Finite Group Databasebeta

← C2×#23767099 #34456094

Subgroups — C2×#23767099 #34456094

Order 20224.

3550 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579159C211yesmaximal, characteristic, complemented
2C22×#14579138C211yesmaximal, characteristic
3C23×Dic79⋊C4C211yesmaximal, characteristic
4#23767099C2116yesmaximal, direct product factor
5C2×#19098494C211yesmaximal, characteristic, complemented
6C2×#19098493C211yesmaximal, characteristic, complemented
7C2×#19098483C211yesmaximal, characteristic, complemented
8C2×#19098482C211yesmaximal, characteristic, complemented
9C2×#19098458C211yesmaximal, characteristic, complemented
10C2×#19098458C211yesmaximal, characteristic, complemented
11C2×#19098436C211yesmaximal, characteristic
12C2×#19098435C211yesmaximal, characteristic
13C2×#19098432C211yesmaximal, characteristic, complemented
14C2×#19098421C211yesmaximal, characteristic
15C2×C22⋊C4×Dic79C211yesmaximal, characteristic
16C22×C22⋊Q8×C79C211yesmaximal, characteristic
17C23×Dic158C2211yescharacteristic
18C24×Dic79C2211yescharacteristic
19C24×Dic79C2211yescharacteristic
20C2×#14579159—28no—
21C2×#14579159C2218yescomplemented
22C2×#14579138—28no—
23C2×#14579138C2218yes—
24C22×C4⋊Dic79C2211yescharacteristic
25C22×Dic79⋊C4—28no—
26C22×Dic79⋊C4C2211yescharacteristic
27C22×Dic79⋊C4C2211yescharacteristic
28C22×Dic79⋊C4C2211yescharacteristic
29C22×Dic79⋊C4C2218yes—
30C22×Dic79⋊C4C2211yescharacteristic
31C22×Dic79⋊C4C2211yescharacteristic
32C22×Dic79⋊C4C2211yescharacteristic
33C22×Dic79⋊C4C2211yescharacteristic
34C22×Dic79⋊C4C2211yescharacteristic
35C22×Dic79⋊C4C2211yescharacteristic
36C22×Dic79⋊C4C2211yescharacteristic
37C22×Dic79⋊C4C2211yescharacteristic
38C22×Dic79⋊C4C2211yescharacteristic
39C22×C22⋊Dic79C2211yescharacteristic
40C22×C22⋊Dic79C2211yescharacteristic
41C22×C4×Dic79C2211yescharacteristic
42C22×C4×Dic79C2211yescharacteristic
43#19098494C2218yescomplemented
44#19098493C2218yescomplemented
45#19098483C2218yescomplemented
46#19098482C2218yescomplemented
47#19098458C2218yescomplemented
48#19098458C2218yescomplemented
49#19098436C2218yes—
50#19098435C2218yes—
51#19098432C2218yescomplemented
52#19098421C2218yes—
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
62C23×Q8×C79C2211yescharacteristic
63C24×C4×C79C2211yescharacteristic
64C2×C22⋊Q8×C79—28no—
65C2×C22⋊Q8×C79C2218yes—
66C22×C4⋊C4×C79C2211yescharacteristic
67C22×C4⋊C4×C79C2211yescharacteristic
68C22×C4⋊C4×C79C2211yescharacteristic
69C22×C22⋊C4×C79C2211yescharacteristic
70C22×C22⋊C4×C79C2211yescharacteristic
71C22×Dic158—24no—
72C22×Dic158—24no—
73C22×Dic158—42no—
74C22×Dic158C2314yes—
75C23×Dic79—24no—
76C23×Dic79—24no—
77C23×Dic79—24no—
78C23×Dic79—24no—
79C23×Dic79—42no—
80C23×Dic79Q818yescomplemented
81C23×Dic79C2311yescharacteristic
82C23×Dic79C2311yescharacteristic
83C23×Dic79C2311yescharacteristic
84C23×Dic79C2314yes—
85C23×Dic79C2311yescharacteristic
86C23×Dic79C2311yescharacteristic
87C23×Dic79C2311yescharacteristic
88C23×Dic79C2311yescharacteristic
89C23×Dic79C2314yes—
90C23×Dic79C2311yescharacteristic
91#14579159—232no—
92#14579138—232no—
93C2×C4⋊Dic79—24no—
94C2×C4⋊Dic79C2314yes—
95C2×Dic79⋊C4—24no—
96C2×Dic79⋊C4—24no—
97C2×Dic79⋊C4—24no—
98C2×Dic79⋊C4—24no—
99C2×Dic79⋊C4—24no—
100C2×Dic79⋊C4—24no—
101C2×Dic79⋊C4—24no—
102C2×Dic79⋊C4—24no—
103C2×Dic79⋊C4—24no—
104C2×Dic79⋊C4—232no—
105C2×Dic79⋊C4—42no—
106C2×Dic79⋊C4—42no—
107C2×Dic79⋊C4D418yes—
108C2×Dic79⋊C4C2314yes—
109C2×Dic79⋊C4C2314yes—
110C2×Dic79⋊C4C2314yes—
111C2×Dic79⋊C4C2314yes—
112C2×Dic79⋊C4C2314yes—
113C2×Dic79⋊C4C2314yes—
114C2×Dic79⋊C4C2314yes—
115C2×Dic79⋊C4C2314yes—
116C2×Dic79⋊C4C2314yes—
117C2×Dic79⋊C4C2314yes—
118C2×Dic79⋊C4C2314yes—
119C2×Dic79⋊C4C2314yes—
120C2×C22⋊Dic79—24no—
121C2×C22⋊Dic79Q818yescomplemented
122C2×C22⋊Dic79C2314yes—
123C2×C22⋊Dic79C2314yes—
124C2×C4×Dic79—24no—
125C2×C4×Dic79—24no—
126C2×C4×Dic79C2314yes—
127C2×C4×Dic79C2314yes—
128C79⋊#95C2314yes—
129C79⋊#95C2314yes—
130C79⋊#95C2314yes—
131C79⋊#95C2314yes—
132C79⋊#95C2314yes—
133C79⋊#95C2314yes—
134C79⋊#95C2314yes—
135C79⋊#95C2314yes—
136C25×C79C2311yescharacteristic
137C22×Q8×C79—24no—
138C22×Q8×C79—24no—
139C22×Q8×C79—42no—
140C22×Q8×C79C2314yes—
141C23×C4×C79—24no—
142C23×C4×C79—24no—
143C23×C4×C79—42no—
144C23×C4×C79C2311yescharacteristic
145C23×C4×C79C2311yescharacteristic
146C23×C4×C79C2311yescharacteristic
147C23×C4×C79C2314yes—
148C23×C4×C79C2311yescharacteristic
149C23×C4×C79C2311yescharacteristic
150C23×C4×C79C2311yescharacteristic
151C22⋊Q8×C79—232no—
152C2×C4⋊C4×C79—24no—
153C2×C4⋊C4×C79—24no—
154C2×C4⋊C4×C79—24no—
155C2×C4⋊C4×C79C2314yes—
156C2×C4⋊C4×C79C2314yes—
157C2×C4⋊C4×C79C2314yes—
158C2×C22⋊C4×C79—24no—
159C2×C22⋊C4×C79D418yes—
160C2×C22⋊C4×C79C2314yes—
161C2×C22⋊C4×C79C2314yes—
162C2×Dic158—28no—
163C2×Dic158—28no—
164C2×Dic158—44no—
165C2×Dic158—416no—
166C22×Dic79—232no—
167C22×Dic79—28no—
168C22×Dic79—28no—
169C22×Dic79—28no—
170C22×Dic79—22no—
171C22×Dic79—22no—
172C22×Dic79—22no—
173C22×Dic79—22no—
174C22×Dic79—22no—
175C22×Dic79—22no—
176C22×Dic79—22no—
177C22×Dic79—22no—
178C22×Dic79—28no—
179C22×Dic79—22no—
180C22×Dic79—22no—
181C22×Dic79—22no—
182C22×Dic79—22no—
183C22×Dic79—22no—
184C22×Dic79—22no—
185C22×Dic79—22no—
186C22×Dic79—22no—
187C22×Dic79—22no—
188C22×Dic79—44no—
189C22×Dic79—416no—
190C22×Dic79C2×D414yes—
191C22×Dic79C2×D414yes—
192C22×Dic79C2×Q814yes—
193C22×Dic79C2×Q814yes—
194C22×Dic79C2×Q814yes—
195C22×Dic79C2×Q814yes—
196C22×Dic79C2×Q8116yescomplemented
197C22×Dic79#4114yes—
198C22×Dic79C2412yes—
199C22×Dic79C2412yes—
200C22×Dic79C2412yes—
201C22×Dic79C2412yes—
202C22×Dic79C2412yes—
203C22×Dic79C2412yes—
204C22×Dic79C2412yes—
205C22×Dic79C2412yes—
206C4⋊Dic79—28no—
207Dic79⋊C4—28no—
208Dic79⋊C4—28no—
209Dic79⋊C4—28no—
210Dic79⋊C4—28no—
211Dic79⋊C4—28no—
212Dic79⋊C4—28no—
213Dic79⋊C4—28no—
214Dic79⋊C4—28no—
215Dic79⋊C4—28no—
216Dic79⋊C4—44no—
217Dic79⋊C4—44no—
218Dic79⋊C4C2×D4116yes—
219C22⋊Dic79—28no—
220C22⋊Dic79C2×Q8116yescomplemented
221C4×Dic79—28no—
222C4×Dic79—28no—
223C24×C79—22no—
224C24×C79—22no—
225C24×C79—22no—
226C24×C79—22no—
227C24×C79C2×D414yes—
228C24×C79C2×Q814yes—
229C24×C79C2×Q814yes—
230C24×C79C2412yes—
231C24×C79C2411yescharacteristic
232C2×Q8×C79—28no—
233C2×Q8×C79—28no—
234C2×Q8×C79—44no—
235C2×Q8×C79—416no—
236C22×C4×C79—22no—
237C22×C4×C79—22no—
238C22×C4×C79—22no—
239C22×C4×C79—22no—
240C22×C4×C79—22no—
241C22×C4×C79—22no—
242C22×C4×C79—22no—
243C22×C4×C79—22no—
244C22×C4×C79—22no—
245C22×C4×C79—28no—
246C22×C4×C79—22no—
247C22×C4×C79—22no—
248C22×C4×C79—22no—
249C22×C4×C79—22no—
250C22×C4×C79—22no—
251C22×C4×C79—22no—
252C22×C4×C79—28no—
253C22×C4×C79—44no—
254C22×C4×C79—416no—
255C22×C4×C79C2×D414yes—
256C22×C4×C79C2×D414yes—
257C22×C4×C79C2×D414yes—
258C22×C4×C79C2412yes—
259C22×C4×C79C2412yes—
260C22×C4×C79C2412yes—
261C22×C4×C79C2412yes—
262C22×C4×C79C2412yes—
263C22×C4×C79C2412yes—
264C4⋊C4×C79—28no—
265C4⋊C4×C79—28no—
266C4⋊C4×C79—28no—
267C22⋊C4×C79—28no—
268C22⋊C4×C79C2×D4116yes—
269C23×C79—28no—
270C23×C79—28no—
271C23×C79—28no—
272C23×C79—28no—
273C23×C79—28no—
274C23×C79—28no—
275C23×C79—22no—
276C23×C79—22no—
277C23×C79—22no—
278C23×C79—22no—
279C23×C79C4⋊Q8116yescomplemented
280C23×C79C22×D412yes—
281C23×C79C22×D414yes—
282C23×C79C22×D412yes—
283C23×C79C22×Q814yes—
284C23×C79C22×Q814yes—
285C23×C79C22×Q812yes—
286C23×C79C22×Q812yes—
287C23×C79C2×#4112yes—
288C23×C79H(5,𝔽2)12yes—
289C23×C792−1+412yes—
290C23×C79C2511yescharacteristic
291Q8×C79—416no—
292C2×C4×C79—28no—
293C2×C4×C79—28no—
294C2×C4×C79—28no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79—22no—
301C2×C4×C79—22no—
302C2×C4×C79—22no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—416no—
311C2×C4×C79—44no—
312C2×C4×C79—44no—
313C2×C4×C79—44no—
314C2×C4×C79C22×D414yes—
315C2×C4×C79C22×D414yes—
316C2×C4×C79C22×D414yes—
317C2×Dic79—28no—
318C2×Dic79—28no—
319C2×Dic79—28no—
320C2×Dic79—28no—
321C2×Dic79—22no—
322C2×Dic79—22no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—232no—
330C2×Dic79—22no—
331C2×Dic79—22no—
332C2×Dic79—22no—
333C2×Dic79—22no—
334C2×Dic79—22no—
335C2×Dic79—22no—
336C2×Dic79—22no—
337C2×Dic79—22no—
338C2×Dic79—22no—
339C2×Dic79—416no—
340C2×Dic79—44no—
341C2×Dic79—44no—
342C2×Dic79—44no—
343C2×Dic79C22⋊Q8116yescomplemented
344C2×Dic79C22×D414yes—
345C2×Dic79C22×D414yes—
346C2×Dic79C22×Q814yes—
347C2×Dic79C22×Q814yes—
348C2×Dic79C22×Q814yes—
349C2×Dic79C22×Q814yes—
350C2×Dic79C2×#4114yes—
351Dic158—416no—
352C22×C79—24no—
353C22×C79—24no—
354C22×C79—24no—
355C22×C79—232no—
356C22×C79—24no—
357C22×C79—24no—
358C22×C79—24no—
359C22×C79C2×C22⋊Q814yes—
360C22×C79C2×C4⋊Q814yes—
361C22×C79C2×C4⋊Q818yescomplemented
362C22×C79#54414yes—
363C22×C79D4214yes—
364C22×C79#54714yes—
365C22×C79D4×Q814yes—
366C22×C79#55414yes—
367C22×C79C23×D411yescharacteristic
368C22×C79C23×D411yescharacteristic
369C22×C79C23×Q811yescharacteristic
370C22×C79C23×Q811yescharacteristic
371C22×C79C22×#4111yescharacteristic
372C22×C79C2×H(5,𝔽2)11yescharacteristic
373C22×C79C2×2−1+411yescharacteristic
374C4×C79—24no—
375C4×C79—24no—
376C4×C79—24no—
377C4×C79—42no—
378C4×C79—42no—
379C4×C79—42no—
380Dic79—24no—
381Dic79—24no—
382Dic79—24no—
383Dic79—24no—
384Dic79—42no—
385Dic79—42no—
386Dic79—42no—
387Dic79C2×C22⋊Q818yescomplemented
388C2×#2440—791nomaximal, Sylow
389C2×C79—28no—
390C2×C79#244018yescomplemented
391C2×C79C22×C22⋊Q811yescharacteristic
392C2×C79C22×C4⋊Q811yescharacteristic
393C2×C79C2×#54411yescharacteristic
394C2×C79C2×D4211yescharacteristic
395C2×C79C2×#54711yescharacteristic
396C2×C79C2×D4×Q811yescharacteristic
397C2×C79C2×#55411yescharacteristic
398C22×C4⋊Q8—791no—
399C22×C22⋊Q8—791no—
400C22×C22⋊Q8D7911yescharacteristic
401C23×C4⋊C4—791no—
402#2440—7916no—
403C2×#398—791no—
404C2×#398—791no—
405C2×#395—791no—
406C2×#395—791no—
407C2×#389—791no—
408C2×#389—791no—
409C2×#385—791no—
410C2×#385—791no—
411C2×#384—791no—
412C2×#380—791no—
413C2×C4×C22⋊C4—791no—
414C79C2×#244011yescharacteristic, complemented, Sylow
415C23×Q8—791no—
416C23×Q8C2×D7911yescharacteristic
417C24×C4—791no—
418C24×C4—791no—
419C24×C4C2×D7911yescharacteristic
420C2×C4⋊Q8—798no—
421C2×C4⋊Q8—1588no—
422C2×C22⋊Q8—28no—
423C2×C22⋊Q8—798no—
424C2×C22⋊Q8—1588no—
425C2×C22⋊Q8C2×D7918yes—
426C22×C4⋊C4—791no—
427C22×C4⋊C4—791no—
428C22×C4⋊C4—791no—
429C22×C4⋊C4—791no—
430C22×C4⋊C4—791no—
431C22×C4⋊C4—791no—
432C22×C4⋊C4—791no—
433C22×C4⋊C4—791no—
434C22×C4⋊C4—791no—
435C22×C4⋊C4—791no—
436C22×C4⋊C4—798no—
437C22×C4⋊C4—791no—
438C22×C4⋊C4—791no—
439C22×C4⋊C4—791no—
440C22×C4⋊C4—1588no—
441C22×C4⋊C4C2×D7911yescharacteristic
442C22×C4⋊C4C2×D7911yescharacteristic
443C22×C4⋊C4C2×D7911yescharacteristic
444C22×C22⋊C4—791no—
445C22×C22⋊C4—791no—
446C22×C22⋊C4C2×D7911yescharacteristic
447C22×C22⋊C4C2×D7911yescharacteristic
448C22×C42—791no—
449C22×C42—791no—
450#398—798no—
451#398—798no—
452#395—798no—
453#395—798no—
454#389—798no—
455#389—798no—
456#385—798no—
457#385—798no—
458#384—798no—
459#380—798no—
460C4×C22⋊C4—798no—
461C2×#95—791no—
462C2×#95—791no—
463C2×#95—791no—
464C2×#95—791no—
465C2×#95—791no—
466C2×#95—791no—
467C2×#95—791no—
468C2×#95—791no—
469C25C22×D7911yescharacteristic
470C22×Q8—24no—
471C22×Q8—24no—
472C22×Q8—42no—
473C22×Q8—3162no—
474C22×Q8—794no—
475C22×Q8—1584no—
476C22×Q8—1584no—
477C22×Q8C22×D7914yes—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—3162no—
482C23×C4—794no—
483C23×C4—791no—
484C23×C4—798no—
485C23×C4—794no—
486C23×C4—791no—
487C23×C4—791no—
488C23×C4—791no—
489C23×C4—791no—
490C23×C4—791no—
491C23×C4—791no—
492C23×C4—791no—
493C23×C4—1584no—
494C23×C4—1584no—
495C23×C4—1584no—
496C23×C4—1584no—
497C23×C4C22×D7911yescharacteristic
498C23×C4C22×D7911yescharacteristic
499C23×C4C22×D7911yescharacteristic
500C23×C4C22×D7914yes—
501C23×C4C22×D7911yescharacteristic
502C23×C4C22×D7911yescharacteristic
503C23×C4C22×D7911yescharacteristic
504C4⋊Q8—15832no—
505C22⋊Q8—232no—
506C22⋊Q8—15832no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—3162no—
511C2×C4⋊C4—3162no—
512C2×C4⋊C4—794no—
513C2×C4⋊C4—794no—
514C2×C4⋊C4—798no—
515C2×C4⋊C4—794no—
516C2×C4⋊C4—794no—
517C2×C4⋊C4—794no—
518C2×C4⋊C4—794no—
519C2×C4⋊C4—794no—
520C2×C4⋊C4—794no—
521C2×C4⋊C4—794no—
522C2×C4⋊C4—794no—
523C2×C4⋊C4—794no—
524C2×C4⋊C4—794no—
525C2×C4⋊C4—794no—
526C2×C4⋊C4—15832no—
527C2×C4⋊C4—1584no—
528C2×C4⋊C4—1584no—
529C2×C4⋊C4—1584no—
530C2×C4⋊C4—1584no—
531C2×C4⋊C4—1584no—
532C2×C4⋊C4—1584no—
533C2×C4⋊C4—1584no—
534C2×C4⋊C4—1584no—
535C2×C4⋊C4—1584no—
536C2×C4⋊C4—1584no—
537C2×C4⋊C4C22×D7914yes—
538C2×C4⋊C4C22×D7914yes—
539C2×C4⋊C4C22×D7914yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—798no—
542C2×C22⋊C4—794no—
543C2×C22⋊C4—794no—
544C2×C22⋊C4—1584no—
545C2×C22⋊C4C22⋊D7918yes—
546C2×C22⋊C4C22×D7914yes—
547C2×C22⋊C4C22×D7914yes—
548C2×C42—794no—
549C2×C42—794no—
550C2×C42—1584no—
551C2×C42—1584no—
552#95—794no—
553#95—794no—
554#95—794no—
555#95—794no—
556#95—794no—
557#95—794no—
558#95—794no—
559#95—794no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24C2×C22⋊D7914yes—
565C24Q8×D7914yes—
566C24Q8×D7914yes—
567C24C23×D7912yes—
568C24C23×D7911yescharacteristic
569C2×Q8—28no—
570C2×Q8—28no—
571C2×Q8—44no—
572C2×Q8—416no—
573C2×Q8—31616no—
574C2×Q8—3164no—
575C2×Q8—1588no—
576C2×Q8—1588no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—44no—
595C22×C4—416no—
596C22×C4—31616no—
597C22×C4—3164no—
598C22×C4—794no—
599C22×C4—794no—
600C22×C4—792no—
601C22×C4—794no—
602C22×C4—794no—
603C22×C4—794no—
604C22×C4—794no—
605C22×C4—7916no—
606C22×C4—792no—
607C22×C4—792no—
608C22×C4—792no—
609C22×C4—792no—
610C22×C4—794no—
611C22×C4—792no—
612C22×C4—792no—
613C22×C4—792no—
614C22×C4—1588no—
615C22×C4—1582no—
616C22×C4—1582no—
617C22×C4—1582no—
618C22×C4—1582no—
619C22×C4—1582no—
620C22×C4—1582no—
621C22×C4—1582no—
622C22×C4—1582no—
623C22×C4—1582no—
624C22×C4—1588no—
625C22×C4—1588no—
626C22×C4—15832no—
627C22×C4—1588no—
628C22×C4—1582no—
629C22×C4—1582no—
630C22×C4—1582no—
631C22×C4—1582no—
632C22×C4—1582no—
633C22×C4—1582no—
634C22×C4—1582no—
635C22×C4—1582no—
636C22×C4D4×D7914yes—
637C22×C4C2×C22⋊D7914yes—
638C22×C4C2×C22⋊D7914yes—
639C22×C4C23×D7912yes—
640C22×C4C23×D7912yes—
641C22×C4C23×D7912yes—
642C22×C4C23×D7912yes—
643C22×C4C23×D7912yes—
644C22×C4C23×D7912yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—3164no—
649C4⋊C4—3164no—
650C4⋊C4—7916no—
651C4⋊C4—1588no—
652C4⋊C4—1588no—
653C4⋊C4—1588no—
654C4⋊C4—1588no—
655C4⋊C4—1588no—
656C4⋊C4—1588no—
657C4⋊C4—1588no—
658C4⋊C4—1588no—
659C4⋊C4—1588no—
660C4⋊C4—1588no—
661C22⋊C4—28no—
662C22⋊C4—7916no—
663C22⋊C4—1588no—
664C22⋊C4C2×C22⋊D79116yes—
665C42—1588no—
666C42—1588no—
667C23—22no—
668C23—22no—
669C23—28no—
670C23—28no—
671C23—28no—
672C23—28no—
673C23—28no—
674C23—28no—
675C23—22no—
676C23—22no—
677C23#14579159116yescomplemented
678C23C2×D4×D7912yes—
679C23C22×C22⋊D7914yes—
680C23C22×C22⋊D7912yes—
681C23C2×Q8×D7914yes—
682C23C2×Q8×D7914yes—
683C23C2×Q8×D7912yes—
684C23C2×Q8×D7912yes—
685C23#41×D7912yes—
686C23#1457920612yes—
687C23#1457920812yes—
688C23C24×D7911yescharacteristic
689Q8—416no—
690Q8—31616no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—416no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—3164no—
714C2×C4—3164no—
715C2×C4—3164no—
716C2×C4—31616no—
717C2×C4—7916no—
718C2×C4—794no—
719C2×C4—794no—
720C2×C4—794no—
721C2×C4—794no—
722C2×C4—794no—
723C2×C4—794no—
724C2×C4—794no—
725C2×C4—1582no—
726C2×C4—1582no—
727C2×C4—1582no—
728C2×C4—1582no—
729C2×C4—1582no—
730C2×C4—1582no—
731C2×C4—1582no—
732C2×C4—1582no—
733C2×C4—1582no—
734C2×C4—15832no—
735C2×C4—1582no—
736C2×C4—1582no—
737C2×C4—1582no—
738C2×C4—1588no—
739C2×C4—1588no—
740C2×C4—1588no—
741C2×C4—1588no—
742C2×C4—1582no—
743C2×C4—1582no—
744C2×C4—1582no—
745C2×C4—1582no—
746C2×C4—1582no—
747C2×C4C2×D4×D7914yes—
748C2×C4C22×C22⋊D7914yes—
749C2×C4C22×C22⋊D7914yes—
750C22—24no—
751C22—232no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22C22⋊Q8×D7914yes—
758C22C2×#1457915914yes—
759C22C2×#1457915918yescomplemented
760C22#1909919214yes—
761C22D4×C22⋊D7914yes—
762C22#1909921214yes—
763C22#1909922614yes—
764C22#1909926714yes—
765C22C22×D4×D7911yescharacteristic
766C22C23×C22⋊D7911yescharacteristic
767C22C22×Q8×D7911yescharacteristic
768C22C22×Q8×D7911yescharacteristic
769C22C2×#41×D7911yescharacteristic
770C22C2×#1457920611yescharacteristic
771C22C2×#1457920811yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—3162no—
779C4—3162no—
780C4—3162no—
781C4—798no—
782C4—1584no—
783C4—1584no—
784C4—1584no—
785C4—1584no—
786C2—28no—
787C2#2376709918yesdirect product factor
788C2C2×C22⋊Q8×D7911yescharacteristic
789C2C22×#1457915911yescharacteristic
790C2C2×#1909919211yescharacteristic
791C2C2×D4×C22⋊D7911yescharacteristic
792C2C2×#1909921211yescharacteristic
793C2C2×#1909922611yescharacteristic
794C2C2×#1909926711yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC22×C22⋊Q8×C79C2
socleC24×C79C24
prime radicalC25×C79C23
hypercenterC22×C22⋊Q8D79
hypocenterC79C2×#2440
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14579159C2semidirect
4. #23767099C2direct (N × H)
5. C2×#19098494C2semidirect
6. C2×#19098493C2semidirect
7. C2×#19098483C2semidirect
8. C2×#19098482C2semidirect
9. C2×#19098458C2semidirect
10. C2×#19098458C2semidirect
13. C2×#19098432C2semidirect
21. C2×#14579159C22semidirect
43. #19098494C22semidirect
44. #19098493C22semidirect
45. #19098483C22semidirect
46. #19098482C22semidirect
47. #19098458C22semidirect
48. #19098458C22semidirect
51. #19098432C22semidirect
80. C23×Dic79Q8semidirect
121. C2×C22⋊Dic79Q8semidirect
196. C22×Dic79C2×Q8semidirect
220. C22⋊Dic79C2×Q8semidirect
279. C23×C79C4⋊Q8semidirect
343. C2×Dic79C22⋊Q8semidirect
361. C22×C79C2×C4⋊Q8semidirect
387. Dic79C2×C22⋊Q8semidirect
390. C2×C79#2440semidirect
414. C79C2×#2440semidirect
677. C23#14579159semidirect
759. C22C2×#14579159semidirect
787. C2#23767099direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791592
C22×#145791382
C23×Dic79⋊C42
#237670992
C2×#190984942
C2×#190984932
C2×#190984832
C2×#190984822
C2×#190984582
C2×#190984362
C2×#190984352
C2×#190984322
C2×#190984212
C2×C22⋊C4×Dic792
C22×C22⋊Q8×C792
C2×#244079