Finite Group Databasebeta

← C2×#22613603 #33254625

Subgroups — C2×#22613603 #33254625

Order 18688.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556547C211yesmaximal, characteristic
2#22613603C2116yesmaximal, direct product factor
3C2×#17988525C211yesmaximal, characteristic, complemented
4C2×#17988520C211yesmaximal, characteristic, complemented
5C2×#17988520C211yesmaximal, characteristic, complemented
6C2×#17988506C211yesmaximal, characteristic, complemented
7C2×#17988494C211yesmaximal, characteristic, complemented
8C2×#17988483C211yesmaximal, characteristic, complemented
9C2×#17988468C211yesmaximal, characteristic, complemented
10C2×#17988468C211yesmaximal, characteristic, complemented
11C2×#17988462C211yesmaximal, characteristic
12C2×#17988460C211yesmaximal, characteristic
13C2×#17988448C211yesmaximal, characteristic
14C2×#17988445C211yesmaximal, characteristic
15C22×#14556498C211yesmaximal, characteristic
16C22×C22⋊Q8×C73C211yesmaximal, characteristic
17C24×Dic73C2211yescharacteristic
18C24×Dic73C2211yescharacteristic
19C2×#14556547—28no—
20C2×#14556547C2218yes—
21C22×C4⋊Dic73C2211yescharacteristic
22C22×C4⋊Dic73C2211yescharacteristic
23C22×#11924007C2211yescharacteristic
24C22×#11924007C2211yescharacteristic
25C22×#11924007C2211yescharacteristic
26C22×#11924007C2211yescharacteristic
27C22×#11924007C2211yescharacteristic
28C22×#11924007C2211yescharacteristic
29C22×C22⋊Dic73C2211yescharacteristic
30C22×C22⋊Dic73C2211yescharacteristic
31C22×C4×Dic73C2211yescharacteristic
32C22×C4×Dic73C2211yescharacteristic
33#17988525C2218yescomplemented
34#17988520C2218yescomplemented
35#17988520C2218yescomplemented
36#17988506C2218yescomplemented
37#17988494C2218yescomplemented
38#17988483C2218yescomplemented
39#17988468C2218yescomplemented
40#17988468C2218yescomplemented
41#17988462C2218yes—
42#17988460C2218yes—
43#17988448C2218yes—
44#17988445C2218yes—
45C2×#14556498C2218yes—
46C2×#14556498C2211yescharacteristic
47C2×#14556498C2211yescharacteristic
48C2×#14556498C2211yescharacteristic
49C2×#14556498C2211yescharacteristic
50C2×#14556498C2211yescharacteristic
51C2×#14556498C2211yescharacteristic
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C23×Q8×C73C2211yescharacteristic
61C24×C4×C73C2211yescharacteristic
62C2×C22⋊Q8×C73—28no—
63C2×C22⋊Q8×C73C2218yes—
64C22×C4⋊C4×C73C2211yescharacteristic
65C22×C4⋊C4×C73C2211yescharacteristic
66C22×C4⋊C4×C73C2211yescharacteristic
67C22×C22⋊C4×C73C2211yescharacteristic
68C22×C22⋊C4×C73C2211yescharacteristic
69C23×Dic73—24no—
70C23×Dic73—24no—
71C23×Dic73—24no—
72C23×Dic73—24no—
73C23×Dic73—42no—
74C23×Dic73Q818yescomplemented
75C23×Dic73C2311yescharacteristic
76C23×Dic73C2311yescharacteristic
77C23×Dic73C2311yescharacteristic
78C23×Dic73C2311yescharacteristic
79C23×Dic73C2311yescharacteristic
80C23×Dic73C2314yes—
81C23×Dic73C2311yescharacteristic
82C23×Dic73C2311yescharacteristic
83C23×Dic73C2314yes—
84C23×Dic73C2311yescharacteristic
85#14556547—232no—
86C2×C4⋊Dic73—24no—
87C2×C4⋊Dic73—42no—
88C2×C4⋊Dic73C2314yes—
89C2×C4⋊Dic73C2314yes—
90C2×#11924007—24no—
91C2×#11924007—24no—
92C2×#11924007—24no—
93C2×#11924007—24no—
94C2×#11924007—42no—
95C2×#11924007—42no—
96C2×#11924007C2314yes—
97C2×#11924007C2314yes—
98C2×#11924007C2314yes—
99C2×#11924007C2314yes—
100C2×#11924007C2314yes—
101C2×#11924007C2314yes—
102C2×C22⋊Dic73—24no—
103C2×C22⋊Dic73—24no—
104C2×C22⋊Dic73C2314yes—
105C2×C22⋊Dic73C2314yes—
106C2×C4×Dic73—24no—
107C2×C4×Dic73—24no—
108C2×C4×Dic73C2314yes—
109C2×C4×Dic73C2314yes—
110#14556498C2314yes—
111#14556498C2314yes—
112#14556498C2314yes—
113#14556498C2314yes—
114#14556498C2314yes—
115#14556498C2314yes—
116#14556498C2314yes—
117#14556498C2314yes—
118#14556498C2314yes—
119#14556498C2314yes—
120#14556498C2314yes—
121#14556498C2314yes—
122#14556498C2314yes—
123#14556498C2314yes—
124C25×C73C2311yescharacteristic
125C22×Q8×C73—24no—
126C22×Q8×C73—24no—
127C22×Q8×C73—42no—
128C22×Q8×C73C2314yes—
129C23×C4×C73—24no—
130C23×C4×C73—24no—
131C23×C4×C73—42no—
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C23×C4×C73C2311yescharacteristic
135C23×C4×C73C2314yes—
136C23×C4×C73C2311yescharacteristic
137C23×C4×C73C2311yescharacteristic
138C23×C4×C73C2311yescharacteristic
139C22⋊Q8×C73—232no—
140C2×C4⋊C4×C73—24no—
141C2×C4⋊C4×C73—24no—
142C2×C4⋊C4×C73—24no—
143C2×C4⋊C4×C73C2314yes—
144C2×C4⋊C4×C73C2314yes—
145C2×C4⋊C4×C73C2314yes—
146C2×C22⋊C4×C73—24no—
147C2×C22⋊C4×C73D418yes—
148C2×C22⋊C4×C73C2314yes—
149C2×C22⋊C4×C73C2314yes—
150C22×Dic73—232no—
151C22×Dic73—22no—
152C22×Dic73—22no—
153C22×Dic73—28no—
154C22×Dic73—22no—
155C22×Dic73—22no—
156C22×Dic73—28no—
157C22×Dic73—22no—
158C22×Dic73—22no—
159C22×Dic73—22no—
160C22×Dic73—22no—
161C22×Dic73—22no—
162C22×Dic73—22no—
163C22×Dic73—22no—
164C22×Dic73—22no—
165C22×Dic73—22no—
166C22×Dic73—22no—
167C22×Dic73—22no—
168C22×Dic73—28no—
169C22×Dic73—22no—
170C22×Dic73—22no—
171C22×Dic73—22no—
172C22×Dic73—22no—
173C22×Dic73—22no—
174C22×Dic73—22no—
175C22×Dic73—28no—
176C22×Dic73—44no—
177C22×Dic73—416no—
178C22×Dic73C2×Q814yes—
179C22×Dic73C2×Q814yes—
180C22×Dic73C2×Q8116yescomplemented
181C22×Dic73#4114yes—
182C22×Dic73C2412yes—
183C22×Dic73C2412yes—
184C22×Dic73C2412yes—
185C22×Dic73C2412yes—
186C22×Dic73C2412yes—
187C22×Dic73C2412yes—
188C22×Dic73C2412yes—
189C22×Dic73C2412yes—
190C4⋊Dic73—28no—
191C4⋊Dic73—44no—
192#11924007—28no—
193#11924007—28no—
194#11924007—28no—
195#11924007—28no—
196#11924007—44no—
197#11924007—44no—
198C22⋊Dic73—28no—
199C22⋊Dic73—28no—
200C4×Dic73—28no—
201C4×Dic73—28no—
202C24×C73—22no—
203C24×C73—22no—
204C24×C73—22no—
205C24×C73—22no—
206C24×C73C2×D414yes—
207C24×C73C2×Q814yes—
208C24×C73#4114yes—
209C24×C73C2412yes—
210C24×C73C2411yescharacteristic
211C2×Q8×C73—28no—
212C2×Q8×C73—28no—
213C2×Q8×C73—44no—
214C2×Q8×C73—416no—
215C22×C4×C73—22no—
216C22×C4×C73—22no—
217C22×C4×C73—22no—
218C22×C4×C73—22no—
219C22×C4×C73—22no—
220C22×C4×C73—22no—
221C22×C4×C73—22no—
222C22×C4×C73—22no—
223C22×C4×C73—22no—
224C22×C4×C73—28no—
225C22×C4×C73—22no—
226C22×C4×C73—22no—
227C22×C4×C73—22no—
228C22×C4×C73—22no—
229C22×C4×C73—22no—
230C22×C4×C73—22no—
231C22×C4×C73—28no—
232C22×C4×C73—44no—
233C22×C4×C73—416no—
234C22×C4×C73C2×D414yes—
235C22×C4×C73C2×D414yes—
236C22×C4×C73#4114yes—
237C22×C4×C73C2412yes—
238C22×C4×C73C2412yes—
239C22×C4×C73C2412yes—
240C22×C4×C73C2412yes—
241C22×C4×C73C2412yes—
242C22×C4×C73C2412yes—
243C4⋊C4×C73—28no—
244C4⋊C4×C73—28no—
245C4⋊C4×C73—28no—
246C22⋊C4×C73—28no—
247C22⋊C4×C73C2×D4116yes—
248C23×C73—28no—
249C23×C73—28no—
250C23×C73—28no—
251C23×C73—28no—
252C23×C73—28no—
253C23×C73—28no—
254C23×C73—22no—
255C23×C73—22no—
256C23×C73—22no—
257C23×C73—22no—
258C23×C73C22⋊Q8116yes—
259C23×C73C22×D414yes—
260C23×C73C22×D412yes—
261C23×C73C22×Q814yes—
262C23×C73C22×Q812yes—
263C23×C73C2×#4112yes—
264C23×C73C2×#4112yes—
265C23×C73C2×#4114yes—
266C23×C73C2×#4112yes—
267C23×C73H(5,𝔽2)12yes—
268C23×C732−1+412yes—
269C23×C73C2511yescharacteristic
270Q8×C73—416no—
271C2×C4×C73—28no—
272C2×C4×C73—28no—
273C2×C4×C73—28no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—416no—
290C2×C4×C73—44no—
291C2×C4×C73—44no—
292C2×C4×C73—44no—
293C2×C4×C73C22×D414yes—
294C2×C4×C73C22×D414yes—
295C2×C4×C73C2×#4114yes—
296C2×Dic73—28no—
297C2×Dic73—28no—
298C2×Dic73—232no—
299C2×Dic73—28no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—416no—
322C2×Dic73—44no—
323C2×Dic73—44no—
324C2×Dic73—44no—
325C2×Dic73—44no—
326C2×Dic73—44no—
327C2×Dic73C22×Q814yes—
328C2×Dic73C22×Q814yes—
329C2×Dic73C2×#4114yes—
330C22×C73—24no—
331C22×C73—24no—
332C22×C73—232no—
333C22×C73—24no—
334C22×C73—24no—
335C22×C73—24no—
336C22×C73—24no—
337C22×C73C2×C22⋊Q818yes—
338C22×C73C2×C22⋊Q814yes—
339C22×C73#53314yes—
340C22×C73#54414yes—
341C22×C73#54614yes—
342C22×C73#54714yes—
343C22×C73#55114yes—
344C22×C73#55214yes—
345C22×C73C23×D411yescharacteristic
346C22×C73C23×Q811yescharacteristic
347C22×C73C22×#4111yescharacteristic
348C22×C73C22×#4111yescharacteristic
349C22×C73C22×#4111yescharacteristic
350C22×C73C2×H(5,𝔽2)11yescharacteristic
351C22×C73C2×2−1+411yescharacteristic
352C4×C73—24no—
353C4×C73—24no—
354C4×C73—24no—
355C4×C73—42no—
356C4×C73—42no—
357C4×C73—42no—
358Dic73—24no—
359Dic73—24no—
360Dic73—24no—
361Dic73—42no—
362Dic73—42no—
363Dic73—42no—
364Dic73—42no—
365Dic73—42no—
366C2×#2438—731nomaximal, Sylow
367C2×C73—28no—
368C2×C73#243818yescomplemented
369C2×C73C22×C22⋊Q811yescharacteristic
370C2×C73C2×#53311yescharacteristic
371C2×C73C2×#54411yescharacteristic
372C2×C73C2×#54611yescharacteristic
373C2×C73C2×#54711yescharacteristic
374C2×C73C2×#55111yescharacteristic
375C2×C73C2×#55211yescharacteristic
376C22×C22⋊Q8D7311yescharacteristic
377C22×#117—731no—
378#2438—7316no—
379C2×#400—731no—
380C2×#398—731no—
381C2×#398—731no—
382C2×#395—731no—
383C2×#391—731no—
384C2×#389—731no—
385C2×#387—731no—
386C2×#387—731no—
387C2×#385—731no—
388C2×#385—731no—
389C2×#381—731no—
390C2×#380—731no—
391C22×#95—731no—
392C73C2×#243811yescharacteristic, complemented, Sylow
393C23×Q8C2×D7311yescharacteristic
394C24×C4—731no—
395C24×C4—731no—
396C24×C4C2×D7311yescharacteristic
397C2×C22⋊Q8—28no—
398C2×C22⋊Q8C2×D7318yes—
399C2×#117—738no—
400C2×#117—1468no—
401C22×C4⋊C4—731no—
402C22×C4⋊C4—731no—
403C22×C4⋊C4—731no—
404C22×C4⋊C4—731no—
405C22×C4⋊C4—731no—
406C22×C4⋊C4—731no—
407C22×C4⋊C4—731no—
408C22×C4⋊C4—731no—
409C22×C4⋊C4C2×D7311yescharacteristic
410C22×C4⋊C4C2×D7311yescharacteristic
411C22×C4⋊C4C2×D7311yescharacteristic
412C22×C22⋊C4—731no—
413C22×C22⋊C4—731no—
414C22×C22⋊C4C2×D7311yescharacteristic
415C22×C22⋊C4C2×D7311yescharacteristic
416C22×C42—731no—
417C22×C42—731no—
418#400—738no—
419#398—738no—
420#398—738no—
421#395—738no—
422#391—738no—
423#389—738no—
424#387—738no—
425#387—738no—
426#385—738no—
427#385—738no—
428#381—738no—
429#380—738no—
430C2×#95—731no—
431C2×#95—731no—
432C2×#95—731no—
433C2×#95—731no—
434C2×#95—731no—
435C2×#95—731no—
436C2×#95—731no—
437C2×#95—731no—
438C2×#95—731no—
439C2×#95—731no—
440C2×#95—738no—
441C2×#95—731no—
442C2×#95—731no—
443C2×#95—731no—
444C2×#95—731no—
445C25C22×D7311yescharacteristic
446C22×Q8—24no—
447C22×Q8—24no—
448C22×Q8—42no—
449C22×Q8C22×D7314yes—
450C23×C4—24no—
451C23×C4—24no—
452C23×C4—42no—
453C23×C4—2922no—
454C23×C4—734no—
455C23×C4—738no—
456C23×C4—734no—
457C23×C4—731no—
458C23×C4—731no—
459C23×C4—731no—
460C23×C4—731no—
461C23×C4—731no—
462C23×C4—731no—
463C23×C4—731no—
464C23×C4—731no—
465C23×C4—1464no—
466C23×C4—1464no—
467C23×C4—1464no—
468C23×C4—1464no—
469C23×C4C22×D7311yescharacteristic
470C23×C4C22×D7311yescharacteristic
471C23×C4C22×D7311yescharacteristic
472C23×C4C22×D7314yes—
473C23×C4C22×D7311yescharacteristic
474C23×C4C22×D7311yescharacteristic
475C23×C4C22×D7311yescharacteristic
476C22⋊Q8—232no—
477#117—14632no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—2922no—
482C2×C4⋊C4—2922no—
483C2×C4⋊C4—2922no—
484C2×C4⋊C4—734no—
485C2×C4⋊C4—734no—
486C2×C4⋊C4—734no—
487C2×C4⋊C4—734no—
488C2×C4⋊C4—734no—
489C2×C4⋊C4—734no—
490C2×C4⋊C4—734no—
491C2×C4⋊C4—734no—
492C2×C4⋊C4—1464no—
493C2×C4⋊C4—1464no—
494C2×C4⋊C4—1464no—
495C2×C4⋊C4—1464no—
496C2×C4⋊C4—1464no—
497C2×C4⋊C4C22×D7314yes—
498C2×C4⋊C4C22×D7314yes—
499C2×C4⋊C4C22×D7314yes—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—734no—
502C2×C22⋊C4—734no—
503C2×C22⋊C4—1464no—
504C2×C22⋊C4—1464no—
505C2×C22⋊C4C22⋊D7318yes—
506C2×C22⋊C4C22×D7314yes—
507C2×C22⋊C4C22×D7314yes—
508C2×C42—734no—
509C2×C42—734no—
510C2×C42—1464no—
511C2×C42—1464no—
512#95—734no—
513#95—734no—
514#95—734no—
515#95—734no—
516#95—734no—
517#95—734no—
518#95—734no—
519#95—734no—
520#95—734no—
521#95—734no—
522#95—734no—
523#95—734no—
524#95—734no—
525#95—734no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24C2×C22⋊D7314yes—
531C24Q8×D7314yes—
532C24#1192402914yes—
533C24C23×D7312yes—
534C24C23×D7311yescharacteristic
535C2×Q8—28no—
536C2×Q8—28no—
537C2×Q8—44no—
538C2×Q8—416no—
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—28no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—28no—
556C22×C4—44no—
557C22×C4—416no—
558C22×C4—29216no—
559C22×C4—2924no—
560C22×C4—734no—
561C22×C4—734no—
562C22×C4—7316no—
563C22×C4—734no—
564C22×C4—732no—
565C22×C4—732no—
566C22×C4—732no—
567C22×C4—732no—
568C22×C4—732no—
569C22×C4—732no—
570C22×C4—732no—
571C22×C4—732no—
572C22×C4—1468no—
573C22×C4—1462no—
574C22×C4—1462no—
575C22×C4—1462no—
576C22×C4—1462no—
577C22×C4—1462no—
578C22×C4—1462no—
579C22×C4—1462no—
580C22×C4—1462no—
581C22×C4—1462no—
582C22×C4—1462no—
583C22×C4—1468no—
584C22×C4—1462no—
585C22×C4—1462no—
586C22×C4—1462no—
587C22×C4—1462no—
588C22×C4—1462no—
589C22×C4—14632no—
590C22×C4—1462no—
591C22×C4—1462no—
592C22×C4—1468no—
593C22×C4—1462no—
594C22×C4—1468no—
595C22×C4—1462no—
596C22×C4—1462no—
597C22×C4—1462no—
598C22×C4C2×C22⋊D7314yes—
599C22×C4C2×C22⋊D7314yes—
600C22×C4#1192402714yes—
601C22×C4C23×D7312yes—
602C22×C4C23×D7312yes—
603C22×C4C23×D7312yes—
604C22×C4C23×D7312yes—
605C22×C4C23×D7312yes—
606C22×C4C23×D7312yes—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—2924no—
611C4⋊C4—2924no—
612C4⋊C4—2924no—
613C4⋊C4—1468no—
614C4⋊C4—1468no—
615C4⋊C4—1468no—
616C4⋊C4—1468no—
617C4⋊C4—1468no—
618C22⋊C4—28no—
619C22⋊C4—1468no—
620C22⋊C4—1468no—
621C22⋊C4C2×C22⋊D73116yes—
622C42—1468no—
623C42—1468no—
624C23—28no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—28no—
630C23—28no—
631C23—28no—
632C23—28no—
633C23—28no—
634C23#14556567116yes—
635C23C22×C22⋊D7314yes—
636C23C22×C22⋊D7312yes—
637C23C2×Q8×D7314yes—
638C23C2×Q8×D7312yes—
639C23#41×D7312yes—
640C23C2×#1192402712yes—
641C23C2×#1192402914yes—
642C23C2×#1192402912yes—
643C23#1455663612yes—
644C23#1455663812yes—
645C23C24×D7311yescharacteristic
646Q8—416no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—28no—
654C2×C4—28no—
655C2×C4—28no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—416no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—2924no—
670C2×C4—2924no—
671C2×C4—2924no—
672C2×C4—2924no—
673C2×C4—2924no—
674C2×C4—29216no—
675C2×C4—734no—
676C2×C4—734no—
677C2×C4—734no—
678C2×C4—1462no—
679C2×C4—1462no—
680C2×C4—1462no—
681C2×C4—1462no—
682C2×C4—1462no—
683C2×C4—1462no—
684C2×C4—1462no—
685C2×C4—1462no—
686C2×C4—1462no—
687C2×C4—1462no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1462no—
697C2×C4—1462no—
698C2×C4—1462no—
699C2×C4—1468no—
700C2×C4—14632no—
701C2×C4—1468no—
702C2×C4—1468no—
703C2×C4C22×C22⋊D7314yes—
704C2×C4C22×C22⋊D7314yes—
705C2×C4C2×#1192402714yes—
706C22—24no—
707C22—232no—
708C22—24no—
709C22—24no—
710C22—24no—
711C22—24no—
712C22—24no—
713C22C2×#1455656718yes—
714C22C2×#1455656714yes—
715C22#1798913914yes—
716C22#1798921614yes—
717C22#1798923114yes—
718C22#1798923614yes—
719C22#1798926414yes—
720C22#1798927914yes—
721C22C23×C22⋊D7311yescharacteristic
722C22C22×Q8×D7311yescharacteristic
723C22C2×#41×D7311yescharacteristic
724C22C22×#1192402711yescharacteristic
725C22C22×#1192402911yescharacteristic
726C22C2×#1455663611yescharacteristic
727C22C2×#1455663811yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—2922no—
735C4—2922no—
736C4—2922no—
737C4—2922no—
738C4—2922no—
739C4—1464no—
740C4—1464no—
741C4—1464no—
742C2—28no—
743C2#2261360318yesdirect product factor
744C2C22×#1455656711yescharacteristic
745C2C2×#1798913911yescharacteristic
746C2C2×#1798921611yescharacteristic
747C2C2×#1798923111yescharacteristic
748C2C2×#1798923611yescharacteristic
749C2C2×#1798926411yescharacteristic
750C2C2×#1798927911yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC22×C22⋊Q8×C73C2
socleC24×C73C24
prime radicalC25×C73C23
hypercenterC22×C22⋊Q8D73
hypocenterC73C2×#2438
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #22613603C2direct (N × H)
3. C2×#17988525C2semidirect
4. C2×#17988520C2semidirect
5. C2×#17988520C2semidirect
6. C2×#17988506C2semidirect
7. C2×#17988494C2semidirect
8. C2×#17988483C2semidirect
9. C2×#17988468C2semidirect
10. C2×#17988468C2semidirect
33. #17988525C22semidirect
34. #17988520C22semidirect
35. #17988520C22semidirect
36. #17988506C22semidirect
37. #17988494C22semidirect
38. #17988483C22semidirect
39. #17988468C22semidirect
40. #17988468C22semidirect
74. C23×Dic73Q8semidirect
180. C22×Dic73C2×Q8semidirect
368. C2×C73#2438semidirect
392. C73C2×#2438semidirect
743. C2#22613603direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565472
#226136032
C2×#179885252
C2×#179885202
C2×#179885062
C2×#179884942
C2×#179884832
C2×#179884682
C2×#179884622
C2×#179884602
C2×#179884482
C2×#179884452
C22×#145564982
C22×C22⋊Q8×C732
C2×#243873