Finite Group Databasebeta

← C2×#22612530 #33244568

Subgroups — C2×#22612530 #33244568

Order 18688.

2894 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D73C211yesmaximal, characteristic
2#22612530C2116yesmaximal, direct product factor
3C2×#17988474C211yesmaximal, characteristic, complemented
4C2×#17988473C211yesmaximal, characteristic, complemented
5C2×#17988472C211yesmaximal, characteristic, complemented
6C2×#17988471C211yesmaximal, characteristic, complemented
7C2×#17988470C211yesmaximal, characteristic, complemented
8C2×#17988469C211yesmaximal, characteristic, complemented
9C2×#17988468C211yesmaximal, characteristic, complemented
10C2×#17988449C211yesmaximal, characteristic
11C2×#17988449C211yesmaximal, characteristic
12C2×#17988446C211yesmaximal, characteristic
13C2×#17988444C211yesmaximal, characteristic
14C2×C4×#11924005C211yesmaximal, characteristic
15C2×#17988434C211yesmaximal, characteristic
16C2×#387×C73C211yesmaximal, characteristic, complemented
17C23×C4×D73C2211yescharacteristic
18C23×C4×D73C2211yescharacteristic
19C23×C4×D73C2211yescharacteristic
20C22×C4⋊Dic73C2211yescharacteristic
21C22×C4⋊Dic73C2211yescharacteristic
22C22×#11924007C2211yescharacteristic
23C22×#11924007C2211yescharacteristic
24C22×#11924007C2211yescharacteristic
25C22×#11924007C2211yescharacteristic
26C2×C4⋊C4×D73C4116yescomplemented
27C2×C4⋊C4×D73C2218yes—
28C22×#11924005C2211yescharacteristic
29C22×#11924005C2211yescharacteristic
30C22×#11924005C2211yescharacteristic
31C22×#11924005C2211yescharacteristic
32C22×C4×Dic73C2211yescharacteristic
33C22×C4×Dic73C2211yescharacteristic
34C22×C4×Dic73C2211yescharacteristic
35#17988474C2218yescomplemented
36#17988473C2218yescomplemented
37#17988472C2218yescomplemented
38#17988471C2218yescomplemented
39#17988470C2218yescomplemented
40#17988469C2218yescomplemented
41#17988468C2218yescomplemented
42#17988449C2218yes—
43#17988449C2218yes—
44#17988446C2218yes—
45#17988444C2218yes—
46C4×#11924005C2218yes—
47#17988434C2218yes—
48C2×#14556498C2211yescharacteristic
49C2×#14556498C2211yescharacteristic
50C2×#14556498C2211yescharacteristic
51C2×#14556498C2211yescharacteristic
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
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×D73—42no—
79C22×C4×D73—42no—
80C22×C4×D73—42no—
81C22×C4×D73—42no—
82C22×C4×D73C2×C418yes—
83C22×C4×D73C2×C418yes—
84C22×C4×D73C2×C418yes—
85C22×C4×D73C2314yes—
86C22×C4×D73C2314yes—
87C22×C4×D73C2314yes—
88C2×C4⋊Dic73—42no—
89C2×C4⋊Dic73C2×C418yes—
90C2×C4⋊Dic73C2314yes—
91C2×C4⋊Dic73C2314yes—
92C2×#11924007—42no—
93C2×#11924007—42no—
94C2×#11924007C2×C418yes—
95C2×#11924007C2×C418yes—
96C2×#11924007C2314yes—
97C2×#11924007C2314yes—
98C2×#11924007C2314yes—
99C2×#11924007C2314yes—
100C4⋊C4×D73C2×C4164yescomplemented
101C2×#11924005—24no—
102C2×#11924005—24no—
103C2×#11924005—24no—
104C2×#11924005—24no—
105C2×#11924005C2314yes—
106C2×#11924005C2314yes—
107C2×#11924005C2314yes—
108C2×#11924005C2314yes—
109C2×C4×Dic73—42no—
110C2×C4×Dic73—42no—
111C2×C4×Dic73—42no—
112C2×C4×Dic73C2314yes—
113C2×C4×Dic73C2314yes—
114C2×C4×Dic73C2314yes—
115#14556498C2314yes—
116#14556498C2314yes—
117#14556498C2314yes—
118#14556498C2314yes—
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—42no—
135C2×C4⋊C4×C73C2×C418yes—
136C2×C4⋊C4×C73C2314yes—
137C2×C4⋊C4×C73C2314yes—
138C2×C42×C73—42no—
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×D73C22×C414yes—
149C23×D73#4114yes—
150C23×D73#4114yes—
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×Dic73—22no—
167C22×Dic73—22no—
168C22×Dic73—22no—
169C22×Dic73—22no—
170C22×Dic73C22×C414yes—
171C22×Dic73C22×C414yes—
172C22×Dic73C22×C414yes—
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×D73—416no—
184C2×C4×D73—416no—
185C2×C4×D73—44no—
186C2×C4×D73—44no—
187C2×C4×D73—44no—
188C2×C4×D73—44no—
189C2×C4×D73C22×C4116yes—
190C2×C4×D73C22×C4116yes—
191C2×C4×D73C22×C4116yes—
192C4⋊Dic73—44no—
193C4⋊Dic73C22×C4116yes—
194#11924007—44no—
195#11924007—44no—
196#11924007C22×C4116yes—
197#11924007C22×C4116yes—
198#11924005—28no—
199#11924005—28no—
200#11924005—28no—
201#11924005—28no—
202C4×Dic73—44no—
203C4×Dic73—44no—
204C4×Dic73—44no—
205C24×C73C2411yescharacteristic
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×C73—22no—
221C22×C4×C73—22no—
222C22×C4×C73—22no—
223C22×C4×C73—22no—
224C22×C4×C73C22×C414yes—
225C22×C4×C73C22×C414yes—
226C22×C4×C73C22×C414yes—
227C22×C4×C73C2412yes—
228C22×C4×C73C2412yes—
229C22×C4×C73C2412yes—
230C22×C4×C73C2412yes—
231C22×C4×C73C2412yes—
232C22×C4×C73C2412yes—
233C22×C4×C73C2412yes—
234C4⋊C4×C73—44no—
235C4⋊C4×C73C22×C4116yes—
236C42×C73—44no—
237C23×C73C23×C412yes—
238C23×C73C2×#4112yes—
239C23×C73C2×#4112yes—
240C23×C73H(5,𝔽2)12yes—
241C23×C73H(5,𝔽2)12yes—
242C23×C732−1+412yes—
243C23×C732−1+412yes—
244C23×C73C2511yescharacteristic
245C22×D73—28no—
246C22×D73—28no—
247C22×D73—28no—
248C22×D73—28no—
249C22×D73—28no—
250C22×D73—28no—
251C22×D73—22no—
252C22×D73—22no—
253C22×D73—22no—
254C22×D73—22no—
255C22×D73#117116yes—
256C22×D73C23×C414yes—
257C22×D73C2×#4114yes—
258C22×D73C2×#4114yes—
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—22no—
279C2×C4×C73—22no—
280C2×C4×C73—44no—
281C2×C4×C73—44no—
282C2×C4×C73—44no—
283C2×C4×C73—44no—
284C2×C4×C73C23×C414yes—
285C2×C4×C73C23×C414yes—
286C2×C4×C73C23×C414yes—
287C2×Dic73—28no—
288C2×Dic73—28no—
289C2×Dic73—28no—
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—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—44no—
309C2×Dic73—44no—
310C2×Dic73—44no—
311C2×Dic73—44no—
312C2×Dic73C23×C414yes—
313C2×Dic73C23×C414yes—
314C2×Dic73C23×C414yes—
315C4×D73—232no—
316C4×D73—416no—
317C4×D73—416no—
318C22×C73C2×#11714yes—
319C22×C73#51814yes—
320C22×C73#51914yes—
321C22×C73#53914yes—
322C22×C73#53914yes—
323C22×C73#53914yes—
324C22×C73#53914yes—
325C22×C73C24×C411yescharacteristic
326C22×C73C22×#4111yescharacteristic
327C22×C73C22×#4111yescharacteristic
328C22×C73C2×H(5,𝔽2)11yescharacteristic
329C22×C73C2×H(5,𝔽2)11yescharacteristic
330C22×C73C2×2−1+411yescharacteristic
331C22×C73C2×2−1+411yescharacteristic
332C2×D73—232no—
333C2×D73—24no—
334C2×D73—24no—
335C2×D73—24no—
336C2×D73—24no—
337C2×D73—24no—
338C2×D73—24no—
339C2×D73C2×#11718yes—
340C4×C73—24no—
341C4×C73—24no—
342C4×C73—24no—
343C4×C73—42no—
344C4×C73—42no—
345C4×C73—42no—
346C4×C73—42no—
347Dic73—24no—
348Dic73—24no—
349Dic73—24no—
350Dic73—42no—
351Dic73—42no—
352Dic73—42no—
353Dic73—42no—
354C2×#2313—731nomaximal, Sylow
355C2×C73#231318yescomplemented
356C2×C73C22×#11711yescharacteristic
357C2×C73C2×#51811yescharacteristic
358C2×C73C2×#51911yescharacteristic
359C2×C73C2×#53911yescharacteristic
360C2×C73C2×#53911yescharacteristic
361C2×C73C2×#53911yescharacteristic
362C2×C73C2×#53911yescharacteristic
363D73—28no—
364C23×C4⋊C4—731no—
365#2313—7316no—
366C2×#387—731no—
367C2×#387—731no—
368C2×#387—731no—
369C2×#387—731no—
370C2×#387—731no—
371C2×#387—731no—
372C2×#387—731no—
373C2×#387D7311yescharacteristic, complemented
374C2×#381—731no—
375C2×#381—731no—
376C2×#380—731no—
377C2×#380—731no—
378C2×C4×C22⋊C4—731no—
379C2×C4×C22⋊C4—731no—
380C73C2×#231311yescharacteristic, complemented, Sylow
381C24×C4—731no—
382C24×C4—731no—
383C24×C4—731no—
384C22×C4⋊C4—731no—
385C22×C4⋊C4—731no—
386C22×C4⋊C4—731no—
387C22×C4⋊C4—731no—
388C22×C4⋊C4—731no—
389C22×C4⋊C4—731no—
390C22×C4⋊C4—7316no—
391C22×C4⋊C4—738no—
392C22×C4⋊C4C2×D7311yescharacteristic
393C22×C4⋊C4C2×D7311yescharacteristic
394C22×C22⋊C4—731no—
395C22×C22⋊C4—731no—
396C22×C22⋊C4—731no—
397C22×C22⋊C4—731no—
398C22×C42—731no—
399C22×C42—731no—
400C22×C42—731no—
401C22×C42C2×D7311yescharacteristic
402#387—738no—
403#387—738no—
404#387—738no—
405#387—738no—
406#387—738no—
407#387—738no—
408#387—738no—
409#387C2×D7318yescomplemented
410#381—738no—
411#381—738no—
412#380—738no—
413#380—738no—
414C4×C22⋊C4—738no—
415C4×C22⋊C4—738no—
416C2×#95—731no—
417C2×#95—731no—
418C2×#95—731no—
419C2×#95—731no—
420C2×#95—731no—
421C2×#95—731no—
422C2×#95—731no—
423C2×#95—731no—
424C2×#95—731no—
425C2×#95—731no—
426C2×#95—731no—
427C2×#95—731no—
428C2×#95C2×D7311yescharacteristic
429C2×#95C2×D7311yescharacteristic
430C2×#95C2×D7311yescharacteristic
431C2×#95C2×D7311yescharacteristic
432C25—731no—
433C23×C4—2922no—
434C23×C4—2922no—
435C23×C4—2922no—
436C23×C4—2922no—
437C23×C4—738no—
438C23×C4—738no—
439C23×C4—734no—
440C23×C4—734no—
441C23×C4—731no—
442C23×C4—731no—
443C23×C4—731no—
444C23×C4—738no—
445C23×C4—734no—
446C23×C4—731no—
447C23×C4—731no—
448C23×C4—731no—
449C23×C4—731no—
450C23×C4—1464no—
451C23×C4—1464no—
452C23×C4C22×D7311yescharacteristic
453C23×C4C22×D7311yescharacteristic
454C23×C4C22×D7311yescharacteristic
455C23×C4C22×D7311yescharacteristic
456C23×C4C22×D7311yescharacteristic
457C23×C4C22×D7311yescharacteristic
458C23×C4C22×D7311yescharacteristic
459C2×C4⋊C4—42no—
460C2×C4⋊C4—2922no—
461C2×C4⋊C4—2922no—
462C2×C4⋊C4—2922no—
463C2×C4⋊C4—734no—
464C2×C4⋊C4—734no—
465C2×C4⋊C4—734no—
466C2×C4⋊C4—738no—
467C2×C4⋊C4—738no—
468C2×C4⋊C4—738no—
469C2×C4⋊C4—734no—
470C2×C4⋊C4—734no—
471C2×C4⋊C4—734no—
472C2×C4⋊C4—7364no—
473C2×C4⋊C4C4×D7318yes—
474C2×C4⋊C4C22×D7314yes—
475C2×C4⋊C4C22×D7314yes—
476C2×C22⋊C4—734no—
477C2×C22⋊C4—734no—
478C2×C22⋊C4—734no—
479C2×C22⋊C4—734no—
480C2×C22⋊C4—1464no—
481C2×C22⋊C4—1464no—
482C2×C22⋊C4—1464no—
483C2×C22⋊C4—1464no—
484C2×C42—42no—
485C2×C42—2922no—
486C2×C42—2922no—
487C2×C42—2922no—
488C2×C42—734no—
489C2×C42—734no—
490C2×C42—734no—
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#95—734no—
501#95—734no—
502#95—734no—
503#95—734no—
504#95C22×D7314yes—
505#95C22×D7314yes—
506#95C22×D7314yes—
507#95C22×D7314yes—
508C24—734no—
509C24—734no—
510C24—734no—
511C24—732no—
512C24—1462no—
513C24—1462no—
514C24—1462no—
515C24—1462no—
516C24C23×D7311yescharacteristic
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—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—2924no—
536C22×C4—2924no—
537C22×C4—2924no—
538C22×C4—2924no—
539C22×C4—29216no—
540C22×C4—29216no—
541C22×C4—7316no—
542C22×C4—7316no—
543C22×C4—734no—
544C22×C4—734no—
545C22×C4—734no—
546C22×C4—732no—
547C22×C4—732no—
548C22×C4—732no—
549C22×C4—7316no—
550C22×C4—732no—
551C22×C4—732no—
552C22×C4—732no—
553C22×C4—732no—
554C22×C4—1468no—
555C22×C4—1468no—
556C22×C4—14632no—
557C22×C4—1462no—
558C22×C4—1462no—
559C22×C4—1462no—
560C22×C4—1462no—
561C22×C4—1462no—
562C22×C4—1462no—
563C22×C4—1462no—
564C22×C4—1462no—
565C22×C4—1462no—
566C22×C4—1462no—
567C22×C4—1462no—
568C22×C4—1462no—
569C22×C4—1462no—
570C22×C4—1462no—
571C22×C4—1462no—
572C22×C4—1462no—
573C22×C4—1462no—
574C22×C4—1462no—
575C22×C4C2×C4×D7314yes—
576C22×C4C2×C4×D7314yes—
577C22×C4C2×C4×D7314yes—
578C22×C4C23×D7312yes—
579C22×C4C23×D7312yes—
580C22×C4C23×D7312yes—
581C22×C4C23×D7312yes—
582C22×C4C23×D7312yes—
583C22×C4C23×D7312yes—
584C22×C4C23×D7312yes—
585C4⋊C4—44no—
586C4⋊C4—2924no—
587C4⋊C4—2924no—
588C4⋊C4—2924no—
589C4⋊C4—7316no—
590C4⋊C4—7316no—
591C4⋊C4—7316no—
592C4⋊C4C2×C4×D73116yes—
593C22⋊C4—1468no—
594C22⋊C4—1468no—
595C22⋊C4—1468no—
596C22⋊C4—1468no—
597C42—44no—
598C42—2924no—
599C42—2924no—
600C42—2924no—
601C23—734no—
602C23—734no—
603C23—734no—
604C23—7316no—
605C23—1462no—
606C23—1462no—
607C23—1462no—
608C23—1462no—
609C23—1468no—
610C23—1468no—
611C23—1468no—
612C23—1468no—
613C23—1468no—
614C23—1468no—
615C23C22×C4×D7312yes—
616C23#41×D7312yes—
617C23#41×D7312yes—
618C23#1455663612yes—
619C23#1455663712yes—
620C23#1455663812yes—
621C23#1455663912yes—
622C23C24×D7311yescharacteristic
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
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—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—29216no—
649C2×C4—29216no—
650C2×C4—2924no—
651C2×C4—2924no—
652C2×C4—2924no—
653C2×C4—2924no—
654C2×C4—734no—
655C2×C4—734no—
656C2×C4—734no—
657C2×C4—14632no—
658C2×C4—1462no—
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—1462no—
668C2×C4—1462no—
669C2×C4—1462no—
670C2×C4—1462no—
671C2×C4—1462no—
672C2×C4—1462no—
673C2×C4—1462no—
674C2×C4—1462no—
675C2×C4—1462no—
676C2×C4—1468no—
677C2×C4—1468no—
678C2×C4—1468no—
679C2×C4C22×C4×D7314yes—
680C2×C4C22×C4×D7314yes—
681C2×C4C22×C4×D7314yes—
682C22—738no—
683C22—1464no—
684C22—1464no—
685C22—1464no—
686C22—14632no—
687C22—1464no—
688C22—1464no—
689C22—1464no—
690C22#117×D7314yes—
691C22#1798905914yes—
692C22#1798906314yes—
693C22#1798917814yes—
694C22#1798918014yes—
695C22#1798918314yes—
696C22#1798918514yes—
697C22C23×C4×D7311yescharacteristic
698C22C2×#41×D7311yescharacteristic
699C22C2×#41×D7311yescharacteristic
700C22C2×#1455663611yescharacteristic
701C22C2×#1455663711yescharacteristic
702C22C2×#1455663811yescharacteristic
703C22C2×#1455663911yescharacteristic
704C4—24no—
705C4—24no—
706C4—24no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—2922no—
712C4—2922no—
713C4—2922no—
714C4—2922no—
715C4—1464no—
716C4—1464no—
717C4—1464no—
718C2—1468no—
719C2#2261253018yesdirect product factor
720C2C2×#117×D7311yescharacteristic
721C2C2×#1798905911yescharacteristic
722C2C2×#1798906311yescharacteristic
723C2C2×#1798917811yescharacteristic
724C2C2×#1798918011yescharacteristic
725C2C2×#1798918311yescharacteristic
726C2C2×#1798918511yescharacteristic
subgroupG/H
centerC24C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC2×#387×C73C2
socleC24×C73C24
prime radicalC24×D73C23
cosocleC23×C73C25
hypercenterC2×#387D73
hypocenterC73C2×#2313
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #22612530C2direct (N × H)
3. C2×#17988474C2semidirect
4. C2×#17988473C2semidirect
5. C2×#17988472C2semidirect
6. C2×#17988471C2semidirect
7. C2×#17988470C2semidirect
8. C2×#17988469C2semidirect
9. C2×#17988468C2semidirect
16. C2×#387×C73C2semidirect
26. C2×C4⋊C4×D73C4semidirect
35. #17988474C22semidirect
36. #17988473C22semidirect
37. #17988472C22semidirect
38. #17988471C22semidirect
39. #17988470C22semidirect
40. #17988469C22semidirect
41. #17988468C22semidirect
63. #387×C73C22semidirect
100. C4⋊C4×D73C2×C4semidirect
355. C2×C73#2313semidirect
373. C2×#387D73semidirect
380. C73C2×#2313semidirect
409. #387C2×D73semidirect
719. C2#22612530direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D732
#226125302
C2×#179884742
C2×#179884732
C2×#179884722
C2×#179884712
C2×#179884702
C2×#179884692
C2×#179884682
C2×#179884492
C2×#179884462
C2×#179884442
C2×C4×#119240052
C2×#179884342
C2×#387×C732
C2×#231373