8—798no—
744C2×Q8—798no—
745C2×Q8—1588no—
746C2×Q8—15816no—
747C2×Q8—15816no—
748C2×Q8—15816no—
749C2×Q8—158128no—
750C2×Q8—15864no—
751C2×Q8—15864no—
752C2×Q8—15864no—
753C2×Q8—1588no—
754C2×Q8C23×D7918yes—
755C2×D4—216no—
756C2×D4—24no—
757C2×D4—798no—
758C2×D4—7916no—
759C2×D4—798no—
760C2×D4—798no—
761C2×D4—7916no—
762C2×D4—798no—
763C2×D4—794no—
764C2×D4—798no—
765C2×D4—1588no—
766C2×D4—1588no—
767C2×D4—1588no—
768C2×D4—1588no—
769C2×D4—15816no—
770C2×D4—1584no—
771C2×D4D4×D7918yes—
772C2×D4C23×D7914yes—
773C2×D4C23×D79116yes—
774C2×D4C23×D7914yes—
775C22×C4—216no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—798no—
779C22×C4—791no—
780C22×C4—791no—
781C22×C4—792no—
782C22×C4—7916no—
783C22×C4—794no—
784C22×C4—798no—
785C22×C4—798no—
786C22×C4—7916no—
787C22×C4—7916no—
788C22×C4—792no—
789C22×C4—791no—
790C22×C4—792no—
791C22×C4—794no—
792C22×C4—794no—
793C22×C4—794no—
794C22×C4—7916no—
795C22×C4—7916no—
796C22×C4—798no—
797C22×C4—1584no—
798C22×C4—15816no—
799C22×C4—15816no—
800C22×C4—1588no—
801C22×C4—15816no—
802C22×C4—15816no—
803C22×C4—1584no—
804C22×C4—1588no—
805C22×C4C23×D7918yes—
806C22×C4C23×D79116yes—
807C22×C4C23×D7918yes—
808C22×C4C23×D7912yes—
809C22×C4C23×D7911yescharacteristic
810C22×C4C23×D7914yes—
811C22×C4C23×D7912yes—
812C22×C4C23×D7911yescharacteristic
813C22×C4C23×D7911yescharacteristic
814C4⋊C4—7916no—
815C4⋊C4—798no—
816C4⋊C4—7916no—
817C4⋊C4—7916no—
818C4⋊C4—7916no—
819C4⋊C4—798no—
820C4⋊C4—798no—
821C4⋊C4—798no—
822C4⋊C4—794no—
823C4⋊C4—7916no—
824C4⋊C4—798no—
825C4⋊C4—794no—
826C4⋊C4C23×D7918yes—
827C4⋊C4C23×D7918yes—
828C4⋊C4C23×D7914yes—
829C4⋊C4C23×D79116yes—
830C4⋊C4C23×D7914yes—
831C22⋊C4—798no—
832C22⋊C4—798no—
833C22⋊C4—7916no—
834C22⋊C4—798no—
835C22⋊C4—7916no—
836C22⋊C4—798no—
837C22⋊C4—7916no—
838C22⋊C4—798no—
839C22⋊C4C23×D7918yes—
840C22⋊C4C23×D79116yes—
841C22⋊C4C23×D7918yes—
842C42—794no—
843C42—798no—
844C42—794no—
845C42—798no—
846C42—794no—
847C42—798no—
848C42C23×D7914yes—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—792no—
855C23—794no—
856C23—794no—
857C23—1584no—
858C23—1584no—
859C23—1584no—
860C23—1582no—
861C23—1582no—
862C23C2×D4×D7918yes—
863C23C24×D7914yes—
864C23C24×D7914yes—
865C23C24×D7911yescharacteristic
866Q8—216no—
867Q8—7916no—
868Q8—15816no—
869Q8—15832no—
870Q8—15832no—
871Q8—15832no—
872Q8—15816no—
873D4—232no—
874D4—28no—
875D4—7932no—
876D4—15816no—
877D4—15816no—
878D4—15816no—
879D4—15816no—
880D4—15832no—
881D4—1588no—
882D4C2×D4×D79116yes—
883C2×C4—22no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—28no—
887C2×C4—232no—
888C2×C4—216no—
889C2×C4—216no—
890C2×C4—794no—
891C2×C4—792no—
892C2×C4—792no—
893C2×C4—794no—
894C2×C4—794no—
895C2×C4—798no—
896C2×C4—7932no—
897C2×C4—7916no—
898C2×C4—794no—
899C2×C4—792no—
900C2×C4—794no—
901C2×C4—798no—
902C2×C4—15832no—
903C2×C4—1588no—
904C2×C4—15832no—
905C2×C4—15832no—
906C2×C4—15816no—
907C2×C4—1584no—
908C2×C4—1582no—
909C2×C4—1588no—
910C2×C4—1584no—
911C2×C4—15832no—
912C2×C4—1588no—
913C2×C4—15816no—
914C2×C4C2×D4×D7914yes—
915C2×C4#1457920814yescomplemented
916C2×C4C24×D7914yes—
917C2×C4C24×D7912yes—
918C2×C4C24×D7918yes—
919C2×C4C24×D7914yes—
920C2×C4C24×D7912yes—
921C2×C4C24×D7912yes—
922C22—216no—
923C22—24no—
924C22—24no—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—48no—
929C22—3168no—
930C22—794no—
931C22—1584no—
932C22—1584no—
933C22—1584no—
934C22—1588no—
935C22—1582no—
936C22—1582no—
937C22C22×D4×D7918yes—
938C22C22×D4×D7912yes—
939C222−1+4×D7912yes—
940C22C2×#1457920812yes—
941C22C25×D7911yescharacteristic
942C4—24no—
943C4—28no—
944C4—22no—
945C4—24no—
946C4—794no—
947C4—798no—
948C4—794no—
949C4—1588no—
950C4—1584no—
951C4—1584no—
952C4—1582no—
953C4C22×D4×D7914yes—
954C4C2×#1457920814yescomplemented
955C2—28no—
956C2—44no—
957C2—3164no—
958C2—1584no—
959C2#2377717914yesdirect product factor
960C2C23×D4×D7911yescharacteristic
961C2C2×2−1+4×D7911yescharacteristic
962C2C22×#1457920811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#547×C79C2
socleC23×C79C25
hypercenterC2×#547D79
hypocenterC79C2×#3499
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C22×#14579208C2semidirect
2. #23777179C2direct (N × H)
3. C2×D4×Dic158C2semidirect
4. C2×#19099228C2semidirect
5. C2×#19099226C2semidirect
6. C2×#19099217C2semidirect
7. C2×#19099214C2semidirect
8. C2×#19099213C2semidirect
9. C2×#19099212C2semidirect
10. C2×#19099211C2semidirect
11. C2×#19099136C2semidirect
12. C2×#19099135C2semidirect
13. C2×#19099110C2semidirect
14. C2×#19099108C2semidirect
15. C22×#14579160C2semidirect
16. C2×C4⋊Q8×D79C2semidirect
17. C2×C4×#11929623C2semidirect
18. C2×#547×C79C2semidirect
20. C2×#14579208C22semidirect
31. D4×Dic158C22semidirect
32. #19099228C22semidirect
33. #19099226C22semidirect
34. #19099217C22semidirect
35. #19099214C22semidirect
36. #19099213C22semidirect
37. #19099212C22semidirect
38. #19099211C22semidirect
39. #19099136C22semidirect
40. #19099135C22semidirect
41. #19099110C22semidirect
42. #19099108C22semidirect
51. C2×#14579160C22semidirect
53. C4⋊Q8×D79C22semidirect
74. C4×#11929623C22semidirect
94. #547×C79C22semidirect
110. C2×#11929623D4semidirect
251. #11929623C2×D4semidirect
396. C2×C4×C792−1+4semidirect
418. C2×Dic792−1+4semidirect
465. C4×C79C2×2−1+4semidirect
472. Dic79C2×2−1+4semidirect
476. C2×C79#3499semidirect
492. C2×#547D79semidirect
500. C79C2×#3499semidirect
522. #547C2×D79semidirect
915. C2×C4#14579208semidirect
954. C4C2×#14579208semidirect
959. C2#23777179direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145792082
#237771792
C2×D4×Dic1582
C2×#190992282
C2×#190992262
C2×#190992172
C2×#190992142
C2×#190992132
C2×#190992122
C2×#190992112
C2×#190991362
C2×#190991352
C2×#190991102
C2×#190991082
C22×#145791602
C2×C4⋊Q8×D792
C2×C4×#119296232
C2×#547×C792
C2×#349979