Finite Group Databasebeta

← C2×#22613626 #33253808

Subgroups — C2×#22613626 #33253808

Order 18688.

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×#14556589C211yesmaximal, characteristic, complemented
2C22×#14556569C211yesmaximal, characteristic
3C22×#14556567C211yesmaximal, characteristic
4C22×C4⋊C4×D73C211yesmaximal, characteristic
5#22613626C2116yesmaximal, direct product factor
6C2×#17988521C211yesmaximal, characteristic, complemented
7C2×#17988520C211yesmaximal, characteristic, complemented
8C2×#17988508C211yesmaximal, characteristic, complemented
9C2×#17988484C211yesmaximal, characteristic, complemented
10C2×#17988482C211yesmaximal, characteristic, complemented
11C2×#17988461C211yesmaximal, characteristic
12C2×#17988458C211yesmaximal, characteristic
13C2×#17988456C211yesmaximal, characteristic, complemented
14C2×#17988446C211yesmaximal, characteristic
15C2×#17988434C211yesmaximal, characteristic
16C2×#395×C73C211yesmaximal, characteristic, complemented
17C23×Dic146C2211yescharacteristic
18C23×C4×D73C2211yescharacteristic
19C23×C4×D73C2211yescharacteristic
20C23×C4×D73C2211yescharacteristic
21C2×#14556589—28no—
22C2×#14556589C2218yescomplemented
23C2×#14556569—28no—
24C2×#14556569C2218yes—
25C2×#14556567—28no—
26C2×#14556567C2218yes—
27C22×C4⋊Dic73C2211yescharacteristic
28C22×C4⋊Dic73C2211yescharacteristic
29C22×C4⋊Dic73C2211yescharacteristic
30C22×#11924007C2211yescharacteristic
31C22×#11924007C2211yescharacteristic
32C22×#11924007C2211yescharacteristic
33C22×#11924007C2211yescharacteristic
34C22×#11924007C2211yescharacteristic
35C22×#11924007C2211yescharacteristic
36C22×#11924007C2211yescharacteristic
37C22×#11924007C2211yescharacteristic
38C22×#11924007C2211yescharacteristic
39C22×#11924007C2211yescharacteristic
40C2×C4⋊C4×D73—28no—
41C2×C4⋊C4×D73C2218yes—
42C22×#11924005C2211yescharacteristic
43C22×#11924005C2211yescharacteristic
44C22×#11924005C2211yescharacteristic
45C22×#11924005C2211yescharacteristic
46C22×C4×Dic73C2211yescharacteristic
47C22×C4×Dic73C2211yescharacteristic
48#17988521C2218yescomplemented
49#17988520C2218yescomplemented
50#17988508C2218yescomplemented
51#17988484C2218yescomplemented
52#17988482C2218yescomplemented
53#17988461C2218yes—
54#17988458C2218yes—
55#17988456C2218yescomplemented
56#17988446C2218yes—
57#17988434C2218yes—
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C2×#14556498C2211yescharacteristic
61C2×#14556498C2211yescharacteristic
62C2×#14556498C2211yescharacteristic
63C23×Q8×C73C2211yescharacteristic
64C22×C4⋊C4×C73C2211yescharacteristic
65C22×C4⋊C4×C73C2211yescharacteristic
66C22×C4⋊C4×C73C2211yescharacteristic
67#395×C73C2218yescomplemented
68C2×#95×C73C2211yescharacteristic
69C2×#95×C73C2211yescharacteristic
70C2×#95×C73C2211yescharacteristic
71C24×D73C2311yescharacteristic
72C22×Dic146—24no—
73C22×Dic146—24no—
74C22×Dic146—42no—
75C22×Dic146C2314yes—
76C23×Dic73C2311yescharacteristic
77C23×Dic73C2311yescharacteristic
78C23×Dic73C2311yescharacteristic
79C23×Dic73C2311yescharacteristic
80C23×Dic73C2311yescharacteristic
81C23×Dic73C2311yescharacteristic
82C23×Dic73C2311yescharacteristic
83C22×C4×D73—24no—
84C22×C4×D73—24no—
85C22×C4×D73—24no—
86C22×C4×D73—24no—
87C22×C4×D73—24no—
88C22×C4×D73—24no—
89C22×C4×D73—42no—
90C22×C4×D73—42no—
91C22×C4×D73Q818yescomplemented
92C22×C4×D73C2314yes—
93C22×C4×D73C2314yes—
94C22×C4×D73C2314yes—
95#14556589—232no—
96#14556569—232no—
97#14556567—232no—
98C2×C4⋊Dic73—24no—
99C2×C4⋊Dic73—24no—
100C2×C4⋊Dic73—42no—
101C2×C4⋊Dic73C2314yes—
102C2×C4⋊Dic73C2314yes—
103C2×C4⋊Dic73C2314yes—
104C2×#11924007—24no—
105C2×#11924007—24no—
106C2×#11924007—24no—
107C2×#11924007—24no—
108C2×#11924007—24no—
109C2×#11924007—24no—
110C2×#11924007—24no—
111C2×#11924007—24no—
112C2×#11924007—24no—
113C2×#11924007D418yes—
114C2×#11924007C2314yes—
115C2×#11924007C2314yes—
116C2×#11924007C2314yes—
117C2×#11924007C2314yes—
118C2×#11924007C2314yes—
119C2×#11924007C2314yes—
120C2×#11924007C2314yes—
121C2×#11924007C2314yes—
122C2×#11924007C2314yes—
123C2×#11924007C2314yes—
124C4⋊C4×D73—232no—
125C2×#11924005—24no—
126C2×#11924005—24no—
127C2×#11924005D418yes—
128C2×#11924005Q818yescomplemented
129C2×#11924005C2314yes—
130C2×#11924005C2314yes—
131C2×#11924005C2314yes—
132C2×#11924005C2314yes—
133C2×C4×Dic73—24no—
134C2×C4×Dic73—24no—
135C2×C4×Dic73C2314yes—
136C2×C4×Dic73C2314yes—
137#14556498C2314yes—
138#14556498C2314yes—
139#14556498C2314yes—
140#14556498C2314yes—
141#14556498C2314yes—
142C22×Q8×C73—24no—
143C22×Q8×C73—24no—
144C22×Q8×C73—42no—
145C22×Q8×C73C2314yes—
146C23×C4×C73C2311yescharacteristic
147C23×C4×C73C2311yescharacteristic
148C23×C4×C73C2311yescharacteristic
149C23×C4×C73C2311yescharacteristic
150C23×C4×C73C2311yescharacteristic
151C23×C4×C73C2311yescharacteristic
152C23×C4×C73C2311yescharacteristic
153C2×C4⋊C4×C73—24no—
154C2×C4⋊C4×C73—24no—
155C2×C4⋊C4×C73—42no—
156C2×C4⋊C4×C73C2314yes—
157C2×C4⋊C4×C73C2314yes—
158C2×C4⋊C4×C73C2314yes—
159#95×C73C2314yes—
160#95×C73C2314yes—
161#95×C73C2314yes—
162C23×D73—22no—
163C23×D73—22no—
164C23×D73—22no—
165C23×D73—22no—
166C23×D73C2×D414yes—
167C23×D73C2×Q814yes—
168C23×D73C2×Q814yes—
169C23×D73C2412yes—
170C2×Dic146—28no—
171C2×Dic146—28no—
172C2×Dic146—44no—
173C2×Dic146—416no—
174C22×Dic73—22no—
175C22×Dic73—22no—
176C22×Dic73—22no—
177C22×Dic73—22no—
178C22×Dic73—22no—
179C22×Dic73—22no—
180C22×Dic73—22no—
181C22×Dic73—22no—
182C22×Dic73—22no—
183C22×Dic73—22no—
184C22×Dic73—22no—
185C22×Dic73—22no—
186C22×Dic73—22no—
187C22×Dic73—22no—
188C22×Dic73—22no—
189C22×Dic73C2×D414yes—
190C22×Dic73C2×D414yes—
191C22×Dic73C2×D414yes—
192C22×Dic73C2×Q814yes—
193C22×Dic73C2×Q814yes—
194C22×Dic73#4114yes—
195C22×Dic73C2412yes—
196C22×Dic73C2412yes—
197C22×Dic73C2412yes—
198C22×Dic73C2412yes—
199C22×Dic73C2412yes—
200C22×Dic73C2412yes—
201C22×Dic73C2412yes—
202C2×C4×D73—232no—
203C2×C4×D73—28no—
204C2×C4×D73—28no—
205C2×C4×D73—28no—
206C2×C4×D73—28no—
207C2×C4×D73—28no—
208C2×C4×D73—28no—
209C2×C4×D73—44no—
210C2×C4×D73—44no—
211C2×C4×D73—416no—
212C2×C4×D73—416no—
213C2×C4×D73C2×Q8116yescomplemented
214C4⋊Dic73—28no—
215C4⋊Dic73—28no—
216C4⋊Dic73—44no—
217#11924007—28no—
218#11924007—28no—
219#11924007—28no—
220#11924007—28no—
221#11924007—28no—
222#11924007—28no—
223#11924007—28no—
224#11924007—28no—
225#11924007—28no—
226#11924007C2×D4116yes—
227#11924005—28no—
228#11924005—28no—
229#11924005C2×D4116yes—
230#11924005C2×Q8116yescomplemented
231C4×Dic73—28no—
232C4×Dic73—28no—
233C24×C73C2411yescharacteristic
234C2×Q8×C73—28no—
235C2×Q8×C73—28no—
236C2×Q8×C73—44no—
237C2×Q8×C73—416no—
238C22×C4×C73—22no—
239C22×C4×C73—22no—
240C22×C4×C73—22no—
241C22×C4×C73—22no—
242C22×C4×C73—22no—
243C22×C4×C73—22no—
244C22×C4×C73—22no—
245C22×C4×C73—22no—
246C22×C4×C73—22no—
247C22×C4×C73—22no—
248C22×C4×C73—22no—
249C22×C4×C73—22no—
250C22×C4×C73—22no—
251C22×C4×C73—22no—
252C22×C4×C73—22no—
253C22×C4×C73—22no—
254C22×C4×C73—22no—
255C22×C4×C73C2×D414yes—
256C22×C4×C73C2×D414yes—
257C22×C4×C73C2×Q814yes—
258C22×C4×C73C2×Q814yes—
259C22×C4×C73C2412yes—
260C22×C4×C73C2412yes—
261C22×C4×C73C2412yes—
262C22×C4×C73C2412yes—
263C22×C4×C73C2412yes—
264C22×C4×C73C2412yes—
265C22×C4×C73C2412yes—
266C4⋊C4×C73—28no—
267C4⋊C4×C73—28no—
268C4⋊C4×C73—44no—
269C23×C73C22×D412yes—
270C23×C73C22×D412yes—
271C23×C73C22×Q812yes—
272C23×C73C22×Q812yes—
273C23×C73C2×#4112yes—
274C23×C73H(5,𝔽2)12yes—
275C23×C732−1+412yes—
276C23×C73C2511yescharacteristic
277C22×D73—28no—
278C22×D73—28no—
279C22×D73—28no—
280C22×D73—28no—
281C22×D73—28no—
282C22×D73—28no—
283C22×D73—22no—
284C22×D73—22no—
285C22×D73—22no—
286C22×D73—22no—
287C22×D73C4⋊Q8116yescomplemented
288C22×D73C22×D414yes—
289C22×D73C22×Q814yes—
290C22×D73C22×Q814yes—
291Q8×C73—416no—
292C2×C4×C73—28no—
293C2×C4×C73—28no—
294C2×C4×C73—28no—
295C2×C4×C73—28no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—22no—
313C2×C4×C73—44no—
314C2×C4×C73—44no—
315C2×C4×C73—44no—
316C2×C4×C73C22×D414yes—
317C2×C4×C73C22×D414yes—
318C2×C4×C73C22×Q814yes—
319C2×C4×C73C22×Q814yes—
320C2×Dic73—28no—
321C2×Dic73—28no—
322C2×Dic73—28no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—22no—
327C2×Dic73—22no—
328C2×Dic73—22no—
329C2×Dic73—22no—
330C2×Dic73—22no—
331C2×Dic73—22no—
332C2×Dic73—22no—
333C2×Dic73—22no—
334C2×Dic73—22no—
335C2×Dic73—22no—
336C2×Dic73—22no—
337C2×Dic73—22no—
338C2×Dic73—44no—
339C2×Dic73—44no—
340C2×Dic73—44no—
341C2×Dic73C22⋊Q8116yescomplemented
342C2×Dic73C22×D414yes—
343C2×Dic73C22×D414yes—
344C2×Dic73C22×D414yes—
345C2×Dic73C22×Q814yes—
346C2×Dic73C22×Q814yes—
347C2×Dic73C2×#4114yes—
348C4×D73—232no—
349C4×D73—416no—
350C4×D73—416no—
351Dic146—416no—
352C22×C73C2×C22⋊Q814yes—
353C22×C73C2×C4⋊Q814yes—
354C22×C73#54414yes—
355C22×C73D4214yes—
356C22×C73#54714yes—
357C22×C73D4×Q814yes—
358C22×C73#55414yes—
359C22×C73C23×D411yescharacteristic
360C22×C73C23×D411yescharacteristic
361C22×C73C23×Q811yescharacteristic
362C22×C73C23×Q811yescharacteristic
363C22×C73C22×#4111yescharacteristic
364C22×C73C2×H(5,𝔽2)11yescharacteristic
365C22×C73C2×2−1+411yescharacteristic
366C2×D73—24no—
367C2×D73—24no—
368C2×D73—24no—
369C2×D73—232no—
370C2×D73—24no—
371C2×D73—24no—
372C2×D73—24no—
373C2×D73C2×C4⋊Q818yescomplemented
374C4×C73—24no—
375C4×C73—24no—
376C4×C73—24no—
377C4×C73—24no—
378C4×C73—42no—
379C4×C73—42no—
380C4×C73—42no—
381Dic73—24no—
382Dic73—24no—
383Dic73—24no—
384Dic73—42no—
385Dic73—42no—
386Dic73—42no—
387Dic73C2×C22⋊Q818yescomplemented
388C2×#2440—731nomaximal, Sylow
389C2×C73#244018yescomplemented
390C2×C73C22×C22⋊Q811yescharacteristic
391C2×C73C22×C4⋊Q811yescharacteristic
392C2×C73C2×#54411yescharacteristic
393C2×C73C2×D4211yescharacteristic
394C2×C73C2×#54711yescharacteristic
395C2×C73C2×D4×Q811yescharacteristic
396C2×C73C2×#55411yescharacteristic
397D73—28no—
398C22×C4⋊Q8—731no—
399C22×C22⋊Q8—731no—
400C22×C22⋊Q8—731no—
401C23×C4⋊C4—731no—
402#2440—7316no—
403C2×#398—731no—
404C2×#398—731no—
405C2×#395—731no—
406C2×#395D7311yescharacteristic, complemented
407C2×#389—731no—
408C2×#389—731no—
409C2×#385—731no—
410C2×#385—731no—
411C2×#384—731no—
412C2×#380—731no—
413C2×C4×C22⋊C4—731no—
414C73C2×#244011yescharacteristic, complemented, Sylow
415C23×Q8—731no—
416C23×Q8C2×D7311yescharacteristic
417C24×C4—731no—
418C24×C4—731no—
419C24×C4—731no—
420C2×C4⋊Q8—738no—
421C2×C4⋊Q8—1468no—
422C2×C22⋊Q8—738no—
423C2×C22⋊Q8—738no—
424C2×C22⋊Q8—1468no—
425C2×C22⋊Q8—1468no—
426C22×C4⋊C4—731no—
427C22×C4⋊C4—731no—
428C22×C4⋊C4—731no—
429C22×C4⋊C4—731no—
430C22×C4⋊C4—731no—
431C22×C4⋊C4—731no—
432C22×C4⋊C4—731no—
433C22×C4⋊C4—731no—
434C22×C4⋊C4—731no—
435C22×C4⋊C4—731no—
436C22×C4⋊C4—731no—
437C22×C4⋊C4—731no—
438C22×C4⋊C4—731no—
439C22×C4⋊C4—738no—
440C22×C4⋊C4—1468no—
441C22×C4⋊C4C2×D7311yescharacteristic
442C22×C4⋊C4C2×D7311yescharacteristic
443C22×C4⋊C4C2×D7311yescharacteristic
444C22×C22⋊C4—731no—
445C22×C22⋊C4—731no—
446C22×C22⋊C4—731no—
447C22×C22⋊C4—731no—
448C22×C42—731no—
449C22×C42—731no—
450#398—738no—
451#398—738no—
452#395—738no—
453#395C2×D7318yescomplemented
454#389—738no—
455#389—738no—
456#385—738no—
457#385—738no—
458#384—738no—
459#380—738no—
460C4×C22⋊C4—738no—
461C2×#95—731no—
462C2×#95—731no—
463C2×#95—731no—
464C2×#95—731no—
465C2×#95—731no—
466C2×#95C2×D7311yescharacteristic
467C2×#95C2×D7311yescharacteristic
468C2×#95C2×D7311yescharacteristic
469C25—731no—
470C22×Q8—24no—
471C22×Q8—24no—
472C22×Q8—42no—
473C22×Q8—2922no—
474C22×Q8—734no—
475C22×Q8—1464no—
476C22×Q8—1464no—
477C22×Q8C22×D7314yes—
478C23×C4—2922no—
479C23×C4—2922no—
480C23×C4—734no—
481C23×C4—734no—
482C23×C4—731no—
483C23×C4—731no—
484C23×C4—731no—
485C23×C4—731no—
486C23×C4—738no—
487C23×C4—734no—
488C23×C4—731no—
489C23×C4—731no—
490C23×C4—731no—
491C23×C4—1464no—
492C23×C4—1464no—
493C23×C4—1464no—
494C23×C4—1464no—
495C23×C4—1464no—
496C23×C4—1464no—
497C23×C4C22×D7311yescharacteristic
498C23×C4C22×D7311yescharacteristic
499C23×C4C22×D7311yescharacteristic
500C23×C4C22×D7311yescharacteristic
501C23×C4C22×D7311yescharacteristic
502C23×C4C22×D7311yescharacteristic
503C23×C4C22×D7311yescharacteristic
504C4⋊Q8—14632no—
505C22⋊Q8—14632no—
506C22⋊Q8—14632no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—42no—
510C2×C4⋊C4—2922no—
511C2×C4⋊C4—734no—
512C2×C4⋊C4—738no—
513C2×C4⋊C4—734no—
514C2×C4⋊C4—734no—
515C2×C4⋊C4—734no—
516C2×C4⋊C4—734no—
517C2×C4⋊C4—734no—
518C2×C4⋊C4—734no—
519C2×C4⋊C4—734no—
520C2×C4⋊C4—734no—
521C2×C4⋊C4—734no—
522C2×C4⋊C4—734no—
523C2×C4⋊C4—734no—
524C2×C4⋊C4—734no—
525C2×C4⋊C4—14632no—
526C2×C4⋊C4—1464no—
527C2×C4⋊C4—1464no—
528C2×C4⋊C4—1464no—
529C2×C4⋊C4—1464no—
530C2×C4⋊C4—1464no—
531C2×C4⋊C4—1464no—
532C2×C4⋊C4—1464no—
533C2×C4⋊C4—1464no—
534C2×C4⋊C4—1464no—
535C2×C4⋊C4—1464no—
536C2×C4⋊C4—1464no—
537C2×C4⋊C4C22×D7314yes—
538C2×C4⋊C4C22×D7314yes—
539C2×C4⋊C4C22×D7314yes—
540C2×C22⋊C4—738no—
541C2×C22⋊C4—738no—
542C2×C22⋊C4—734no—
543C2×C22⋊C4—734no—
544C2×C22⋊C4—734no—
545C2×C22⋊C4—734no—
546C2×C22⋊C4—1464no—
547C2×C22⋊C4—1464no—
548C2×C42—734no—
549C2×C42—734no—
550C2×C42—1464no—
551C2×C42—1464no—
552#95—734no—
553#95—734no—
554#95—734no—
555#95—734no—
556#95—734no—
557#95C22×D7314yes—
558#95C22×D7314yes—
559#95C22×D7314yes—
560C24—734no—
561C24—734no—
562C24—734no—
563C24—732no—
564C24—1462no—
565C24—1462no—
566C24—1462no—
567C24—1462no—
568C24C23×D7311yescharacteristic
569C2×Q8—28no—
570C2×Q8—28no—
571C2×Q8—44no—
572C2×Q8—416no—
573C2×Q8—29216no—
574C2×Q8—2924no—
575C2×Q8—1468no—
576C2×Q8—1468no—
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—22no—
593C22×C4—22no—
594C22×C4—29216no—
595C22×C4—2924no—
596C22×C4—2924no—
597C22×C4—29216no—
598C22×C4—734no—
599C22×C4—734no—
600C22×C4—734no—
601C22×C4—732no—
602C22×C4—734no—
603C22×C4—734no—
604C22×C4—734no—
605C22×C4—732no—
606C22×C4—732no—
607C22×C4—732no—
608C22×C4—7316no—
609C22×C4—732no—
610C22×C4—732no—
611C22×C4—732no—
612C22×C4—1468no—
613C22×C4—1468no—
614C22×C4—1468no—
615C22×C4—1468no—
616C22×C4—1468no—
617C22×C4—14632no—
618C22×C4—1462no—
619C22×C4—1462no—
620C22×C4—1462no—
621C22×C4—1462no—
622C22×C4—1462no—
623C22×C4—1462no—
624C22×C4—1462no—
625C22×C4—1462no—
626C22×C4—1462no—
627C22×C4—1468no—
628C22×C4—1462no—
629C22×C4—1462no—
630C22×C4—1462no—
631C22×C4—1462no—
632C22×C4—1462no—
633C22×C4—1462no—
634C22×C4D4×D7314yes—
635C22×C4D4×D7314yes—
636C22×C4Q8×D7314yes—
637C22×C4Q8×D7314yes—
638C22×C4C23×D7312yes—
639C22×C4C23×D7312yes—
640C22×C4C23×D7312yes—
641C22×C4C23×D7312yes—
642C22×C4C23×D7312yes—
643C22×C4C23×D7312yes—
644C22×C4C23×D7312yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—44no—
648C4⋊C4—2924no—
649C4⋊C4—7316no—
650C4⋊C4—1468no—
651C4⋊C4—1468no—
652C4⋊C4—1468no—
653C4⋊C4—1468no—
654C4⋊C4—1468no—
655C4⋊C4—1468no—
656C4⋊C4—1468no—
657C4⋊C4—1468no—
658C4⋊C4—1468no—
659C4⋊C4—1468no—
660C4⋊C4—1468no—
661C22⋊C4—7316no—
662C22⋊C4—7316no—
663C22⋊C4—1468no—
664C22⋊C4—1468no—
665C42—1468no—
666C42—1468no—
667C23—7316no—
668C23—734no—
669C23—734no—
670C23—734no—
671C23—1462no—
672C23—1462no—
673C23—1462no—
674C23—1462no—
675C23—1468no—
676C23—1468no—
677C23—1468no—
678C23—1468no—
679C23—1468no—
680C23—1468no—
681C23C2×D4×D7312yes—
682C23C2×D4×D7312yes—
683C23C2×Q8×D7312yes—
684C23C2×Q8×D7312yes—
685C23#41×D7312yes—
686C23#1455663612yes—
687C23#1455663912yes—
688C23C24×D7311yescharacteristic
689Q8—416no—
690Q8—29216no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—29216no—
716C2×C4—29216no—
717C2×C4—2924no—
718C2×C4—2924no—
719C2×C4—2924no—
720C2×C4—734no—
721C2×C4—734no—
722C2×C4—734no—
723C2×C4—7316no—
724C2×C4—734no—
725C2×C4—734no—
726C2×C4—734no—
727C2×C4—14632no—
728C2×C4—1462no—
729C2×C4—1462no—
730C2×C4—1462no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1462no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4—1462no—
738C2×C4—1462no—
739C2×C4—1462no—
740C2×C4—1462no—
741C2×C4—1462no—
742C2×C4—1462no—
743C2×C4—1468no—
744C2×C4—1468no—
745C2×C4—1468no—
746C2×C4C2×D4×D7314yes—
747C2×C4C2×D4×D7314yes—
748C2×C4C2×Q8×D7314yes—
749C2×C4C2×Q8×D7314yes—
750C22—738no—
751C22—1464no—
752C22—14632no—
753C22—1464no—
754C22—1464no—
755C22—1464no—
756C22—1464no—
757C22—1464no—
758C22C22⋊Q8×D7314yes—
759C22C4⋊Q8×D7314yes—
760C22#1798921414yes—
761C22#1798921914yes—
762C22#1798923914yes—
763C22#1798925214yes—
764C22#1798929114yes—
765C22C22×D4×D7311yescharacteristic
766C22C22×D4×D7311yescharacteristic
767C22C22×Q8×D7311yescharacteristic
768C22C22×Q8×D7311yescharacteristic
769C22C2×#41×D7311yescharacteristic
770C22C2×#1455663611yescharacteristic
771C22C2×#1455663911yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—2922no—
780C4—2922no—
781C4—2922no—
782C4—738no—
783C4—1464no—
784C4—1464no—
785C4—1464no—
786C2—1468no—
787C2#2261362618yesdirect product factor
788C2C2×C22⋊Q8×D7311yescharacteristic
789C2C2×C4⋊Q8×D7311yescharacteristic
790C2C2×#1798921411yescharacteristic
791C2C2×#1798921911yescharacteristic
792C2C2×#1798923911yescharacteristic
793C2C2×#1798925211yescharacteristic
794C2C2×#1798929111yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#395×C73C2
socleC24×C73C24
prime radicalC24×D73C23
hypercenterC2×#395D73
hypocenterC73C2×#2440
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
1. C22×#14556589C2semidirect
5. #22613626C2direct (N × H)
6. C2×#17988521C2semidirect
7. C2×#17988520C2semidirect
8. C2×#17988508C2semidirect
9. C2×#17988484C2semidirect
10. C2×#17988482C2semidirect
13. C2×#17988456C2semidirect
16. C2×#395×C73C2semidirect
22. C2×#14556589C22semidirect
48. #17988521C22semidirect
49. #17988520C22semidirect
50. #17988508C22semidirect
51. #17988484C22semidirect
52. #17988482C22semidirect
55. #17988456C22semidirect
67. #395×C73C22semidirect
91. C22×C4×D73Q8semidirect
128. C2×#11924005Q8semidirect
213. C2×C4×D73C2×Q8semidirect
230. #11924005C2×Q8semidirect
287. C22×D73C4⋊Q8semidirect
341. C2×Dic73C22⋊Q8semidirect
373. C2×D73C2×C4⋊Q8semidirect
387. Dic73C2×C22⋊Q8semidirect
389. C2×C73#2440semidirect
406. C2×#395D73semidirect
414. C73C2×#2440semidirect
453. #395C2×D73semidirect
787. C2#22613626direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565892
C22×#145565692
C22×#145565672
C22×C4⋊C4×D732
#226136262
C2×#179885212
C2×#179885202
C2×#179885082
C2×#179884842
C2×#179884822
C2×#179884612
C2×#179884582
C2×#179884562
C2×#179884462
C2×#179884342
C2×#395×C732
C2×#244073