Finite Group Databasebeta

← C2×#22612423 #33244377

Subgroups — C2×#22612423 #33244377

Order 18688.

2902 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556549C211yesmaximal, characteristic
2#22612423C2116yesmaximal, direct product factor
3C2×#17988479C211yesmaximal, characteristic
4C2×#17988478C211yesmaximal, characteristic
5C2×#17988477C211yesmaximal, characteristic
6C2×#17988476C211yesmaximal, characteristic
7C2×#17988473C211yesmaximal, characteristic, complemented
8C2×#17988472C211yesmaximal, characteristic, complemented
9C2×#17988470C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×Dic73C211yesmaximal, characteristic, complemented
11C2×#17988438C211yesmaximal, characteristic, complemented
12C2×#17988434C211yesmaximal, characteristic
13C2×#17988434C211yesmaximal, characteristic
14C2×#17988432C211yesmaximal, characteristic, complemented
15C2×C42×Dic73C211yesmaximal, characteristic, complemented
16C2×#387×C73C211yesmaximal, characteristic, complemented
17C23×C4×D73C2211yescharacteristic
18C2×#14556549C4116yescomplemented
19C2×#14556549C2218yes—
20C22×C4⋊Dic73C2211yescharacteristic
21C22×C4⋊Dic73C2211yescharacteristic
22C22×#11924007C2211yescharacteristic
23C22×#11924007C2211yescharacteristic
24C22×#11924005C2211yescharacteristic
25C22×#11924005C2211yescharacteristic
26C22×#11924005C2211yescharacteristic
27C22×#11924005C2211yescharacteristic
28C22×#11924005C2211yescharacteristic
29C22×#11924005C2211yescharacteristic
30C22×C4×Dic73C2211yescharacteristic
31C22×C4×Dic73C2211yescharacteristic
32C22×C4×Dic73C2211yescharacteristic
33C22×C4×Dic73C2211yescharacteristic
34C22×C4×Dic73C2211yescharacteristic
35C22×C4×Dic73C2211yescharacteristic
36C22×C4×Dic73C2211yescharacteristic
37C22×C4×Dic73C2211yescharacteristic
38C22×C4×Dic73C2211yescharacteristic
39#17988479C2218yes—
40#17988478C2218yes—
41#17988477C2218yes—
42#17988476C2218yes—
43#17988473C2218yescomplemented
44#17988472C2218yescomplemented
45#17988470C2218yescomplemented
46C4⋊C4×Dic73C2218yescomplemented
47#17988438C2218yescomplemented
48#17988434C2218yes—
49#17988434C2218yes—
50#17988432C2218yescomplemented
51C2×#14556498C2211yescharacteristic
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C42×Dic73C2218yescomplemented
60C22×C4⋊C4×C73C2211yescharacteristic
61C22×C4⋊C4×C73C2211yescharacteristic
62C22×C42×C73C2211yescharacteristic
63#387×C73C2218yescomplemented
64C2×#95×C73C2211yescharacteristic
65C2×#95×C73C2211yescharacteristic
66C2×#95×C73C2211yescharacteristic
67C2×#95×C73C2211yescharacteristic
68C24×D73C2311yescharacteristic
69C23×Dic73C2311yescharacteristic
70C23×Dic73C2311yescharacteristic
71C23×Dic73C2311yescharacteristic
72C23×Dic73C2311yescharacteristic
73C23×Dic73C2311yescharacteristic
74C23×Dic73C2311yescharacteristic
75C23×Dic73C2311yescharacteristic
76C22×C4×D73—24no—
77C22×C4×D73—24no—
78C22×C4×D73C2×C418yes—
79C22×C4×D73C2314yes—
80#14556549C2×C4164yescomplemented
81C2×C4⋊Dic73—24no—
82C2×C4⋊Dic73C2×C418yes—
83C2×C4⋊Dic73C2314yes—
84C2×C4⋊Dic73C2314yes—
85C2×#11924007—24no—
86C2×#11924007—24no—
87C2×#11924007C2314yes—
88C2×#11924007C2314yes—
89C2×#11924005—24no—
90C2×#11924005—24no—
91C2×#11924005—24no—
92C2×#11924005—24no—
93C2×#11924005C2×C418yes—
94C2×#11924005C2×C418yes—
95C2×#11924005C2314yes—
96C2×#11924005C2314yes—
97C2×#11924005C2314yes—
98C2×#11924005C2314yes—
99C2×#11924005C2314yes—
100C2×#11924005C2314yes—
101C2×C4×Dic73—24no—
102C2×C4×Dic73—24no—
103C2×C4×Dic73—24no—
104C2×C4×Dic73—24no—
105C2×C4×Dic73—24no—
106C2×C4×Dic73—24no—
107C2×C4×Dic73—24no—
108C2×C4×Dic73C2×C418yes—
109C2×C4×Dic73C2×C418yes—
110C2×C4×Dic73C2314yes—
111C2×C4×Dic73C2314yes—
112C2×C4×Dic73C2314yes—
113C2×C4×Dic73C2314yes—
114C2×C4×Dic73C2314yes—
115C2×C4×Dic73C2314yes—
116C2×C4×Dic73C2314yes—
117C2×C4×Dic73C2314yes—
118C2×C4×Dic73C2314yes—
119#14556498C2314yes—
120#14556498C2314yes—
121#14556498C2314yes—
122#14556498C2314yes—
123#14556498C2314yes—
124#14556498C2314yes—
125#14556498C2314yes—
126#14556498C2314yes—
127C23×C4×C73C2311yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C2×C4⋊C4×C73—24no—
135C2×C4⋊C4×C73C2×C418yes—
136C2×C4⋊C4×C73C2314yes—
137C2×C4⋊C4×C73C2314yes—
138C2×C42×C73—24no—
139C2×C42×C73C2314yes—
140#95×C73C2314yes—
141#95×C73C2314yes—
142#95×C73C2314yes—
143#95×C73C2314yes—
144C23×D73—22no—
145C23×D73—22no—
146C23×D73—22no—
147C23×D73—22no—
148C23×D73—22no—
149C23×D73—22no—
150C23×D73C22×C414yes—
151C23×D73C2412yes—
152C22×Dic73—22no—
153C22×Dic73—22no—
154C22×Dic73—22no—
155C22×Dic73—22no—
156C22×Dic73—22no—
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×Dic73C22×C414yes—
167C22×Dic73C22×C414yes—
168C22×Dic73C22×C414yes—
169C22×Dic73#4114yes—
170C22×Dic73#4114yes—
171C22×Dic73#4114yes—
172C22×Dic73#4114yes—
173C22×Dic73C2412yes—
174C22×Dic73C2412yes—
175C22×Dic73C2412yes—
176C22×Dic73C2412yes—
177C22×Dic73C2412yes—
178C22×Dic73C2412yes—
179C22×Dic73C2412yes—
180C2×C4×D73—232no—
181C2×C4×D73—28no—
182C2×C4×D73—28no—
183C2×C4×D73C22×C4116yes—
184C4⋊Dic73—28no—
185C4⋊Dic73C22×C4116yes—
186#11924007—28no—
187#11924007—28no—
188#11924005—28no—
189#11924005—28no—
190#11924005—28no—
191#11924005—28no—
192#11924005C22×C4116yes—
193#11924005C22×C4116yes—
194C4×Dic73—28no—
195C4×Dic73—28no—
196C4×Dic73—28no—
197C4×Dic73—28no—
198C4×Dic73—28no—
199C4×Dic73—28no—
200C4×Dic73—28no—
201C4×Dic73C22×C4116yes—
202C4×Dic73C22×C4116yes—
203C24×C73C2411yescharacteristic
204C22×C4×C73—22no—
205C22×C4×C73—22no—
206C22×C4×C73—22no—
207C22×C4×C73—22no—
208C22×C4×C73—22no—
209C22×C4×C73—22no—
210C22×C4×C73—22no—
211C22×C4×C73—22no—
212C22×C4×C73—22no—
213C22×C4×C73—22no—
214C22×C4×C73—22no—
215C22×C4×C73—22no—
216C22×C4×C73—22no—
217C22×C4×C73—22no—
218C22×C4×C73—22no—
219C22×C4×C73—22no—
220C22×C4×C73C22×C414yes—
221C22×C4×C73C22×C414yes—
222C22×C4×C73C22×C414yes—
223C22×C4×C73#4114yes—
224C22×C4×C73#4114yes—
225C22×C4×C73C2412yes—
226C22×C4×C73C2412yes—
227C22×C4×C73C2412yes—
228C22×C4×C73C2412yes—
229C22×C4×C73C2412yes—
230C22×C4×C73C2412yes—
231C22×C4×C73C2412yes—
232C4⋊C4×C73—28no—
233C4⋊C4×C73C22×C4116yes—
234C42×C73—28no—
235C23×C73C23×C412yes—
236C23×C73C2×#4112yes—
237C23×C73C2×#4112yes—
238C23×C73C2×#4112yes—
239C23×C73C2×#4112yes—
240C23×C73C2×#4112yes—
241C23×C73C2×#4112yes—
242C23×C73C2511yescharacteristic
243C22×D73—28no—
244C22×D73—28no—
245C22×D73—28no—
246C22×D73—22no—
247C22×D73—22no—
248C22×D73—22no—
249C22×D73—22no—
250C22×D73—22no—
251C22×D73—22no—
252C22×D73—44no—
253C22×D73—44no—
254C22×D73—44no—
255C22×D73—44no—
256C22×D73C23×C414yes—
257C2×C4×C73—28no—
258C2×C4×C73—28no—
259C2×C4×C73—28no—
260C2×C4×C73—28no—
261C2×C4×C73—28no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
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—44no—
279C2×C4×C73—44no—
280C2×C4×C73C23×C414yes—
281C2×C4×C73C23×C414yes—
282C2×C4×C73C23×C414yes—
283C2×C4×C73C2×#4114yes—
284C2×C4×C73C2×#4114yes—
285C2×Dic73—28no—
286C2×Dic73—28no—
287C2×Dic73—28no—
288C2×Dic73—28no—
289C2×Dic73—22no—
290C2×Dic73—22no—
291C2×Dic73—22no—
292C2×Dic73—22no—
293C2×Dic73—22no—
294C2×Dic73—22no—
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—44no—
304C2×Dic73—44no—
305C2×Dic73#117116yes—
306C2×Dic73C23×C414yes—
307C2×Dic73C23×C414yes—
308C2×Dic73C23×C414yes—
309C2×Dic73C2×#4114yes—
310C2×Dic73C2×#4114yes—
311C2×Dic73C2×#4114yes—
312C2×Dic73C2×#4114yes—
313C4×D73—232no—
314C22×C73C2×#11714yes—
315C22×C73C4×#4114yes—
316C22×C73C4×#4114yes—
317C22×C73#52914yes—
318C22×C73#52914yes—
319C22×C73#52914yes—
320C22×C73#52914yes—
321C22×C73C24×C411yescharacteristic
322C22×C73C22×#4111yescharacteristic
323C22×C73C22×#4111yescharacteristic
324C22×C73C22×#4111yescharacteristic
325C22×C73C22×#4111yescharacteristic
326C22×C73C22×#4111yescharacteristic
327C22×C73C22×#4111yescharacteristic
328C2×D73—24no—
329C2×D73—24no—
330C2×D73—24no—
331C2×D73—42no—
332C2×D73—42no—
333C2×D73—42no—
334C2×D73—42no—
335C2×D73—416no—
336C4×C73—24no—
337C4×C73—24no—
338C4×C73—24no—
339C4×C73—24no—
340C4×C73—24no—
341C4×C73—42no—
342C4×C73—42no—
343Dic73—24no—
344Dic73—24no—
345Dic73—24no—
346Dic73—24no—
347Dic73—42no—
348Dic73—42no—
349Dic73C2×#11718yes—
350C2×#2298—731nomaximal, Sylow
351C2×C73#229818yescomplemented
352C2×C73C22×#11711yescharacteristic
353C2×C73C2×C4×#4111yescharacteristic
354C2×C73C2×C4×#4111yescharacteristic
355C2×C73C2×#52911yescharacteristic
356C2×C73C2×#52911yescharacteristic
357C2×C73C2×#52911yescharacteristic
358C2×C73C2×#52911yescharacteristic
359D73—44no—
360C22×#117—731no—
361#2298—7316no—
362C2×#388—731no—
363C2×#388—731no—
364C2×#388—731no—
365C2×#388—731no—
366C2×#387—731no—
367C2×#387—731no—
368C2×#387—731no—
369C2×#387D7311yescharacteristic, complemented
370C2×C4×C4⋊C4—731no—
371C2×C4×C4⋊C4—731no—
372C2×C4×C22⋊C4—731no—
373C2×C4×C22⋊C4—731no—
374C2×#376—731no—
375C2×C43—731no—
376C73C2×#229811yescharacteristic, complemented, Sylow
377C24×C4—731no—
378C2×#117—7316no—
379C2×#117—738no—
380C22×C4⋊C4—731no—
381C22×C4⋊C4—731no—
382C22×C4⋊C4—731no—
383C22×C4⋊C4—731no—
384C22×C4⋊C4C2×D7311yescharacteristic
385C22×C4⋊C4C2×D7311yescharacteristic
386C22×C22⋊C4—731no—
387C22×C22⋊C4—731no—
388C22×C22⋊C4—731no—
389C22×C22⋊C4—731no—
390C22×C22⋊C4—731no—
391C22×C22⋊C4—731no—
392C22×C42—731no—
393C22×C42—731no—
394C22×C42—731no—
395C22×C42—731no—
396C22×C42—731no—
397C22×C42—731no—
398C22×C42—731no—
399C22×C42—731no—
400C22×C42—731no—
401C22×C42C2×D7311yescharacteristic
402#388—738no—
403#388—738no—
404#388—738no—
405#388—738no—
406#387—738no—
407#387—738no—
408#387—738no—
409#387C2×D7318yescomplemented
410C4×C4⋊C4—738no—
411C4×C4⋊C4—738no—
412C4×C22⋊C4—738no—
413C4×C22⋊C4—738no—
414#376—738no—
415C2×#95—731no—
416C2×#95—731no—
417C2×#95—731no—
418C2×#95—731no—
419C2×#95—731no—
420C2×#95—731no—
421C2×#95—731no—
422C2×#95—731no—
423C2×#95C2×D7311yescharacteristic
424C2×#95C2×D7311yescharacteristic
425C2×#95C2×D7311yescharacteristic
426C2×#95C2×D7311yescharacteristic
427C43—738no—
428C25—731no—
429C23×C4—731no—
430C23×C4—731no—
431C23×C4—731no—
432C23×C4—731no—
433C23×C4—731no—
434C23×C4—738no—
435C23×C4—734no—
436C23×C4—731no—
437C23×C4—731no—
438C23×C4—1464no—
439C23×C4—1464no—
440C23×C4C22×D7311yescharacteristic
441C23×C4C22×D7311yescharacteristic
442C23×C4C22×D7311yescharacteristic
443C23×C4C22×D7311yescharacteristic
444C23×C4C22×D7311yescharacteristic
445C23×C4C22×D7311yescharacteristic
446C23×C4C22×D7311yescharacteristic
447#117—7364no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—738no—
450C2×C4⋊C4—734no—
451C2×C4⋊C4—734no—
452C2×C4⋊C4—734no—
453C2×C4⋊C4—734no—
454C2×C4⋊C4—1464no—
455C2×C4⋊C4—1464no—
456C2×C4⋊C4—1464no—
457C2×C4⋊C4C4×D7318yes—
458C2×C4⋊C4C22×D7314yes—
459C2×C4⋊C4C22×D7314yes—
460C2×C22⋊C4—738no—
461C2×C22⋊C4—738no—
462C2×C22⋊C4—734no—
463C2×C22⋊C4—734no—
464C2×C22⋊C4—734no—
465C2×C22⋊C4—734no—
466C2×C22⋊C4—734no—
467C2×C22⋊C4—734no—
468C2×C22⋊C4—1464no—
469C2×C22⋊C4—1464no—
470C2×C22⋊C4—1464no—
471C2×C22⋊C4—1464no—
472C2×C42—24no—
473C2×C42—738no—
474C2×C42—738no—
475C2×C42—734no—
476C2×C42—734no—
477C2×C42—734no—
478C2×C42—734no—
479C2×C42—734no—
480C2×C42—734no—
481C2×C42—734no—
482C2×C42—734no—
483C2×C42—734no—
484C2×C42—1464no—
485C2×C42—1464no—
486C2×C42—1464no—
487C2×C42—1464no—
488C2×C42—1464no—
489C2×C42—1464no—
490C2×C42—1464no—
491C2×C42C22×D7314yes—
492#95—734no—
493#95—734no—
494#95—734no—
495#95—734no—
496#95—734no—
497#95—734no—
498#95—734no—
499#95—734no—
500#95C22×D7314yes—
501#95C22×D7314yes—
502#95C22×D7314yes—
503#95C22×D7314yes—
504C24—734no—
505C24—732no—
506C24—1462no—
507C24—1462no—
508C24—1462no—
509C24—1462no—
510C24—1462no—
511C24—1462no—
512C24C23×D7311yescharacteristic
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—734no—
530C22×C4—734no—
531C22×C4—734no—
532C22×C4—732no—
533C22×C4—734no—
534C22×C4—734no—
535C22×C4—734no—
536C22×C4—734no—
537C22×C4—732no—
538C22×C4—732no—
539C22×C4—732no—
540C22×C4—732no—
541C22×C4—7316no—
542C22×C4—732no—
543C22×C4—732no—
544C22×C4—1468no—
545C22×C4—1468no—
546C22×C4—14632no—
547C22×C4—1462no—
548C22×C4—1462no—
549C22×C4—1462no—
550C22×C4—1462no—
551C22×C4—1462no—
552C22×C4—1462no—
553C22×C4—1462no—
554C22×C4—1462no—
555C22×C4—1462no—
556C22×C4—1462no—
557C22×C4—1462no—
558C22×C4—1462no—
559C22×C4—1462no—
560C22×C4—1462no—
561C22×C4C2×C4×D7314yes—
562C22×C4C2×C4×D7314yes—
563C22×C4C2×C4×D7314yes—
564C22×C4#1192402714yes—
565C22×C4#1192402914yes—
566C22×C4C23×D7312yes—
567C22×C4C23×D7312yes—
568C22×C4C23×D7312yes—
569C22×C4C23×D7312yes—
570C22×C4C23×D7312yes—
571C22×C4C23×D7312yes—
572C22×C4C23×D7312yes—
573C4⋊C4—28no—
574C4⋊C4—7316no—
575C4⋊C4—1468no—
576C4⋊C4—1468no—
577C4⋊C4—1468no—
578C4⋊C4C2×C4×D73116yes—
579C22⋊C4—7316no—
580C22⋊C4—7316no—
581C22⋊C4—1468no—
582C22⋊C4—1468no—
583C22⋊C4—1468no—
584C22⋊C4—1468no—
585C42—28no—
586C42—7316no—
587C42—7316no—
588C42—1468no—
589C42—1468no—
590C42—1468no—
591C42—1468no—
592C42—1468no—
593C42—1468no—
594C42—1468no—
595C23—2924no—
596C23—2924no—
597C23—2924no—
598C23—2924no—
599C23—734no—
600C23—1462no—
601C23—1462no—
602C23—1462no—
603C23—1462no—
604C23—1462no—
605C23—1462no—
606C23—1468no—
607C23—1468no—
608C23—1468no—
609C23C22×C4×D7312yes—
610C23#41×D7312yes—
611C23#41×D7312yes—
612C23#41×D7312yes—
613C23#41×D7312yes—
614C23C2×#1192402712yes—
615C23C2×#1192402912yes—
616C23C24×D7311yescharacteristic
617C2×C4—28no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—28no—
629C2×C4—28no—
630C2×C4—28no—
631C2×C4—28no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—2924no—
641C2×C4—2924no—
642C2×C4—734no—
643C2×C4—734no—
644C2×C4—734no—
645C2×C4—7316no—
646C2×C4—734no—
647C2×C4—734no—
648C2×C4—734no—
649C2×C4—734no—
650C2×C4—14632no—
651C2×C4—1462no—
652C2×C4—1462no—
653C2×C4—1462no—
654C2×C4—1462no—
655C2×C4—1462no—
656C2×C4—1462no—
657C2×C4—1468no—
658C2×C4—1468no—
659C2×C4—1462no—
660C2×C4—1462no—
661C2×C4—1462no—
662C2×C4—1462no—
663C2×C4—1462no—
664C2×C4—1462no—
665C2×C4—1462no—
666C2×C4—1462no—
667C2×C4—1468no—
668C2×C4—1468no—
669C2×C4C22×C4×D7314yes—
670C2×C4C22×C4×D7314yes—
671C2×C4C22×C4×D7314yes—
672C2×C4C2×#1192402714yes—
673C2×C4C2×#1192402914yes—
674C22—29216no—
675C22—2922no—
676C22—2922no—
677C22—2922no—
678C22—2922no—
679C22—1464no—
680C22—1464no—
681C22—1464no—
682C22#117×D7314yes—
683C22C4×#1192402714yes—
684C22C4×#1192402914yes—
685C22#1798911414yes—
686C22#1798912014yes—
687C22#1798912214yes—
688C22#1798912314yes—
689C22C23×C4×D7311yescharacteristic
690C22C2×#41×D7311yescharacteristic
691C22C2×#41×D7311yescharacteristic
692C22C2×#41×D7311yescharacteristic
693C22C2×#41×D7311yescharacteristic
694C22C22×#1192402711yescharacteristic
695C22C22×#1192402911yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—24no—
701C4—42no—
702C4—42no—
703C4—2922no—
704C4—2922no—
705C4—738no—
706C4—1464no—
707C4—1464no—
708C4—1464no—
709C4—1464no—
710C2—2924no—
711C2#2261242318yesdirect product factor
712C2C2×#117×D7311yescharacteristic
713C2C2×C4×#1192402711yescharacteristic
714C2C2×C4×#1192402911yescharacteristic
715C2C2×#1798911411yescharacteristic
716C2C2×#1798912011yescharacteristic
717C2C2×#1798912211yescharacteristic
718C2C2×#1798912311yescharacteristic
subgroupG/H
centerC24C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC2×#387×C73C2
socleC24×C73C24
prime radicalC24×D73C23
cosocleC23×C73C25
hypercenterC2×#387D73
hypocenterC73C2×#2298
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #22612423C2direct (N × H)
7. C2×#17988473C2semidirect
8. C2×#17988472C2semidirect
9. C2×#17988470C2semidirect
10. C2×C4⋊C4×Dic73C2semidirect
11. C2×#17988438C2semidirect
14. C2×#17988432C2semidirect
15. C2×C42×Dic73C2semidirect
16. C2×#387×C73C2semidirect
18. C2×#14556549C4semidirect
43. #17988473C22semidirect
44. #17988472C22semidirect
45. #17988470C22semidirect
46. C4⋊C4×Dic73C22semidirect
47. #17988438C22semidirect
50. #17988432C22semidirect
59. C42×Dic73C22semidirect
63. #387×C73C22semidirect
80. #14556549C2×C4semidirect
351. C2×C73#2298semidirect
369. C2×#387D73semidirect
376. C73C2×#2298semidirect
409. #387C2×D73semidirect
711. C2#22612423direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565492
#226124232
C2×#179884792
C2×#179884782
C2×#179884772
C2×#179884762
C2×#179884732
C2×#179884722
C2×#179884702
C2×C4⋊C4×Dic732
C2×#179884382
C2×#179884342
C2×#179884322
C2×C42×Dic732
C2×#387×C732
C2×#229873