Finite Group Databasebeta

← C2×#22614074 #33253582

Subgroups — C2×#22614074 #33253582

Order 18688.

2942 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×#14556581C211yesmaximal, characteristic, complemented
2C23×#11924007C211yesmaximal, characteristic
3#22614074C2116yesmaximal, direct product factor
4C2×#17988528C211yesmaximal, characteristic, complemented
5C2×#17988521C211yesmaximal, characteristic, complemented
6C2×#17988520C211yesmaximal, characteristic, complemented
7C2×#17988518C211yesmaximal, characteristic, complemented
8C2×#17988482C211yesmaximal, characteristic, complemented
9C2×#17988472C211yesmaximal, characteristic, complemented
10C2×#17988469C211yesmaximal, characteristic, complemented
11C2×#17988462C211yesmaximal, characteristic
12C2×#17988459C211yesmaximal, characteristic
13C2×#17988459C211yesmaximal, characteristic
14C2×#17988445C211yesmaximal, characteristic
15C2×C4×C22⋊Dic73C211yesmaximal, characteristic
16C2×#385×C73C211yesmaximal, characteristic
17C24×Dic73C2211yescharacteristic
18C24×Dic73C2211yescharacteristic
19C2×#14556581—28no—
20C2×#14556581C2218yescomplemented
21C22×C4⋊Dic73C2211yescharacteristic
22C22×C4⋊Dic73C2211yescharacteristic
23C22×#11924007—28no—
24C22×#11924007C2218yes—
25C22×#11924007C2211yescharacteristic
26C22×#11924007C2211yescharacteristic
27C22×#11924007C2211yescharacteristic
28C22×#11924007C2211yescharacteristic
29C22×#11924007C2211yescharacteristic
30C22×#11924007C2211yescharacteristic
31C22×#11924007C2211yescharacteristic
32C22×#11924007C2211yescharacteristic
33C22×#11924007C2211yescharacteristic
34C22×#11924007C2211yescharacteristic
35C22×C22⋊Dic73C2211yescharacteristic
36C22×C22⋊Dic73C2211yescharacteristic
37C22×C4×Dic73C2211yescharacteristic
38C22×C4×Dic73C2211yescharacteristic
39#17988528C2218yescomplemented
40#17988521C2218yescomplemented
41#17988520C2218yescomplemented
42#17988518C2218yescomplemented
43#17988482C2218yescomplemented
44#17988472C2218yescomplemented
45#17988469C2218yescomplemented
46#17988462C2218yes—
47#17988459C2218yes—
48#17988459C2218yes—
49#17988445C2218yes—
50C4×C22⋊Dic73C2218yes—
51C2×#14556498C2211yescharacteristic
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C2×#14556498C2211yescharacteristic
61C24×C4×C73C2211yescharacteristic
62C22×C4⋊C4×C73C2211yescharacteristic
63C22×C4⋊C4×C73C2211yescharacteristic
64C22×C22⋊C4×C73C2211yescharacteristic
65C22×C22⋊C4×C73C2211yescharacteristic
66#385×C73C2218yes—
67C2×#95×C73C2211yescharacteristic
68C2×#95×C73C2211yescharacteristic
69C23×Dic73—24no—
70C23×Dic73—24no—
71C23×Dic73—24no—
72C23×Dic73—24no—
73C23×Dic73—24no—
74C23×Dic73—42no—
75C23×Dic73C2311yescharacteristic
76C23×Dic73C2314yes—
77C23×Dic73C2311yescharacteristic
78C23×Dic73C2311yescharacteristic
79C23×Dic73C2314yes—
80C23×Dic73C2311yescharacteristic
81C23×Dic73C2311yescharacteristic
82C23×Dic73C2311yescharacteristic
83C23×Dic73C2311yescharacteristic
84C23×Dic73C2311yescharacteristic
85#14556581—232no—
86C2×C4⋊Dic73—24no—
87C2×C4⋊Dic73—24no—
88C2×C4⋊Dic73C2314yes—
89C2×C4⋊Dic73C2314yes—
90C2×#11924007—24no—
91C2×#11924007—24no—
92C2×#11924007—24no—
93C2×#11924007—24no—
94C2×#11924007—24no—
95C2×#11924007—24no—
96C2×#11924007—232no—
97C2×#11924007—24no—
98C2×#11924007—42no—
99C2×#11924007—42no—
100C2×#11924007D418yes—
101C2×#11924007C2314yes—
102C2×#11924007C2314yes—
103C2×#11924007C2314yes—
104C2×#11924007C2314yes—
105C2×#11924007C2314yes—
106C2×#11924007C2314yes—
107C2×#11924007C2314yes—
108C2×#11924007C2314yes—
109C2×#11924007C2314yes—
110C2×#11924007C2314yes—
111C2×C22⋊Dic73—24no—
112C2×C22⋊Dic73Q818yes—
113C2×C22⋊Dic73C2314yes—
114C2×C22⋊Dic73C2314yes—
115C2×C4×Dic73—24no—
116C2×C4×Dic73—42no—
117C2×C4×Dic73C2314yes—
118C2×C4×Dic73C2314yes—
119#14556498C2314yes—
120#14556498C2314yes—
121#14556498C2314yes—
122#14556498C2314yes—
123#14556498C2314yes—
124#14556498C2314yes—
125#14556498C2314yes—
126#14556498C2314yes—
127#14556498C2314yes—
128#14556498C2314yes—
129C25×C73C2311yescharacteristic
130C23×C4×C73—24no—
131C23×C4×C73—24no—
132C23×C4×C73—42no—
133C23×C4×C73C2311yescharacteristic
134C23×C4×C73C2311yescharacteristic
135C23×C4×C73C2311yescharacteristic
136C23×C4×C73C2311yescharacteristic
137C23×C4×C73C2311yescharacteristic
138C23×C4×C73C2314yes—
139C23×C4×C73C2311yescharacteristic
140C2×C4⋊C4×C73—24no—
141C2×C4⋊C4×C73—42no—
142C2×C4⋊C4×C73C2314yes—
143C2×C4⋊C4×C73C2314yes—
144C2×C22⋊C4×C73—24no—
145C2×C22⋊C4×C73—24no—
146C2×C22⋊C4×C73C2314yes—
147C2×C22⋊C4×C73C2314yes—
148#95×C73C2314yes—
149#95×C73C2314yes—
150C22×Dic73—232no—
151C22×Dic73—22no—
152C22×Dic73—22no—
153C22×Dic73—22no—
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—28no—
163C22×Dic73—28no—
164C22×Dic73—22no—
165C22×Dic73—22no—
166C22×Dic73—22no—
167C22×Dic73—22no—
168C22×Dic73—22no—
169C22×Dic73—28no—
170C22×Dic73—22no—
171C22×Dic73—22no—
172C22×Dic73—22no—
173C22×Dic73—22no—
174C22×Dic73—28no—
175C22×Dic73—44no—
176C22×Dic73—416no—
177C22×Dic73C2×D414yes—
178C22×Dic73C2×D414yes—
179C22×Dic73C2×Q814yes—
180C22×Dic73C2×Q814yes—
181C22×Dic73#4114yes—
182C22×Dic73C2412yes—
183C22×Dic73C2412yes—
184C22×Dic73C2412yes—
185C22×Dic73C2412yes—
186C22×Dic73C2412yes—
187C22×Dic73C2412yes—
188C22×Dic73C2412yes—
189C22×Dic73C2412yes—
190C4⋊Dic73—28no—
191C4⋊Dic73—28no—
192#11924007—28no—
193#11924007—28no—
194#11924007—28no—
195#11924007—28no—
196#11924007—28no—
197#11924007—28no—
198#11924007—28no—
199#11924007—44no—
200#11924007—44no—
201#11924007C2×D4116yes—
202C22⋊Dic73—28no—
203C22⋊Dic73C2×Q8116yes—
204C4×Dic73—28no—
205C4×Dic73—44no—
206C24×C73—22no—
207C24×C73—22no—
208C24×C73—22no—
209C24×C73—22no—
210C24×C73C2×Q814yes—
211C24×C73#4114yes—
212C24×C73#4114yes—
213C24×C73C2412yes—
214C24×C73C2411yescharacteristic
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—22no—
232C22×C4×C73—22no—
233C22×C4×C73—28no—
234C22×C4×C73—44no—
235C22×C4×C73—416no—
236C22×C4×C73C2×D414yes—
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—44no—
245C22⋊C4×C73—28no—
246C22⋊C4×C73—28no—
247C23×C73—28no—
248C23×C73—28no—
249C23×C73—28no—
250C23×C73—28no—
251C23×C73—28no—
252C23×C73—28no—
253C23×C73—22no—
254C23×C73—22no—
255C23×C73—22no—
256C23×C73—22no—
257C23×C73#125116yescomplemented
258C23×C73C22×D412yes—
259C23×C73C22×Q814yes—
260C23×C73C22×Q812yes—
261C23×C73C2×#4112yes—
262C23×C73C2×#4114yes—
263C23×C73C2×#4112yes—
264C23×C73C2×#4114yes—
265C23×C73C2×#4112yes—
266C23×C73H(5,𝔽2)12yes—
267C23×C732−1+412yes—
268C23×C73C2511yescharacteristic
269C2×C4×C73—28no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
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—416no—
288C2×C4×C73—44no—
289C2×C4×C73—44no—
290C2×C4×C73—44no—
291C2×C4×C73—44no—
292C2×C4×C73—44no—
293C2×C4×C73C22×D414yes—
294C2×Dic73—232no—
295C2×Dic73—28no—
296C2×Dic73—28no—
297C2×Dic73—28no—
298C2×Dic73—28no—
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—416no—
320C2×Dic73—44no—
321C2×Dic73—44no—
322C2×Dic73—44no—
323C2×Dic73C22×D414yes—
324C2×Dic73C22×D414yes—
325C2×Dic73C22×Q814yes—
326C2×Dic73C22×Q814yes—
327C2×Dic73C2×#4114yes—
328C22×C73—24no—
329C22×C73—24no—
330C22×C73—24no—
331C22×C73—24no—
332C22×C73—24no—
333C22×C73—24no—
334C22×C73—232no—
335C22×C73#52514yes—
336C22×C73C2×#12514yes—
337C22×C73C2×#12518yescomplemented
338C22×C73#53914yes—
339C22×C73#54614yes—
340C22×C73D4×Q814yes—
341C22×C73#55214yes—
342C22×C73#55414yes—
343C22×C73C23×D411yescharacteristic
344C22×C73C23×Q811yescharacteristic
345C22×C73C22×#4111yescharacteristic
346C22×C73C22×#4111yescharacteristic
347C22×C73C22×#4111yescharacteristic
348C22×C73C2×H(5,𝔽2)11yescharacteristic
349C22×C73C2×2−1+411yescharacteristic
350C4×C73—24no—
351C4×C73—42no—
352C4×C73—42no—
353C4×C73—42no—
354C4×C73—42no—
355C4×C73—42no—
356Dic73—24no—
357Dic73—24no—
358Dic73—24no—
359Dic73—24no—
360Dic73—24no—
361Dic73—42no—
362Dic73—42no—
363Dic73—42no—
364C2×#2473—731nomaximal, Sylow
365C2×C73—28no—
366C2×C73#247318yescomplemented
367C2×C73C2×#52511yescharacteristic
368C2×C73C22×#12511yescharacteristic
369C2×C73C2×#53911yescharacteristic
370C2×C73C2×#54611yescharacteristic
371C2×C73C2×D4×Q811yescharacteristic
372C2×C73C2×#55211yescharacteristic
373C2×C73C2×#55411yescharacteristic
374C22×#125—731no—
375C23×C4⋊C4—731no—
376#2473—7316no—
377C2×#400—731no—
378C2×#398—731no—
379C2×#398—731no—
380C2×#398—731no—
381C2×#389—731no—
382C2×#387—731no—
383C2×#387—731no—
384C2×#385—731no—
385C2×#385—731no—
386C2×#385—731no—
387C2×#385D7311yescharacteristic
388C2×#380—731no—
389C2×C4×C22⋊C4—731no—
390C73C2×#247311yescharacteristic, complemented, Sylow
391C24×C4—731no—
392C24×C4—731no—
393C24×C4C2×D7311yescharacteristic
394C2×#125—738no—
395C2×#125—1468no—
396C22×C4⋊C4—731no—
397C22×C4⋊C4—731no—
398C22×C4⋊C4—731no—
399C22×C4⋊C4—731no—
400C22×C4⋊C4—731no—
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—738no—
408C22×C4⋊C4—731no—
409C22×C4⋊C4—1468no—
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#398—738no—
422#389—738no—
423#387—738no—
424#387—738no—
425#385—738no—
426#385—738no—
427#385—738no—
428#385C2×D7318yes—
429#380—738no—
430C4×C22⋊C4—738no—
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—731no—
441C2×#95C2×D7311yescharacteristic
442C2×#95C2×D7311yescharacteristic
443C25C22×D7311yescharacteristic
444C23×C4—24no—
445C23×C4—24no—
446C23×C4—42no—
447C23×C4—2922no—
448C23×C4—734no—
449C23×C4—731no—
450C23×C4—731no—
451C23×C4—731no—
452C23×C4—731no—
453C23×C4—731no—
454C23×C4—734no—
455C23×C4—731no—
456C23×C4—731no—
457C23×C4—731no—
458C23×C4—1464no—
459C23×C4—1464no—
460C23×C4—1464no—
461C23×C4—1464no—
462C23×C4—1464no—
463C23×C4C22×D7311yescharacteristic
464C23×C4C22×D7311yescharacteristic
465C23×C4C22×D7311yescharacteristic
466C23×C4C22×D7311yescharacteristic
467C23×C4C22×D7311yescharacteristic
468C23×C4C22×D7314yes—
469C23×C4C22×D7311yescharacteristic
470#125—14632no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—2922no—
474C2×C4⋊C4—2922no—
475C2×C4⋊C4—734no—
476C2×C4⋊C4—734no—
477C2×C4⋊C4—738no—
478C2×C4⋊C4—734no—
479C2×C4⋊C4—734no—
480C2×C4⋊C4—734no—
481C2×C4⋊C4—734no—
482C2×C4⋊C4—734no—
483C2×C4⋊C4—734no—
484C2×C4⋊C4—734no—
485C2×C4⋊C4—734no—
486C2×C4⋊C4—734no—
487C2×C4⋊C4—734no—
488C2×C4⋊C4—14632no—
489C2×C4⋊C4—1464no—
490C2×C4⋊C4—1464no—
491C2×C4⋊C4—1464no—
492C2×C4⋊C4—1464no—
493C2×C4⋊C4—1464no—
494C2×C4⋊C4—1464no—
495C2×C4⋊C4—1464no—
496C2×C4⋊C4—1464no—
497C2×C4⋊C4—1464no—
498C2×C4⋊C4C22×D7314yes—
499C2×C4⋊C4C22×D7314yes—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—738no—
503C2×C22⋊C4—734no—
504C2×C22⋊C4—734no—
505C2×C22⋊C4—1464no—
506C2×C22⋊C4C22×D7314yes—
507C2×C22⋊C4C22×D7314yes—
508C2×C42—2922no—
509C2×C42—734no—
510C2×C42—734no—
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#95C22×D7314yes—
523#95C22×D7314yes—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24Q8×D7314yes—
529C24#1192402714yes—
530C24#1192402814yes—
531C24C23×D7312yes—
532C24C23×D7311yescharacteristic
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—28no—
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—28no—
552C22×C4—44no—
553C22×C4—416no—
554C22×C4—29216no—
555C22×C4—2924no—
556C22×C4—734no—
557C22×C4—734no—
558C22×C4—734no—
559C22×C4—734no—
560C22×C4—734no—
561C22×C4—732no—
562C22×C4—732no—
563C22×C4—732no—
564C22×C4—732no—
565C22×C4—732no—
566C22×C4—732no—
567C22×C4—732no—
568C22×C4—732no—
569C22×C4—1468no—
570C22×C4—1462no—
571C22×C4—1462no—
572C22×C4—1462no—
573C22×C4—1462no—
574C22×C4—1468no—
575C22×C4—1462no—
576C22×C4—1462no—
577C22×C4—1462no—
578C22×C4—1462no—
579C22×C4—1462no—
580C22×C4—1468no—
581C22×C4—1468no—
582C22×C4—14632no—
583C22×C4—1462no—
584C22×C4—1462no—
585C22×C4—1462no—
586C22×C4—1462no—
587C22×C4—1462no—
588C22×C4—1468no—
589C22×C4—1462no—
590C22×C4—1462no—
591C22×C4—1462no—
592C22×C4—1462no—
593C22×C4—1462no—
594C22×C4D4×D7314yes—
595C22×C4C23×D7312yes—
596C22×C4C23×D7312yes—
597C22×C4C23×D7312yes—
598C22×C4C23×D7312yes—
599C22×C4C23×D7312yes—
600C22×C4C23×D7312yes—
601C4⋊C4—28no—
602C4⋊C4—44no—
603C4⋊C4—2924no—
604C4⋊C4—2924no—
605C4⋊C4—7316no—
606C4⋊C4—1468no—
607C4⋊C4—1468no—
608C4⋊C4—1468no—
609C4⋊C4—1468no—
610C4⋊C4—1468no—
611C4⋊C4—1468no—
612C4⋊C4—1468no—
613C4⋊C4—1468no—
614C4⋊C4—1468no—
615C22⋊C4—28no—
616C22⋊C4—28no—
617C22⋊C4—7316no—
618C22⋊C4—1468no—
619C42—2924no—
620C42—1468no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—28no—
626C23—28no—
627C23—28no—
628C23—28no—
629C23—28no—
630C23—28no—
631C23#14556581116yescomplemented
632C23C2×D4×D7312yes—
633C23C2×Q8×D7314yes—
634C23C2×Q8×D7312yes—
635C23#41×D7312yes—
636C23C2×#1192402714yes—
637C23C2×#1192402712yes—
638C23C2×#1192402814yes—
639C23C2×#1192402812yes—
640C23#1455663612yes—
641C23#1455663812yes—
642C23C24×D7311yescharacteristic
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—28no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
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—416no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—2924no—
668C2×C4—2924no—
669C2×C4—2924no—
670C2×C4—29216no—
671C2×C4—734no—
672C2×C4—734no—
673C2×C4—734no—
674C2×C4—734no—
675C2×C4—734no—
676C2×C4—1462no—
677C2×C4—1462no—
678C2×C4—1462no—
679C2×C4—1462no—
680C2×C4—1462no—
681C2×C4—1462no—
682C2×C4—1462no—
683C2×C4—1462no—
684C2×C4—1462no—
685C2×C4—14632no—
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—1468no—
697C2×C4—1468no—
698C2×C4—1468no—
699C2×C4—1468no—
700C2×C4—1468no—
701C2×C4C2×D4×D7314yes—
702C22—24no—
703C22—232no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—24no—
709C22#1798909614yes—
710C22C2×#1455658114yes—
711C22C2×#1455658118yescomplemented
712C22#1798917914yes—
713C22#1798922414yes—
714C22#1798925014yes—
715C22#1798927414yes—
716C22#1798929114yes—
717C22C22×D4×D7311yescharacteristic
718C22C22×Q8×D7311yescharacteristic
719C22C2×#41×D7311yescharacteristic
720C22C22×#1192402711yescharacteristic
721C22C22×#1192402811yescharacteristic
722C22C2×#1455663611yescharacteristic
723C22C2×#1455663811yescharacteristic
724C4—24no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—2922no—
731C4—2922no—
732C4—2922no—
733C4—1464no—
734C4—1464no—
735C4—1464no—
736C4—1464no—
737C4—1464no—
738C2—28no—
739C2#2261407418yesdirect product factor
740C2C2×#1798909611yescharacteristic
741C2C22×#1455658111yescharacteristic
742C2C2×#1798917911yescharacteristic
743C2C2×#1798922411yescharacteristic
744C2C2×#1798925011yescharacteristic
745C2C2×#1798927411yescharacteristic
746C2C2×#1798929111yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#385×C73C2
socleC24×C73C24
prime radicalC25×C73C23
hypercenterC2×#385D73
hypocenterC73C2×#2473
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#14556581C2semidirect
3. #22614074C2direct (N × H)
4. C2×#17988528C2semidirect
5. C2×#17988521C2semidirect
6. C2×#17988520C2semidirect
7. C2×#17988518C2semidirect
8. C2×#17988482C2semidirect
9. C2×#17988472C2semidirect
10. C2×#17988469C2semidirect
20. C2×#14556581C22semidirect
39. #17988528C22semidirect
40. #17988521C22semidirect
41. #17988520C22semidirect
42. #17988518C22semidirect
43. #17988482C22semidirect
44. #17988472C22semidirect
45. #17988469C22semidirect
257. C23×C73#125semidirect
337. C22×C73C2×#125semidirect
366. C2×C73#2473semidirect
390. C73C2×#2473semidirect
631. C23#14556581semidirect
711. C22C2×#14556581semidirect
739. C2#22614074direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565812
C23×#119240072
#226140742
C2×#179885282
C2×#179885212
C2×#179885202
C2×#179885182
C2×#179884822
C2×#179884722
C2×#179884692
C2×#179884622
C2×#179884592
C2×#179884452
C2×C4×C22⋊Dic732
C2×#385×C732
C2×#247373