Finite Group Databasebeta

← C2×#23766430 #34447813

Subgroups — C2×#23766430 #34447813

Order 20224.

3310 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579138C211yesmaximal, characteristic
2C22×C4×Dic158C211yesmaximal, characteristic, complemented
3C22×#14579117C211yesmaximal, characteristic
4#23766430C2116yesmaximal, direct product factor
5C2×#19098467C211yesmaximal, characteristic, complemented
6C2×#19098458C211yesmaximal, characteristic, complemented
7C2×#19098457C211yesmaximal, characteristic
8C2×#19098457C211yesmaximal, characteristic
9C2×#19098456C211yesmaximal, characteristic
10C2×#19098450C211yesmaximal, characteristic, complemented
11C2×#19098448C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic79C211yesmaximal, characteristic, complemented
13C2×C4×Dic79⋊C4C211yesmaximal, characteristic, complemented
14C2×#19098414C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic79C211yesmaximal, characteristic
16C2×#388×C79C211yesmaximal, characteristic
17C23×Dic158C2211yescharacteristic
18C24×Dic79C2211yescharacteristic
19C2×#14579138C4116yescomplemented
20C2×#14579138C2218yes—
21C2×C4×Dic158—28no—
22C2×C4×Dic158C2218yescomplemented
23C2×#14579117—28no—
24C2×#14579117C2218yes—
25C22×C4⋊Dic79C2211yescharacteristic
26C22×C4⋊Dic79C2211yescharacteristic
27C22×Dic79⋊C4C2211yescharacteristic
28C22×Dic79⋊C4C2211yescharacteristic
29C22×Dic79⋊C4C2211yescharacteristic
30C22×Dic79⋊C4C2211yescharacteristic
31C22×Dic79⋊C4C2211yescharacteristic
32C22×Dic79⋊C4C2211yescharacteristic
33C22×C22⋊Dic79C2211yescharacteristic
34C22×C22⋊Dic79C2211yescharacteristic
35C22×C22⋊Dic79C2211yescharacteristic
36C22×C4×Dic79C2211yescharacteristic
37C22×C4×Dic79C2211yescharacteristic
38C22×C4×Dic79C2211yescharacteristic
39C22×C4×Dic79C2211yescharacteristic
40C22×C4×Dic79C2211yescharacteristic
41C22×C4×Dic79C2211yescharacteristic
42C22×C4×Dic79C2211yescharacteristic
43#19098467C2218yescomplemented
44#19098458C2218yescomplemented
45#19098457C2218yes—
46#19098457C2218yes—
47#19098456C2218yes—
48#19098450C2218yescomplemented
49#19098448C2218yescomplemented
50C4⋊C4×Dic79C2218yescomplemented
51C4×Dic79⋊C4C2218yescomplemented
52#19098414C2218yescomplemented
53C22⋊C4×Dic79C2218yes—
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C2×C79⋊#95C2211yescharacteristic
60C2×C79⋊#95C2211yescharacteristic
61C2×C79⋊#95C2211yescharacteristic
62C22×C4⋊C4×C79C2211yescharacteristic
63C22×C22⋊C4×C79C2211yescharacteristic
64C22×C22⋊C4×C79C2211yescharacteristic
65C22×C22⋊C4×C79C2211yescharacteristic
66C22×C42×C79C2211yescharacteristic
67#388×C79C2218yes—
68C2×#95×C79C2211yescharacteristic
69C2×#95×C79C2211yescharacteristic
70C22×Dic158—24no—
71C22×Dic158—24no—
72C22×Dic158C2×C418yes—
73C22×Dic158C2314yes—
74C23×Dic79—24no—
75C23×Dic79—24no—
76C23×Dic79C2×C418yes—
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C23×Dic79C2311yescharacteristic
80C23×Dic79C2311yescharacteristic
81C23×Dic79C2311yescharacteristic
82C23×Dic79C2314yes—
83C23×Dic79C2311yescharacteristic
84C23×Dic79C2311yescharacteristic
85C23×Dic79C2311yescharacteristic
86#14579138C2×C4164yescomplemented
87C4×Dic158—232no—
88#14579117—232no—
89C2×C4⋊Dic79—24no—
90C2×C4⋊Dic79C2×C418yes—
91C2×C4⋊Dic79C2314yes—
92C2×C4⋊Dic79C2314yes—
93C2×Dic79⋊C4—24no—
94C2×Dic79⋊C4—24no—
95C2×Dic79⋊C4—24no—
96C2×Dic79⋊C4C2×C418yes—
97C2×Dic79⋊C4C2×C418yes—
98C2×Dic79⋊C4D418yes—
99C2×Dic79⋊C4C2314yes—
100C2×Dic79⋊C4C2314yes—
101C2×Dic79⋊C4C2314yes—
102C2×Dic79⋊C4C2314yes—
103C2×Dic79⋊C4C2314yes—
104C2×Dic79⋊C4C2314yes—
105C2×C22⋊Dic79—24no—
106C2×C22⋊Dic79—24no—
107C2×C22⋊Dic79C2×C418yes—
108C2×C22⋊Dic79C2314yes—
109C2×C22⋊Dic79C2314yes—
110C2×C22⋊Dic79C2314yes—
111C2×C4×Dic79—24no—
112C2×C4×Dic79—24no—
113C2×C4×Dic79—24no—
114C2×C4×Dic79—24no—
115C2×C4×Dic79—24no—
116C2×C4×Dic79—24no—
117C2×C4×Dic79—24no—
118C2×C4×Dic79C2314yes—
119C2×C4×Dic79C2314yes—
120C2×C4×Dic79C2314yes—
121C2×C4×Dic79C2314yes—
122C2×C4×Dic79C2314yes—
123C2×C4×Dic79C2314yes—
124C2×C4×Dic79C2314yes—
125C79⋊#95C2314yes—
126C79⋊#95C2314yes—
127C79⋊#95C2314yes—
128C79⋊#95C2314yes—
129C79⋊#95C2314yes—
130C79⋊#95C2314yes—
131C79⋊#95C2314yes—
132C79⋊#95C2314yes—
133C25×C79C2311yescharacteristic
134C23×C4×C79C2311yescharacteristic
135C23×C4×C79C2311yescharacteristic
136C23×C4×C79C2311yescharacteristic
137C23×C4×C79C2311yescharacteristic
138C23×C4×C79C2311yescharacteristic
139C23×C4×C79C2311yescharacteristic
140C2×C4⋊C4×C79—24no—
141C2×C4⋊C4×C79C2314yes—
142C2×C22⋊C4×C79—24no—
143C2×C22⋊C4×C79—24no—
144C2×C22⋊C4×C79C2×C418yes—
145C2×C22⋊C4×C79C2314yes—
146C2×C22⋊C4×C79C2314yes—
147C2×C22⋊C4×C79C2314yes—
148C2×C42×C79—24no—
149C2×C42×C79C2314yes—
150#95×C79C2314yes—
151#95×C79C2314yes—
152C2×Dic158—232no—
153C2×Dic158—28no—
154C2×Dic158—28no—
155C2×Dic158C22×C4116yes—
156C22×Dic79—232no—
157C22×Dic79—28no—
158C22×Dic79—28no—
159C22×Dic79—22no—
160C22×Dic79—22no—
161C22×Dic79—22no—
162C22×Dic79—22no—
163C22×Dic79—22no—
164C22×Dic79—22no—
165C22×Dic79—22no—
166C22×Dic79—22no—
167C22×Dic79—22no—
168C22×Dic79—22no—
169C22×Dic79—22no—
170C22×Dic79—22no—
171C22×Dic79—22no—
172C22×Dic79—22no—
173C22×Dic79—22no—
174C22×Dic79—22no—
175C22×Dic79C22×C414yes—
176C22×Dic79C22×C414yes—
177C22×Dic79C22×C414yes—
178C22×Dic79C22×C4116yes—
179C22×Dic79C22×C414yes—
180C22×Dic79C2×D414yes—
181C22×Dic79C2×D414yes—
182C22×Dic79#4114yes—
183C22×Dic79#4114yes—
184C22×Dic79C2412yes—
185C22×Dic79C2412yes—
186C22×Dic79C2412yes—
187C22×Dic79C2412yes—
188C22×Dic79C2412yes—
189C22×Dic79C2412yes—
190C22×Dic79C2412yes—
191C22×Dic79C2412yes—
192C4⋊Dic79—28no—
193C4⋊Dic79C22×C4116yes—
194Dic79⋊C4—28no—
195Dic79⋊C4—28no—
196Dic79⋊C4—28no—
197Dic79⋊C4C22×C4116yes—
198Dic79⋊C4C22×C4116yes—
199Dic79⋊C4C2×D4116yes—
200C22⋊Dic79—28no—
201C22⋊Dic79—28no—
202C22⋊Dic79C22×C4116yes—
203C4×Dic79—28no—
204C4×Dic79—28no—
205C4×Dic79—28no—
206C4×Dic79—28no—
207C4×Dic79—28no—
208C4×Dic79—28no—
209C4×Dic79—28no—
210C24×C79—22no—
211C24×C79—22no—
212C24×C79—22no—
213C24×C79—22no—
214C24×C79—22no—
215C24×C79—22no—
216C24×C79C22×C414yes—
217C24×C79C2412yes—
218C24×C79C2411yescharacteristic
219C22×C4×C79—22no—
220C22×C4×C79—22no—
221C22×C4×C79—22no—
222C22×C4×C79—22no—
223C22×C4×C79—22no—
224C22×C4×C79—22no—
225C22×C4×C79—22no—
226C22×C4×C79—22no—
227C22×C4×C79—22no—
228C22×C4×C79—22no—
229C22×C4×C79—22no—
230C22×C4×C79—22no—
231C22×C4×C79—22no—
232C22×C4×C79—22no—
233C22×C4×C79C22×C414yes—
234C22×C4×C79C22×C414yes—
235C22×C4×C79C2×D414yes—
236C22×C4×C79#4114yes—
237C22×C4×C79C2412yes—
238C22×C4×C79C2412yes—
239C22×C4×C79C2412yes—
240C22×C4×C79C2412yes—
241C22×C4×C79C2412yes—
242C22×C4×C79C2412yes—
243C4⋊C4×C79—28no—
244C22⋊C4×C79—28no—
245C22⋊C4×C79—28no—
246C22⋊C4×C79C22×C4116yes—
247C42×C79—28no—
248C23×C79—28no—
249C23×C79—28no—
250C23×C79—28no—
251C23×C79—22no—
252C23×C79—22no—
253C23×C79—22no—
254C23×C79—22no—
255C23×C79—22no—
256C23×C79—22no—
257C23×C79—44no—
258C23×C79—44no—
259C23×C79—44no—
260C23×C79—44no—
261C23×C79C23×C414yes—
262C23×C79C23×C412yes—
263C23×C79C22×D412yes—
264C23×C79C2×#4112yes—
265C23×C79C2×#4112yes—
266C23×C79C2×#4112yes—
267C23×C792−1+412yes—
268C23×C792−1+412yes—
269C23×C79C2511yescharacteristic
270C2×C4×C79—28no—
271C2×C4×C79—28no—
272C2×C4×C79—28no—
273C2×C4×C79—28no—
274C2×C4×C79—22no—
275C2×C4×C79—22no—
276C2×C4×C79—22no—
277C2×C4×C79—22no—
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—22no—
288C2×C4×C79—44no—
289C2×C4×C79—44no—
290C2×C4×C79C23×C414yes—
291C2×C4×C79C23×C414yes—
292C2×C4×C79C22×D414yes—
293C2×C4×C79C2×#4114yes—
294C2×Dic79—28no—
295C2×Dic79—28no—
296C2×Dic79—28no—
297C2×Dic79—28no—
298C2×Dic79—28no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—232no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—44no—
317C2×Dic79—44no—
318C2×Dic79C4×D4116yes—
319C2×Dic79C23×C414yes—
320C2×Dic79C23×C414yes—
321C2×Dic79C23×C414yes—
322C2×Dic79C23×C414yes—
323C2×Dic79C22×D414yes—
324C2×Dic79C22×D414yes—
325C2×Dic79C2×#4114yes—
326C2×Dic79C2×#4114yes—
327Dic158—232no—
328C22×C79—24no—
329C22×C79—24no—
330C22×C79—24no—
331C22×C79—416no—
332C22×C79—42no—
333C22×C79—42no—
334C22×C79—42no—
335C22×C79—42no—
336C22×C79C2×C4×D414yes—
337C22×C79C4×#4114yes—
338C22×C79#51914yes—
339C22×C79#54714yes—
340C22×C79#54814yes—
341C22×C79#55214yes—
342C22×C79#55614yes—
343C22×C79C24×C411yescharacteristic
344C22×C79C23×D411yescharacteristic
345C22×C79C22×#4111yescharacteristic
346C22×C79C22×#4111yescharacteristic
347C22×C79C22×#4111yescharacteristic
348C22×C79C2×2−1+411yescharacteristic
349C22×C79C2×2−1+411yescharacteristic
350C4×C79—24no—
351C4×C79—24no—
352C4×C79—24no—
353C4×C79—24no—
354C4×C79—42no—
355C4×C79—42no—
356Dic79—24no—
357Dic79—24no—
358Dic79—24no—
359Dic79—24no—
360Dic79—24no—
361Dic79—42no—
362Dic79—42no—
363Dic79C2×C4×D418yes—
364C2×#2362—791nomaximal, Sylow
365C2×C79—44no—
366C2×C79#236218yescomplemented
367C2×C79C22×C4×D411yescharacteristic
368C2×C79C2×C4×#4111yescharacteristic
369C2×C79C2×#51911yescharacteristic
370C2×C79C2×#54711yescharacteristic
371C2×C79C2×#54811yescharacteristic
372C2×C79C2×#55211yescharacteristic
373C2×C79C2×#55611yescharacteristic
374C22×C22⋊Q8—791no—
375C22×C4×Q8—791no—
376C22×#117—791no—
377#2362—7916no—
378C2×#391—791no—
379C2×#389—791no—
380C2×#388—791no—
381C2×#388—791no—
382C2×#388—791no—
383C2×#388D7911yescharacteristic
384C2×#387—791no—
385C2×#387—791no—
386C2×C4×C4⋊C4—791no—
387C2×C4×C4⋊C4—791no—
388C2×C4×C4⋊C4—791no—
389C2×C4×C22⋊C4—791no—
390C79C2×#236211yescharacteristic, complemented, Sylow
391C23×Q8—791no—
392C24×C4—791no—
393C2×C22⋊Q8—798no—
394C2×C22⋊Q8—7916no—
395C2×C4×Q8—798no—
396C2×C4×Q8—1588no—
397C2×#117—798no—
398C2×#117—1588no—
399C22×C4⋊C4—791no—
400C22×C4⋊C4—791no—
401C22×C4⋊C4—791no—
402C22×C4⋊C4—791no—
403C22×C4⋊C4—791no—
404C22×C4⋊C4—791no—
405C22×C4⋊C4—791no—
406C22×C4⋊C4—791no—
407C22×C4⋊C4C2×D7911yescharacteristic
408C22×C22⋊C4—791no—
409C22×C22⋊C4—791no—
410C22×C22⋊C4—791no—
411C22×C22⋊C4C2×D7911yescharacteristic
412C22×C22⋊C4C2×D7911yescharacteristic
413C22×C22⋊C4C2×D7911yescharacteristic
414C22×C42—791no—
415C22×C42—791no—
416C22×C42—791no—
417C22×C42—791no—
418C22×C42—791no—
419C22×C42—791no—
420C22×C42—791no—
421C22×C42C2×D7911yescharacteristic
422#391—798no—
423#389—798no—
424#388—798no—
425#388—798no—
426#388—798no—
427#388C2×D7918yes—
428#387—798no—
429#387—798no—
430C4×C4⋊C4—798no—
431C4×C4⋊C4—798no—
432C4×C4⋊C4—798no—
433C4×C22⋊C4—798no—
434C2×#95—791no—
435C2×#95—791no—
436C2×#95—791no—
437C2×#95—791no—
438C2×#95—791no—
439C2×#95—791no—
440C2×#95—791no—
441C2×#95—791no—
442C2×#95C2×D7911yescharacteristic
443C2×#95C2×D7911yescharacteristic
444C25C22×D7911yescharacteristic
445C22×Q8—798no—
446C22×Q8—794no—
447C22×Q8—1584no—
448C22×Q8—1584no—
449C23×C4—791no—
450C23×C4—798no—
451C23×C4—794no—
452C23×C4—791no—
453C23×C4—791no—
454C23×C4—791no—
455C23×C4—791no—
456C23×C4—791no—
457C23×C4—791no—
458C23×C4—791no—
459C23×C4—1584no—
460C23×C4—1584no—
461C23×C4C22×D7911yescharacteristic
462C23×C4C22×D7911yescharacteristic
463C23×C4C22×D7911yescharacteristic
464C23×C4C22×D7911yescharacteristic
465C23×C4C22×D7911yescharacteristic
466C23×C4C22×D7911yescharacteristic
467C22⋊Q8—7964no—
468C4×Q8—15832no—
469#117—15832no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—798no—
472C2×C4⋊C4—798no—
473C2×C4⋊C4—798no—
474C2×C4⋊C4—798no—
475C2×C4⋊C4—794no—
476C2×C4⋊C4—794no—
477C2×C4⋊C4—794no—
478C2×C4⋊C4—794no—
479C2×C4⋊C4—794no—
480C2×C4⋊C4—794no—
481C2×C4⋊C4—794no—
482C2×C4⋊C4—794no—
483C2×C4⋊C4—1584no—
484C2×C4⋊C4—1584no—
485C2×C4⋊C4—1584no—
486C2×C4⋊C4—1584no—
487C2×C4⋊C4C22×D7914yes—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—798no—
491C2×C22⋊C4—794no—
492C2×C22⋊C4—794no—
493C2×C22⋊C4—794no—
494C2×C22⋊C4—1584no—
495C2×C22⋊C4—1584no—
496C2×C22⋊C4C4×D7918yes—
497C2×C22⋊C4C22×D7914yes—
498C2×C22⋊C4C22×D7914yes—
499C2×C22⋊C4C22×D7914yes—
500C2×C42—24no—
501C2×C42—794no—
502C2×C42—794no—
503C2×C42—794no—
504C2×C42—794no—
505C2×C42—794no—
506C2×C42—794no—
507C2×C42—794no—
508C2×C42—1584no—
509C2×C42—1584no—
510C2×C42—1584no—
511C2×C42—1584no—
512C2×C42—1584no—
513C2×C42—1584no—
514C2×C42—1584no—
515C2×C42C22×D7914yes—
516#95—794no—
517#95—794no—
518#95—794no—
519#95—794no—
520#95—794no—
521#95—794no—
522#95—794no—
523#95—794no—
524#95C22×D7914yes—
525#95C22×D7914yes—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24C2×C4×D7914yes—
533C24C23×D7912yes—
534C24C23×D7911yescharacteristic
535C2×Q8—7916no—
536C2×Q8—1588no—
537C2×Q8—15832no—
538C2×Q8—1588no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—794no—
554C22×C4—792no—
555C22×C4—794no—
556C22×C4—794no—
557C22×C4—794no—
558C22×C4—792no—
559C22×C4—792no—
560C22×C4—792no—
561C22×C4—792no—
562C22×C4—792no—
563C22×C4—794no—
564C22×C4—794no—
565C22×C4—794no—
566C22×C4—7916no—
567C22×C4—794no—
568C22×C4—792no—
569C22×C4—792no—
570C22×C4—1582no—
571C22×C4—1582no—
572C22×C4—1582no—
573C22×C4—1582no—
574C22×C4—1582no—
575C22×C4—1582no—
576C22×C4—1588no—
577C22×C4—15832no—
578C22×C4—1588no—
579C22×C4—1582no—
580C22×C4—1582no—
581C22×C4—1582no—
582C22×C4—1582no—
583C22×C4—1582no—
584C22×C4—1582no—
585C22×C4—1582no—
586C22×C4—1582no—
587C22×C4—1582no—
588C22×C4—1582no—
589C22×C4C2×C4×D7914yes—
590C22×C4C2×C4×D7914yes—
591C22×C4D4×D7914yes—
592C22×C4#1192962314yes—
593C22×C4C23×D7912yes—
594C22×C4C23×D7912yes—
595C22×C4C23×D7912yes—
596C22×C4C23×D7912yes—
597C22×C4C23×D7912yes—
598C22×C4C23×D7912yes—
599C4⋊C4—28no—
600C4⋊C4—7916no—
601C4⋊C4—7916no—
602C4⋊C4—7916no—
603C4⋊C4—7916no—
604C4⋊C4—1588no—
605C4⋊C4—1588no—
606C4⋊C4—1588no—
607C4⋊C4—1588no—
608C22⋊C4—28no—
609C22⋊C4—28no—
610C22⋊C4—7916no—
611C22⋊C4—1588no—
612C22⋊C4—1588no—
613C22⋊C4C2×C4×D79116yes—
614C42—28no—
615C42—1588no—
616C42—1588no—
617C42—1588no—
618C42—1588no—
619C42—1588no—
620C42—1588no—
621C42—1588no—
622C23—22no—
623C23—22no—
624C23—28no—
625C23—28no—
626C23—28no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23C22×C4×D7914yes—
636C23C22×C4×D7912yes—
637C23C2×D4×D7912yes—
638C23#41×D7912yes—
639C23#41×D7912yes—
640C23C2×#1192962312yes—
641C23#1457920812yes—
642C23#1457920812yes—
643C23C24×D7911yescharacteristic
644Q8—15832no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—28no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—3164no—
666C2×C4—3164no—
667C2×C4—7916no—
668C2×C4—794no—
669C2×C4—794no—
670C2×C4—794no—
671C2×C4—794no—
672C2×C4—794no—
673C2×C4—794no—
674C2×C4—794no—
675C2×C4—794no—
676C2×C4—1582no—
677C2×C4—1582no—
678C2×C4—1582no—
679C2×C4—1582no—
680C2×C4—1582no—
681C2×C4—1582no—
682C2×C4—15832no—
683C2×C4—1582no—
684C2×C4—1582no—
685C2×C4—1588no—
686C2×C4—1588no—
687C2×C4—1588no—
688C2×C4—1588no—
689C2×C4—1588no—
690C2×C4—1582no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1582no—
696C2×C4—1582no—
697C2×C4—1582no—
698C2×C4C22×C4×D7914yes—
699C2×C4C22×C4×D7914yes—
700C2×C4C2×D4×D7914yes—
701C2×C4C2×#1192962314yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—416no—
709C22—42no—
710C22C4×D4×D7914yes—
711C22C4×#1192962314yes—
712C22#1909904014yes—
713C22#1909921114yes—
714C22#1909921914yes—
715C22#1909924914yes—
716C22#1909928214yes—
717C22C23×C4×D7911yescharacteristic
718C22C22×D4×D7911yescharacteristic
719C22C2×#41×D7911yescharacteristic
720C22C2×#41×D7911yescharacteristic
721C22C22×#1192962311yescharacteristic
722C22C2×#1457920811yescharacteristic
723C22C2×#1457920811yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—3162no—
731C4—3162no—
732C4—798no—
733C4—1584no—
734C4—1584no—
735C4—1584no—
736C4—1584no—
737C4—1584no—
738C2—44no—
739C2#2376643018yesdirect product factor
740C2C2×C4×D4×D7911yescharacteristic
741C2C2×C4×#1192962311yescharacteristic
742C2C2×#1909904011yescharacteristic
743C2C2×#1909921111yescharacteristic
744C2C2×#1909921911yescharacteristic
745C2C2×#1909924911yescharacteristic
746C2C2×#1909928211yescharacteristic
subgroupG/H
centerC24C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC2×#388×C79C2
socleC24×C79C24
prime radicalC25×C79C23
cosocleC23×C79C25
hypercenterC2×#388D79
hypocenterC79C2×#2362
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic158C2semidirect
4. #23766430C2direct (N × H)
5. C2×#19098467C2semidirect
6. C2×#19098458C2semidirect
10. C2×#19098450C2semidirect
11. C2×#19098448C2semidirect
12. C2×C4⋊C4×Dic79C2semidirect
13. C2×C4×Dic79⋊C4C2semidirect
14. C2×#19098414C2semidirect
19. C2×#14579138C4semidirect
22. C2×C4×Dic158C22semidirect
43. #19098467C22semidirect
44. #19098458C22semidirect
48. #19098450C22semidirect
49. #19098448C22semidirect
50. C4⋊C4×Dic79C22semidirect
51. C4×Dic79⋊C4C22semidirect
52. #19098414C22semidirect
86. #14579138C2×C4semidirect
366. C2×C79#2362semidirect
390. C79C2×#2362semidirect
739. C2#23766430direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791382
C22×C4×Dic1582
C22×#145791172
#237664302
C2×#190984672
C2×#190984582
C2×#190984572
C2×#190984562
C2×#190984502
C2×#190984482
C2×C4⋊C4×Dic792
C2×C4×Dic79⋊C42
C2×#190984142
C2×C22⋊C4×Dic792
C2×#388×C792
C2×#236279