Finite Group Databasebeta

← C2×#22623547 #33993077

Subgroups — C2×#22623547 #33993077

Order 18688.

7706 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623547C2132yesmaximal, direct product factor
2C2×#17989313C211yesmaximal, characteristic, complemented
3C2×#17989306C213yesmaximal, complemented
4C2×#17989277C213yesmaximal, complemented
5C2×#17989271C213yesmaximal, complemented
6C2×Q8×C22⋊D73C211yesmaximal, characteristic, complemented
7C2×#17989244C211yesmaximal, characteristic, complemented
8C2×#17989237C213yesmaximal, complemented
9C2×#17989139C213yesmaximal, complemented
10C2×#17989118C213yesmaximal, complemented
11C2×#17989116C213yesmaximal, complemented
12C2×#41×Dic73C211yesmaximal, characteristic, complemented
13C2×C4×#11924027C213yesmaximal, complemented
14C22×Q8×Dic73C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D73C211yesmaximal, characteristic, complemented
16C2×#548×C73C211yesmaximal, characteristic, complemented
17C22×#11924027C2213yes—
18C22×Q8×D73C2211yescharacteristic
19#17989313C22116yescomplemented
20#17989306C22148yescomplemented
21#17989277C22148yescomplemented
22#17989271C22148yescomplemented
23Q8×C22⋊D73C22116yescomplemented
24#17989244C22116yescomplemented
25#17989237C22148yescomplemented
26#17989139C22148yescomplemented
27C2×#14556590C2213yes—
28C2×#14556589C2213yes—
29#17989118C22148yescomplemented
30#17989116C22148yescomplemented
31C2×#14556584C2216yes—
32C2×#14556584C2216yes—
33C2×#14556583C2213yes—
34C2×#14556582C2213yes—
35C2×#14556581C2216yes—
36C2×#14556578C2213yes—
37C2×#14556573C2216yes—
38C2×#14556572C2216yes—
39C2×#14556570C2213yes—
40C2×#14556570C2213yes—
41C2×#14556568C2216yes—
42C2×#14556567C2213yes—
43C2×#14556562C2213yes—
44#41×Dic73C22116yescomplemented
45C4×#11924027C22148yescomplemented
46C2×Q8×Dic73C2211yescharacteristic
47C2×Q8×Dic73C2211yescharacteristic
48C2×Q8×Dic73C2211yescharacteristic
49C2×Q8×Dic73C2213yes—
50C2×Q8×Dic73C2213yes—
51C2×Q8×Dic73C22116yescomplemented
52C2×C4×Dic146C2213yes—
53C2×C4×Dic146C2213yes—
54C2×#14556556C2213yes—
55C2×#14556556C2213yes—
56C4×Q8×D73C22116yescomplemented
57C2×D4×Dic73C2213yes—
58C2×D4×Dic73C2213yes—
59C2×D4×Dic73C2213yes—
60C2×C4×C22⋊D73C2213yes—
61C2×C4×C22⋊D73C2213yes—
62C2×#14556551C2211yescharacteristic
63C2×#14556551C2213yes—
64C2×#14556550C2213yes—
65C2×#14556549C2213yes—
66C2×#14556547C2213yes—
67C2×#14556547C2213yes—
68C2×#14556547C2216yes—
69C22×C4⋊Dic73C2213yes—
70C2×C4⋊C4×D73C2213yes—
71C22×C4×Dic73C2213yes—
72C22×C4×Dic73C2213yes—
73C2×C42×D73C2213yes—
74C22×#41×C73C2211yescharacteristic
75C23×Q8×C73C2211yescharacteristic
76#548×C73C22116yescomplemented
77C2×#124×C73C2213yes—
78C2×C22⋊Q8×C73C2213yes—
79C2×#121×C73C2213yes—
80C2×C4×Q8×C73C2211yescharacteristic
81C2×C4×D4×C73C2213yes—
82C2×#11924027—224no—
83C2×#11924027C23124yes—
84C22×Dic146C2313yes—
85C22×Dic146C2313yes—
86C2×Q8×D73—28no—
87C2×Q8×D73C2318yes—
88C22×C22⋊D73C2313yes—
89C22×C22⋊D73C2311yescharacteristic
90C23×Dic73C2313yes—
91C23×Dic73C2313yes—
92C23×Dic73C2311yescharacteristic
93C23×Dic73C2313yes—
94C22×C4×D73C2313yes—
95C22×C4×D73C2313yes—
96C22×C4×D73C2311yescharacteristic
97#14556590C23124yes—
98#14556589C23124yes—
99#14556584C23148yes—
100#14556584C23148yes—
101#14556583C23124yes—
102#14556582C23124yes—
103#14556581C23148yes—
104#14556578C23124yes—
105#14556573C23148yes—
106#14556572C23148yes—
107#14556570C23124yes—
108#14556570C23124yes—
109#14556568C23148yes—
110#14556567C23124yes—
111#14556562C23124yes—
112Q8×Dic73C23124yes—
113Q8×Dic73C2318yes—
114Q8×Dic73C2318yes—
115Q8×Dic73C23124yes—
116Q8×Dic73C2318yes—
117C4×Dic146C23124yes—
118C4×Dic146C23124yes—
119#14556556C23124yes—
120#14556556C23124yes—
121D4×Dic73C23124yes—
122D4×Dic73C23124yes—
123D4×Dic73C23124yes—
124C4×C22⋊D73C23124yes—
125C4×C22⋊D73C23124yes—
126#14556551C2318yes—
127#14556551C23124yes—
128#14556550C23124yes—
129#14556549C23124yes—
130#14556547C23148yes—
131#14556547C23124yes—
132#14556547C23124yes—
133C2×C4⋊Dic73C2313yes—
134C2×C4⋊Dic73C23124yes—
135C2×C4⋊Dic73C2313yes—
136C2×C4⋊Dic73C2316yes—
137C2×C4⋊Dic73C2313yes—
138C2×C4⋊Dic73C2313yes—
139C2×#11924007C2313yes—
140C2×#11924007C2316yes—
141C2×#11924007C2316yes—
142C2×#11924007C2316yes—
143C2×#11924007C2311yescharacteristic
144C2×#11924007C2313yes—
145C2×#11924007C2313yes—
146C4⋊C4×D73C23124yes—
147C2×C22⋊Dic73C2313yes—
148C2×C22⋊Dic73C2313yes—
149C2×C22⋊Dic73C2316yes—
150C2×C22⋊Dic73C2316yes—
151C2×#11924005C2311yescharacteristic
152C2×#11924005C2313yes—
153C2×C4×Dic73C2313yes—
154C2×C4×Dic73C23124yes—
155C2×C4×Dic73C2313yes—
156C2×C4×Dic73C2313yes—
157C2×C4×Dic73C2313yes—
158C2×C4×Dic73C2311yescharacteristic
159C2×C4×Dic73C2313yes—
160C2×C4×Dic73C2313yes—
161C2×C4×Dic73C2313yes—
162C2×C4×Dic73C2313yes—
163C2×C4×Dic73C23124yes—
164C42×D73C23124yes—
165C2×#41×C73—28no—
166C2×#41×C73C2318yes—
167C22×Q8×C73—28no—
168C22×Q8×C73C2313yes—
169C22×Q8×C73C2318yes—
170C22×Q8×C73C2311yescharacteristic
171C22×D4×C73C2313yes—
172C22×D4×C73C2313yes—
173C23×C4×C73C2313yes—
174C23×C4×C73C2313yes—
175#124×C73C23124yes—
176C22⋊Q8×C73C23124yes—
177#121×C73C23124yes—
178C4×Q8×C73C2318yes—
179C4×D4×C73C23124yes—
180C2×C4⋊C4×C73C2313yes—
181C2×C4⋊C4×C73C2313yes—
182C2×C22⋊C4×C73C2311yescharacteristic
183C2×C22⋊C4×C73C2313yes—
184C2×C22⋊C4×C73C2316yes—
185C2×C42×C73C2313yes—
186C23×D73C2411yescharacteristic
187#11924027—296no—
188C2×Dic146—212no—
189C2×Dic146—212no—
190C2×Dic146C24112yes—
191C2×Dic146C24112yes—
192Q8×D73—232no—
193C2×C22⋊D73—212no—
194C2×C22⋊D73#4118yescomplemented
195C2×C22⋊D73C24112yes—
196C2×C22⋊D73C2414yes—
197C22×Dic73—212no—
198C22×Dic73—212no—
199C22×Dic73—24no—
200C22×Dic73—212no—
201C22×Dic73C2411yescharacteristic
202C22×Dic73C2414yes—
203C22×Dic73C2413yes—
204C22×Dic73C2413yes—
205C22×Dic73C2413yes—
206C22×Dic73C2413yes—
207C22×Dic73C24112yes—
208C22×Dic73C24112yes—
209C22×Dic73C24112yes—
210C22×Dic73C2411yescharacteristic
211C22×Dic73C2411yescharacteristic
212C2×C4×D73—212no—
213C2×C4×D73—212no—
214C2×C4×D73—24no—
215C2×C4×D73C2414yes—
216C2×C4×D73C24112yes—
217C2×C4×D73C24112yes—
218C4⋊Dic73C24112yes—
219C4⋊Dic73C24112yes—
220C4⋊Dic73C24124yes—
221C4⋊Dic73C24112yes—
222C4⋊Dic73C24112yes—
223#11924007C24124yes—
224#11924007C2414yes—
225#11924007C24112yes—
226#11924007C24112yes—
227#11924007C24112yes—
228#11924007C24124yes—
229#11924007C24124yes—
230C22⋊Dic73C24112yes—
231C22⋊Dic73C24112yes—
232C22⋊Dic73C24124yes—
233C22⋊Dic73C24124yes—
234#11924005C2414yes—
235#11924005C24112yes—
236C4×Dic73C24112yes—
237C4×Dic73C24112yes—
238C4×Dic73C24112yes—
239C4×Dic73C2414yes—
240C4×Dic73C24112yes—
241C4×Dic73C24112yes—
242C4×Dic73C24112yes—
243C4×Dic73C24112yes—
244C4×Dic73C24112yes—
245C24×C73C2413yes—
246C24×C73C2411yescharacteristic
247#41×C73—232no—
248C2×Q8×C73—232no—
249C2×Q8×C73—212no—
250C2×Q8×C73#4118yescomplemented
251C2×Q8×C73C24112yes—
252C2×Q8×C73C2414yes—
253C2×D4×C73—212no—
254C2×D4×C73—212no—
255C2×D4×C73C24112yes—
256C2×D4×C73C24112yes—
257C22×C4×C73—212no—
258C22×C4×C73—212no—
259C22×C4×C73C2411yescharacteristic
260C22×C4×C73C2413yes—
261C22×C4×C73C2413yes—
262C22×C4×C73C2411yescharacteristic
263C22×C4×C73C24112yes—
264C22×C4×C73C24112yes—
265C22×C4×C73C2413yes—
266C4⋊C4×C73C24112yes—
267C4⋊C4×C73C24112yes—
268C22⋊C4×C73C2414yes—
269C22⋊C4×C73C24112yes—
270C22⋊C4×C73C24124yes—
271C42×C73C24112yes—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73—26no—
275C23×C73—26no—
276C23×C73—26no—
277C23×C73C2×#4114yes—
278C23×C73C2516yes—
279C23×C73C2512yes—
280C23×C73C2511yescharacteristic
281C22×D73—22no—
282C22×D73—22no—
283C22×D73C2×#4114yes—
284C22×D73C2512yes—
285Q8×C73—224no—
286Q8×C73C2×#41116yescomplemented
287D4×C73—224no—
288D4×C73—224no—
289C2×C4×C73—22no—
290C2×C4×C73—26no—
291C2×C4×C73—26no—
292C2×C4×C73—22no—
293C2×C4×C73—224no—
294C2×C4×C73—224no—
295C2×C4×C73C2×#41112yes—
296C2×C4×C73C2512yes—
297C2×C4×C73C2516yes—
298C2×C4×C73C2516yes—
299C2×C4×C73C2512yes—
300C2×C4×C73C2516yes—
301C22⋊D73—224no—
302C22⋊D73C2×#41116yescomplemented
303C2×Dic73—26no—
304C2×Dic73—26no—
305C2×Dic73—26no—
306C2×Dic73—224no—
307C2×Dic73—22no—
308C2×Dic73—26no—
309C2×Dic73—224no—
310C2×Dic73—28no—
311C2×Dic73—224no—
312C2×Dic73C2×#4114yes—
313C2×Dic732−1+414yes—
314C2×Dic73C2512yes—
315C2×Dic73C2516yes—
316C2×Dic73C2516yes—
317C2×Dic73C2516yes—
318C2×Dic73C2516yes—
319C2×Dic73C2512yes—
320C2×Dic73C2512yes—
321C4×D73—224no—
322C4×D73—224no—
323C4×D73—28no—
324Dic146—224no—
325Dic146—224no—
326C22×C73—22no—
327C22×C73—22no—
328C22×C73—28no—
329C22×C73—26no—
330C22×C73—26no—
331C22×C73—26no—
332C22×C73—412no—
333C22×C73C22×#4114yes—
334C22×C73C22×#4112yes—
335C22×C73C22×#4112yes—
336C22×C73C2×2−1+412yes—
337C22×C73C2611yescharacteristic
338C2×D73—22no—
339C2×D73—22no—
340C2×D73—28no—
341C2×D73C22×#4114yes—
342C4×C73—26no—
343C4×C73—22no—
344C4×C73—26no—
345C4×C73—22no—
346C4×C73C22×#41112yes—
347Dic73—26no—
348Dic73—26no—
349Dic73—26no—
350Dic73—22no—
351Dic73—26no—
352Dic73C22×#4114yes—
353Dic73C2×2−1+414yes—
354C2×#3482—731nomaximal, Sylow
355C2×C73—24no—
356C2×C73—46no—
357C2×C73#348214yescomplemented
358C2×C73C23×#4111yescharacteristic
359C2×C73C23×#4111yescharacteristic
360C2×C73C22×2−1+411yescharacteristic
361D73—24no—
362#3482—7332no—
363C2×#557—731no—
364C2×#556—733no—
365C2×#552—733no—
366C2×#552—733no—
367C2×D4×Q8—731no—
368C2×#548—731no—
369C2×#548D7311yescharacteristic, complemented
370C2×#547—733no—
371C2×#533—733no—
372C2×#529—733no—
373C2×#529—733no—
374C2×C4×#41—731no—
375C2×C4×#41—733no—
376C22×C4×Q8—731no—
377C22×C4×Q8—731no—
378C73C2×#348211yescharacteristic, complemented, Sylow
379C22×#41—733no—
380C22×#41C2×D7311yescharacteristic
381C23×Q8—731no—
382C23×Q8C2×D7311yescharacteristic
383#557—7316no—
384#556—7348no—
385#552—7348no—
386#552—7348no—
387D4×Q8—7316no—
388#548—7316no—
389#548C2×D73116yescomplemented
390#547—7348no—
391#533—7348no—
392C2×C4⋊Q8—733no—
393C2×C4⋊Q8—733no—
394#529—7348no—
395#529—7348no—
396C2×#126—736no—
397C2×#126—736no—
398C2×#125—733no—
399C2×#125—736no—
400C2×#125—733no—
401C2×#124—733no—
402C2×#124C2×D7313yes—
403C2×#123—736no—
404C2×#123—736no—
405C2×C22⋊Q8—733no—
406C2×C22⋊Q8—733no—
407C2×C22⋊Q8—733no—
408C2×C22⋊Q8—736no—
409C2×C22⋊Q8C2×D7313yes—
410C2×#121—733no—
411C2×#121C2×D7313yes—
412C4×#41—7316no—
413C4×#41—7348no—
414C2×C4×Q8—731no—
415C2×C4×Q8—733no—
416C2×C4×Q8—731no—
417C2×C4×Q8—733no—
418C2×C4×Q8—7316no—
419C2×C4×Q8—731no—
420C2×C4×Q8—7316no—
421C2×C4×Q8—733no—
422C2×C4×Q8—733no—
423C2×C4×Q8—733no—
424C2×C4×Q8—733no—
425C2×C4×Q8C2×D7311yescharacteristic
426C2×C4×D4—733no—
427C2×C4×D4—733no—
428C2×C4×D4—733no—
429C2×C4×D4—733no—
430C2×C4×D4—733no—
431C2×C4×D4—731no—
432C2×C4×D4—733no—
433C2×C4×D4C2×D7313yes—
434C2×#117—733no—
435C2×#117—733no—
436C2×#117—733no—
437C2×#117—733no—
438C2×#117—736no—
439C22×C4⋊C4—733no—
440C22×C4⋊C4—733no—
441C22×C42—733no—
442C22×C42—733no—
443C22×C42—733no—
444C2×#41—28no—
445C2×#41—7324no—
446C2×#41—14624no—
447C2×#41C22×D7318yes—
448C22×Q8—28no—
449C22×Q8—738no—
450C22×Q8—733no—
451C22×Q8—733no—
452C22×Q8—1468no—
453C22×Q8C22×D7313yes—
454C22×Q8C22×D7318yes—
455C22×Q8C22×D7311yescharacteristic
456C22×D4—731no—
457C22×D4—733no—
458C22×D4C22×D7313yes—
459C22×D4C22×D7313yes—
460C23×C4—733no—
461C23×C4—733no—
462C23×C4—733no—
463C23×C4—731no—
464C23×C4—733no—
465C23×C4—733no—
466C23×C4—731no—
467C23×C4C22×D7313yes—
468C23×C4C22×D7313yes—
469C4⋊Q8—7324no—
470C4⋊Q8—7324no—
471#126—7348no—
472#126—7348no—
473#125—7324no—
474#125—7348no—
475#125—7324no—
476#124—7324no—
477#124C22×D73124yes—
478#123—7348no—
479#123—7348no—
480C22⋊Q8—7324no—
481C22⋊Q8—7324no—
482C22⋊Q8—7324no—
483C22⋊Q8—7348no—
484C22⋊Q8C22×D73124yes—
485#121—7324no—
486#121C22×D73124yes—
487C4×Q8—738no—
488C4×Q8—7324no—
489C4×Q8—738no—
490C4×Q8—7324no—
491C4×Q8—738no—
492C4×Q8—7324no—
493C4×Q8—7324no—
494C4×Q8—7324no—
495C4×Q8—7324no—
496C4×Q8C22×D7318yes—
497C4×D4—7324no—
498C4×D4—7324no—
499C4×D4—7324no—
500C4×D4—7324no—
501C4×D4—7324no—
502C4×D4—738no—
503C4×D4—7324no—
504C4×D4C22×D73124yes—
505#117—7324no—
506#117—7324no—
507#117—7324no—
508#117—7324no—
509#117—7348no—
510C2×C4⋊C4—733no—
511C2×C4⋊C4—733no—
512C2×C4⋊C4—736no—
513C2×C4⋊C4—736no—
514C2×C4⋊C4—7324no—
515C2×C4⋊C4—731no—
516C2×C4⋊C4—733no—
517C2×C4⋊C4—733no—
518C2×C4⋊C4—733no—
519C2×C4⋊C4—733no—
520C2×C4⋊C4—733no—
521C2×C4⋊C4—736no—
522C2×C4⋊C4—736no—
523C2×C4⋊C4—7324no—
524C2×C4⋊C4C22×D7313yes—
525C2×C4⋊C4C22×D7313yes—
526C2×C22⋊C4—733no—
527C2×C22⋊C4—736no—
528C2×C22⋊C4—733no—
529C2×C22⋊C4—736no—
530C2×C22⋊C4—731no—
531C2×C22⋊C4—733no—
532C2×C22⋊C4C22×D7311yescharacteristic
533C2×C22⋊C4C22×D7313yes—
534C2×C22⋊C4C22×D7316yes—
535C2×C42—733no—
536C2×C42—733no—
537C2×C42—733no—
538C2×C42—733no—
539C2×C42—733no—
540C2×C42—733no—
541C2×C42—733no—
542C2×C42—731no—
543C2×C42—733no—
544C2×C42—7324no—
545C2×C42—7324no—
546C2×C42—7324no—
547C2×C42C22×D7313yes—
548C24—731no—
549C24C23×D7313yes—
550C24C23×D7311yescharacteristic
551#41—232no—
552#41—14696no—
553C2×Q8—232no—
554C2×Q8—212no—
555C2×Q8—7312no—
556C2×Q8—7312no—
557C2×Q8—14612no—
558C2×Q8—14632no—
559C2×Q8—14612no—
560C2×Q8#1192402718yescomplemented
561C2×Q8C23×D73112yes—
562C2×Q8C23×D7314yes—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—738no—
566C2×D4—734no—
567C2×D4—7312no—
568C2×D4—14612no—
569C2×D4C23×D73112yes—
570C2×D4C23×D73112yes—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—731no—
574C22×C4—731no—
575C22×C4—734no—
576C22×C4—7312no—
577C22×C4—7312no—
578C22×C4—7312no—
579C22×C4—731no—
580C22×C4—733no—
581C22×C4—733no—
582C22×C4—733no—
583C22×C4—733no—
584C22×C4—734no—
585C22×C4—7312no—
586C22×C4—7312no—
587C22×C4—1464no—
588C22×C4—14612no—
589C22×C4—1464no—
590C22×C4—14612no—
591C22×C4—14612no—
592C22×C4—14612no—
593C22×C4—14612no—
594C22×C4C23×D73112yes—
595C22×C4C23×D73112yes—
596C22×C4C23×D7311yescharacteristic
597C22×C4C23×D7311yescharacteristic
598C22×C4C23×D7313yes—
599C22×C4C23×D7313yes—
600C22×C4C23×D7313yes—
601C4⋊C4—7324no—
602C4⋊C4—734no—
603C4⋊C4—7312no—
604C4⋊C4—7312no—
605C4⋊C4—7312no—
606C4⋊C4—7324no—
607C4⋊C4—7324no—
608C4⋊C4—7312no—
609C4⋊C4—7312no—
610C4⋊C4—7324no—
611C4⋊C4—7312no—
612C4⋊C4—7312no—
613C4⋊C4C23×D73112yes—
614C4⋊C4C23×D73112yes—
615C22⋊C4—7312no—
616C22⋊C4—7324no—
617C22⋊C4—7312no—
618C22⋊C4—7324no—
619C22⋊C4—734no—
620C22⋊C4—7312no—
621C22⋊C4C23×D7314yes—
622C22⋊C4C23×D73112yes—
623C22⋊C4C23×D73124yes—
624C42—734no—
625C42—7312no—
626C42—7312no—
627C42—7312no—
628C42—7312no—
629C42—7312no—
630C42—7312no—
631C42—7312no—
632C42—7312no—
633C42C23×D73112yes—
634C23—22no—
635C23—22no—
636C23—26no—
637C23—26no—
638C23—26no—
639C23—734no—
640C23—732no—
641C23—1462no—
642C23—1462no—
643C23#41×D7314yes—
644C23C24×D7316yes—
645C23C24×D7312yes—
646C23C24×D7311yescharacteristic
647Q8—224no—
648Q8—14624no—
649Q8—14624no—
650Q8C2×#11924027116yescomplemented
651D4—224no—
652D4—224no—
653D4—7316no—
654D4—14624no—
655C2×C4—26no—
656C2×C4—22no—
657C2×C4—26no—
658C2×C4—22no—
659C2×C4—224no—
660C2×C4—224no—
661C2×C4—734no—
662C2×C4—734no—
663C2×C4—732no—
664C2×C4—732no—
665C2×C4—732no—
666C2×C4—736no—
667C2×C4—736no—
668C2×C4—736no—
669C2×C4—736no—
670C2×C4—1468no—
671C2×C4—14624no—
672C2×C4—14624no—
673C2×C4—1468no—
674C2×C4—14624no—
675C2×C4—1466no—
676C2×C4—1466no—
677C2×C4—14624no—
678C2×C4—1466no—
679C2×C4—1462no—
680C2×C4—1466no—
681C2×C4—14624no—
682C2×C4C2×#11924027112yes—
683C2×C4C24×D7312yes—
684C2×C4C24×D7312yes—
685C2×C4C24×D7316yes—
686C2×C4C24×D7316yes—
687C2×C4C24×D7316yes—
688C22—28no—
689C22—22no—
690C22—22no—
691C22—26no—
692C22—26no—
693C22—26no—
694C22—412no—
695C22—734no—
696C22—1468no—
697C22—1462no—
698C22—1462no—
699C22C2×#41×D7314yes—
700C22C2×#41×D7312yes—
701C22C22×#1192402712yes—
702C222−1+4×D7312yes—
703C22C25×D7311yescharacteristic
704C4—26no—
705C4—22no—
706C4—26no—
707C4—22no—
708C4—734no—
709C4—734no—
710C4—1466no—
711C4—1466no—
712C4—1466no—
713C4—1462no—
714C4—1466no—
715C4C22×#11924027112yes—
716C2—24no—
717C2—46no—
718C2—1464no—
719C2#2262354714yesdirect product factor
720C2C22×#41×D7311yescharacteristic
721C2C23×#1192402711yescharacteristic
722C2C2×2−1+4×D7311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#548×C73C2
socleC23×C73C25
hypercenterC2×#548D73
hypocenterC73C2×#3482
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #22623547C2direct (N × H)
2. C2×#17989313C2semidirect
3. C2×#17989306C2semidirect
4. C2×#17989277C2semidirect
5. C2×#17989271C2semidirect
6. C2×Q8×C22⋊D73C2semidirect
7. C2×#17989244C2semidirect
8. C2×#17989237C2semidirect
9. C2×#17989139C2semidirect
10. C2×#17989118C2semidirect
11. C2×#17989116C2semidirect
12. C2×#41×Dic73C2semidirect
13. C2×C4×#11924027C2semidirect
14. C22×Q8×Dic73C2semidirect
15. C2×C4×Q8×D73C2semidirect
16. C2×#548×C73C2semidirect
19. #17989313C22semidirect
20. #17989306C22semidirect
21. #17989277C22semidirect
22. #17989271C22semidirect
23. Q8×C22⋊D73C22semidirect
24. #17989244C22semidirect
25. #17989237C22semidirect
26. #17989139C22semidirect
29. #17989118C22semidirect
30. #17989116C22semidirect
44. #41×Dic73C22semidirect
45. C4×#11924027C22semidirect
51. C2×Q8×Dic73C22semidirect
56. C4×Q8×D73C22semidirect
76. #548×C73C22semidirect
194. C2×C22⋊D73#41semidirect
250. C2×Q8×C73#41semidirect
286. Q8×C73C2×#41semidirect
302. C22⋊D73C2×#41semidirect
357. C2×C73#3482semidirect
369. C2×#548D73semidirect
378. C73C2×#3482semidirect
389. #548C2×D73semidirect
560. C2×Q8#11924027semidirect
650. Q8C2×#11924027semidirect
719. C2#22623547direct (N × H)

Maximal subgroups

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

subgroupindex
#226235472
C2×#179893132
C2×#179893062
C2×#179892772
C2×#179892712
C2×Q8×C22⋊D732
C2×#179892442
C2×#179892372
C2×#179891392
C2×#179891182
C2×#179891162
C2×#41×Dic732
C2×C4×#119240272
C22×Q8×Dic732
C2×C4×Q8×D732
C2×#548×C732
C2×#348273