Finite Group Databasebeta

← C2×#22623548 #33993076

Subgroups — C2×#22623548 #33993076

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#22623548C2132yesmaximal, direct product factor
2C2×#17989313C211yesmaximal, characteristic, complemented
3C2×#17989309C213yesmaximal, complemented
4C2×#17989278C213yesmaximal, complemented
5C2×#17989272C213yesmaximal, complemented
6C2×Q8×C22⋊D73C211yesmaximal, characteristic, complemented
7C2×#17989249C211yesmaximal, characteristic, complemented
8C2×#17989248C211yesmaximal, characteristic, complemented
9C2×#17989238C213yesmaximal, complemented
10C2×#17989141C213yesmaximal, complemented
11C2×#17989124C213yesmaximal, complemented
12C2×#17989121C213yesmaximal, complemented
13C2×C4×#11924029C211yesmaximal, characteristic, complemented
14C2×C4×#11924028C213yesmaximal, complemented
15C2×C4×Q8×D73C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×#11924028C2213yes—
19C22×Q8×D73C2211yescharacteristic
20#17989313C22116yescomplemented
21#17989309C22148yescomplemented
22#17989278C22148yescomplemented
23#17989272C22148yescomplemented
24Q8×C22⋊D73C22116yescomplemented
25#17989249C22116yescomplemented
26#17989248C22116yescomplemented
27#17989238C22148yescomplemented
28#17989141C22148yescomplemented
29C2×#14556590C2213yes—
30C2×#14556589C2213yes—
31#17989124C22148yescomplemented
32#17989121C22148yescomplemented
33C2×#14556586C2216yes—
34C2×#14556585C2216yes—
35C2×#14556583C2213yes—
36C2×#14556582C2213yes—
37C2×#14556581C2216yes—
38C2×#14556580C2213yes—
39C2×#14556579C2213yes—
40C2×#14556576C2216yes—
41C2×#14556574C2216yes—
42C2×#14556571C2213yes—
43C2×#14556570C2213yes—
44C2×#14556569C2216yes—
45C2×#14556567C2213yes—
46C2×#14556567C2213yes—
47C2×#14556566C2213yes—
48C2×#14556565C2213yes—
49C4×#11924029C22116yescomplemented
50C4×#11924028C22148yescomplemented
51C2×Q8×Dic73C2211yescharacteristic
52C2×Q8×Dic73C2211yescharacteristic
53C2×C4×Dic146C2213yes—
54C2×C4×Dic146C2213yes—
55C2×C4×Dic146C2213yes—
56C2×#14556556C2213yes—
57C4×Q8×D73C22116yescomplemented
58C2×C4×D292C2213yes—
59C2×C4×D292C2213yes—
60C2×C4×D292C2213yes—
61C2×#14556553C2213yes—
62C2×C4×C22⋊D73C2211yescharacteristic
63C2×C4×C22⋊D73C2213yes—
64C2×C4×C22⋊D73C2213yes—
65C2×C4×C22⋊D73C2213yes—
66C2×#14556550C2213yes—
67C2×#14556549C2213yes—
68C2×#14556548C2213yes—
69C2×#14556548C2213yes—
70C2×#14556548C2216yes—
71C2×C4⋊C4×D73C2213yes—
72C2×C42×D73C2213yes—
73C2×C42×D73C2213yes—
74C23×Q8×C73C2211yescharacteristic
75C2×C4×Q8×C73C2211yescharacteristic
76C2×C4×Q8×C73C2211yescharacteristic
77C2×C4×Q8×C73C2213yes—
78C2×C4×Q8×C73C2213yes—
79C2×C4×Q8×C73C22116yescomplemented
80C22×C4⋊C4×C73C2213yes—
81C22×C42×C73C2213yes—
82C2×#11924029—28no—
83C2×#11924029C2318yes—
84C2×#11924028—224no—
85C2×#11924028C23124yes—
86C22×Dic146C2313yes—
87C22×Dic146C2313yes—
88C2×Q8×D73—28no—
89C2×Q8×D73C2318yes—
90C22×D292C2313yes—
91C22×D292C2313yes—
92C22×C22⋊D73C2313yes—
93C22×C22⋊D73C2311yescharacteristic
94C22×C4×D73C2313yes—
95C22×C4×D73C2313yes—
96C22×C4×D73C2313yes—
97C22×C4×D73C2313yes—
98C22×C4×D73C2311yescharacteristic
99C22×C4×D73C2313yes—
100#14556590C23124yes—
101#14556589C23124yes—
102#14556586C23148yes—
103#14556585C23148yes—
104#14556583C23124yes—
105#14556582C23124yes—
106#14556581C23148yes—
107#14556580C23124yes—
108#14556579C23124yes—
109#14556576C23148yes—
110#14556574C23148yes—
111#14556571C23124yes—
112#14556570C23124yes—
113#14556569C23148yes—
114#14556567C23124yes—
115#14556567C23124yes—
116#14556566C23124yes—
117#14556565C23124yes—
118Q8×Dic73C2318yes—
119Q8×Dic73C2318yes—
120C4×Dic146C23124yes—
121C4×Dic146C23124yes—
122C4×Dic146C23124yes—
123#14556556C23124yes—
124C4×D292C23124yes—
125C4×D292C23124yes—
126C4×D292C23124yes—
127#14556553C23124yes—
128C4×C22⋊D73C23124yes—
129C4×C22⋊D73C23124yes—
130C4×C22⋊D73C23124yes—
131C4×C22⋊D73C2318yes—
132#14556550C23124yes—
133#14556549C23124yes—
134#14556548C23148yes—
135#14556548C23124yes—
136#14556548C23124yes—
137C2×C4⋊Dic73C2313yes—
138C2×C4⋊Dic73C2313yes—
139C2×C4⋊Dic73C2313yes—
140C2×C4⋊Dic73C2313yes—
141C2×#11924007C2313yes—
142C2×#11924007C2316yes—
143C2×#11924007C2316yes—
144C2×#11924007C2316yes—
145C2×#11924007C2311yescharacteristic
146C2×#11924007C2313yes—
147C2×#11924007C2313yes—
148C4⋊C4×D73C23124yes—
149C2×C22⋊Dic73C2311yescharacteristic
150C2×C22⋊Dic73C2313yes—
151C2×#11924005C2311yescharacteristic
152C2×#11924005C2313yes—
153C2×#11924005C2313yes—
154C2×#11924005C2313yes—
155C2×#11924005C2316yes—
156C2×#11924005C2316yes—
157C2×#11924005C2316yes—
158C2×C4×Dic73C2313yes—
159C2×C4×Dic73C2311yescharacteristic
160C2×C4×Dic73C2313yes—
161C2×C4×Dic73C2313yes—
162C2×C4×Dic73C2313yes—
163C2×C4×Dic73C2313yes—
164C42×D73C23124yes—
165C42×D73C23124yes—
166C22×Q8×C73—28no—
167C22×Q8×C73C2313yes—
168C22×Q8×C73C2318yes—
169C22×Q8×C73C2311yescharacteristic
170C23×C4×C73C2313yes—
171C23×C4×C73C2311yescharacteristic
172C23×C4×C73C2313yes—
173C4×Q8×C73C23124yes—
174C4×Q8×C73C2318yes—
175C4×Q8×C73C23124yes—
176C4×Q8×C73C2318yes—
177C2×C4⋊C4×C73C2313yes—
178C2×C4⋊C4×C73C23124yes—
179C2×C4⋊C4×C73C2313yes—
180C2×C4⋊C4×C73C2316yes—
181C2×C42×C73C23124yes—
182C2×C42×C73C2313yes—
183C2×C42×C73C2313yes—
184C2×C42×C73C2313yes—
185C2×C42×C73C2313yes—
186C23×D73C2413yes—
187C23×D73C2411yescharacteristic
188#11924029—232no—
189#11924028—296no—
190C2×Dic146—212no—
191C2×Dic146—212no—
192C2×Dic146C24112yes—
193C2×Dic146C24112yes—
194Q8×D73—232no—
195C2×D292—212no—
196C2×D292—212no—
197C2×D292C24112yes—
198C2×D292C24112yes—
199C2×C22⋊D73—212no—
200C2×C22⋊D73#4118yescomplemented
201C2×C22⋊D73C24112yes—
202C2×C22⋊D73C2414yes—
203C22×Dic73C2411yescharacteristic
204C22×Dic73C2411yescharacteristic
205C22×Dic73C2413yes—
206C22×Dic73C2413yes—
207C22×Dic73C2413yes—
208C22×Dic73C2411yescharacteristic
209C2×C4×D73—212no—
210C2×C4×D73—212no—
211C2×C4×D73—212no—
212C2×C4×D73—24no—
213C2×C4×D73—212no—
214C2×C4×D73—212no—
215C2×C4×D73C2414yes—
216C2×C4×D73C24112yes—
217C2×C4×D73C24112yes—
218C2×C4×D73C24112yes—
219C2×C4×D73C24112yes—
220C2×C4×D73C24112yes—
221C4⋊Dic73C24112yes—
222C4⋊Dic73C24112yes—
223C4⋊Dic73C24112yes—
224C4⋊Dic73C24112yes—
225#11924007C24124yes—
226#11924007C2414yes—
227#11924007C24112yes—
228#11924007C24112yes—
229#11924007C24112yes—
230#11924007C24124yes—
231#11924007C24124yes—
232C22⋊Dic73C2414yes—
233C22⋊Dic73C24112yes—
234#11924005C2414yes—
235#11924005C24112yes—
236#11924005C24112yes—
237#11924005C24112yes—
238#11924005C24124yes—
239#11924005C24124yes—
240#11924005C24124yes—
241C4×Dic73C2414yes—
242C4×Dic73C24112yes—
243C4×Dic73C24112yes—
244C4×Dic73C24112yes—
245C4×Dic73C24112yes—
246C4×Dic73C24112yes—
247C24×C73C2411yescharacteristic
248C2×Q8×C73—232no—
249C2×Q8×C73—212no—
250C2×Q8×C73#4118yescomplemented
251C2×Q8×C73C24112yes—
252C2×Q8×C73C2414yes—
253C22×C4×C73—212no—
254C22×C4×C73—212no—
255C22×C4×C73—24no—
256C22×C4×C73C2411yescharacteristic
257C22×C4×C73C2414yes—
258C22×C4×C73C2413yes—
259C22×C4×C73C2413yes—
260C22×C4×C73C24112yes—
261C22×C4×C73C2413yes—
262C22×C4×C73C24112yes—
263C22×C4×C73C2413yes—
264C22×C4×C73C2411yescharacteristic
265C4⋊C4×C73C24112yes—
266C4⋊C4×C73C24112yes—
267C4⋊C4×C73C24124yes—
268C42×C73C24112yes—
269C42×C73C24112yes—
270C42×C73C24112yes—
271C42×C73C24112yes—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73C2×#4114yes—
275C23×C73C2512yes—
276C23×C73C2511yescharacteristic
277C22×D73—22no—
278C22×D73—22no—
279C22×D73—26no—
280C22×D73—26no—
281C22×D73—26no—
282C22×D73C2×#4114yes—
283C22×D73C2516yes—
284C22×D73C2512yes—
285Q8×C73—224no—
286Q8×C73C2×#41116yescomplemented
287C2×C4×C73—26no—
288C2×C4×C73—26no—
289C2×C4×C73—26no—
290C2×C4×C73—224no—
291C2×C4×C73—22no—
292C2×C4×C73—224no—
293C2×C4×C73—28no—
294C2×C4×C73C2×#41112yes—
295C2×C4×C732−1+414yes—
296C2×C4×C73C2512yes—
297C2×C4×C73C2516yes—
298C2×C4×C73C2516yes—
299C2×C4×C73C2516yes—
300C2×C4×C73C2516yes—
301C2×C4×C73C2512yes—
302C22⋊D73—224no—
303C22⋊D73C2×#41116yescomplemented
304C2×Dic73—22no—
305C2×Dic73—26no—
306C2×Dic73—26no—
307C2×Dic73—22no—
308C2×Dic73—26no—
309C2×Dic73C2×#4114yes—
310C2×Dic73C2512yes—
311C2×Dic73C2512yes—
312C2×Dic73C2516yes—
313C2×Dic73C2516yes—
314C2×Dic73C2516yes—
315C2×Dic73C2512yes—
316D292—224no—
317D292—224no—
318C4×D73—224no—
319C4×D73—224no—
320C4×D73—224no—
321C4×D73—28no—
322C4×D73—224no—
323C4×D73—224no—
324Dic146—224no—
325Dic146—224no—
326C22×C73—22no—
327C22×C73—22no—
328C22×C73—28no—
329C22×C73C22×#4114yes—
330C22×C73C22×#4112yes—
331C22×C73C22×#4112yes—
332C22×C73C2×2−1+412yes—
333C22×C73C2611yescharacteristic
334C2×D73—22no—
335C2×D73—22no—
336C2×D73—28no—
337C2×D73—26no—
338C2×D73—26no—
339C2×D73—26no—
340C2×D73—412no—
341C2×D73C22×#4114yes—
342C4×C73—26no—
343C4×C73—26no—
344C4×C73—26no—
345C4×C73—22no—
346C4×C73C22×#41112yes—
347C4×C73C2×2−1+414yes—
348Dic73—26no—
349Dic73—26no—
350Dic73—22no—
351Dic73—22no—
352Dic73—26no—
353Dic73C22×#4114yes—
354C2×#3482—731nomaximal, Sylow
355C2×C73—24no—
356C2×C73#348214yescomplemented
357C2×C73C23×#4111yescharacteristic
358C2×C73C23×#4111yescharacteristic
359C2×C73C22×2−1+411yescharacteristic
360D73—24no—
361D73—46no—
362#3482—7332no—
363C2×#557—731no—
364C2×#556—733no—
365C2×#552—733no—
366C2×#552—733no—
367C2×D4×Q8—731no—
368C2×#548—731no—
369C2×#548—731no—
370C2×#547—733no—
371C2×#533—733no—
372C2×#529—733no—
373C2×#529—733no—
374C2×C4×#41—733no—
375C2×C4×#41—731no—
376C22×C4×Q8—731no—
377C22×C4×Q8D7311yescharacteristic, complemented
378C73C2×#348211yescharacteristic, complemented, Sylow
379C22×#41—731no—
380C22×#41—733no—
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#548—7316no—
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×#124—733no—
403C2×#123—736no—
404C2×#123—736no—
405C2×C22⋊Q8—733no—
406C2×C22⋊Q8—733no—
407C2×C22⋊Q8—733no—
408C2×C22⋊Q8—736no—
409C2×C22⋊Q8—733no—
410C2×#121—733no—
411C2×#121—733no—
412C4×#41—7316no—
413C4×#41—7348no—
414C2×C4×Q8—731no—
415C2×C4×Q8—731no—
416C2×C4×Q8—7316no—
417C2×C4×Q8—733no—
418C2×C4×Q8—733no—
419C2×C4×Q8—733no—
420C2×C4×Q8—733no—
421C2×C4×Q8C2×D7311yescharacteristic
422C2×C4×Q8C2×D7313yes—
423C2×C4×Q8C2×D7311yescharacteristic
424C2×C4×Q8C2×D7313yes—
425C2×C4×Q8C2×D73116yescomplemented
426C2×C4×D4—731no—
427C2×C4×D4—733no—
428C2×C4×D4—733no—
429C2×C4×D4—733no—
430C2×C4×D4—733no—
431C2×C4×D4—733no—
432C2×C4×D4—733no—
433C2×C4×D4—733no—
434C2×#117—733no—
435C2×#117—733no—
436C2×#117—733no—
437C2×#117—733no—
438C2×#117—736no—
439C22×C4⋊C4—733no—
440C22×C4⋊C4C2×D7313yes—
441C22×C42—733no—
442C22×C42—733no—
443C22×C42C2×D7313yes—
444C2×#41—738no—
445C2×#41—7324no—
446C2×#41—14624no—
447C2×#41—1468no—
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×D4—733no—
459C22×D4—733no—
460C23×C4—733no—
461C23×C4—733no—
462C23×C4—733no—
463C23×C4—733no—
464C23×C4—733no—
465C23×C4—731no—
466C23×C4C22×D7313yes—
467C23×C4C22×D7313yes—
468C23×C4C22×D7311yescharacteristic
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#124—7324no—
478#123—7348no—
479#123—7348no—
480C22⋊Q8—7324no—
481C22⋊Q8—7324no—
482C22⋊Q8—7324no—
483C22⋊Q8—7348no—
484C22⋊Q8—7324no—
485#121—7324no—
486#121—7324no—
487C4×Q8—738no—
488C4×Q8—738no—
489C4×Q8—7324no—
490C4×Q8—7324no—
491C4×Q8—7324no—
492C4×Q8—7324no—
493C4×Q8C22×D7318yes—
494C4×Q8C22×D73124yes—
495C4×Q8C22×D7318yes—
496C4×Q8C22×D73124yes—
497C4×D4—738no—
498C4×D4—7324no—
499C4×D4—7324no—
500C4×D4—7324no—
501C4×D4—7324no—
502C4×D4—7324no—
503C4×D4—7324no—
504C4×D4—7324no—
505#117—7324no—
506#117—7324no—
507#117—7324no—
508#117—7324no—
509#117—7348no—
510C2×C4⋊C4—733no—
511C2×C4⋊C4—736no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4—733no—
514C2×C4⋊C4—733no—
515C2×C4⋊C4—733no—
516C2×C4⋊C4—733no—
517C2×C4⋊C4—733no—
518C2×C4⋊C4—733no—
519C2×C4⋊C4—736no—
520C2×C4⋊C4—736no—
521C2×C4⋊C4—7324no—
522C2×C4⋊C4C22×D7313yes—
523C2×C4⋊C4C22×D7313yes—
524C2×C4⋊C4C22×D7316yes—
525C2×C4⋊C4C22×D73124yes—
526C2×C22⋊C4—731no—
527C2×C22⋊C4—733no—
528C2×C22⋊C4—731no—
529C2×C22⋊C4—733no—
530C2×C22⋊C4—736no—
531C2×C22⋊C4—733no—
532C2×C22⋊C4—733no—
533C2×C22⋊C4—736no—
534C2×C22⋊C4—736no—
535C2×C42—733no—
536C2×C42—733no—
537C2×C42—733no—
538C2×C42—733no—
539C2×C42—733no—
540C2×C42—731no—
541C2×C42—7324no—
542C2×C42—7324no—
543C2×C42C22×D7313yes—
544C2×C42C22×D7313yes—
545C2×C42C22×D73124yes—
546C2×C42C22×D7313yes—
547C2×C42C22×D7313yes—
548C24—731no—
549C24—733no—
550C24C23×D7311yescharacteristic
551#41—14696no—
552#41—14632no—
553C2×Q8—232no—
554C2×Q8—212no—
555C2×Q8—7312no—
556C2×Q8—7312no—
557C2×Q8—14612no—
558C2×Q8—14632no—
559C2×Q8—14612no—
560C2×Q8#1192402818yescomplemented
561C2×Q8C23×D73112yes—
562C2×Q8C23×D7314yes—
563C2×D4—738no—
564C2×D4—734no—
565C2×D4—7312no—
566C2×D4—7312no—
567C2×D4—7312no—
568C2×D4—14612no—
569C2×D4—14612no—
570C2×D4—14612no—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—24no—
574C22×C4—731no—
575C22×C4—731no—
576C22×C4—731no—
577C22×C4—733no—
578C22×C4—733no—
579C22×C4—733no—
580C22×C4—734no—
581C22×C4—7312no—
582C22×C4—7312no—
583C22×C4—7312no—
584C22×C4—7312no—
585C22×C4—7312no—
586C22×C4—14612no—
587C22×C4—14612no—
588C22×C4—14612no—
589C22×C4—14612no—
590C22×C4—14612no—
591C22×C4—1464no—
592C22×C4C23×D7313yes—
593C22×C4C23×D7311yescharacteristic
594C22×C4C23×D7314yes—
595C22×C4C23×D7313yes—
596C22×C4C23×D7313yes—
597C22×C4C23×D73112yes—
598C22×C4C23×D73112yes—
599C22×C4C23×D7313yes—
600C22×C4C23×D7311yescharacteristic
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—7312no—
611C4⋊C4—7312no—
612C4⋊C4C23×D73112yes—
613C4⋊C4C23×D73112yes—
614C4⋊C4C23×D73124yes—
615C22⋊C4—734no—
616C22⋊C4—7312no—
617C22⋊C4—734no—
618C22⋊C4—7312no—
619C22⋊C4—7324no—
620C22⋊C4—7312no—
621C22⋊C4—7312no—
622C22⋊C4—7324no—
623C22⋊C4—7324no—
624C42—734no—
625C42—7312no—
626C42—7312no—
627C42—7312no—
628C42—7312no—
629C42—7312no—
630C42C23×D73112yes—
631C42C23×D73112yes—
632C42C23×D73112yes—
633C42C23×D73112yes—
634C23—22no—
635C23—22no—
636C23—734no—
637C23—732no—
638C23—736no—
639C23—1466no—
640C23—1466no—
641C23—1466no—
642C23—1462no—
643C23—1462no—
644C23#41×D7314yes—
645C23C24×D7312yes—
646C23C24×D7311yescharacteristic
647Q8—224no—
648Q8—14624no—
649Q8—14624no—
650Q8C2×#11924028116yescomplemented
651D4—7316no—
652D4—14624no—
653D4—14624no—
654D4—14624no—
655C2×C4—26no—
656C2×C4—26no—
657C2×C4—224no—
658C2×C4—26no—
659C2×C4—22no—
660C2×C4—224no—
661C2×C4—28no—
662C2×C4—734no—
663C2×C4—732no—
664C2×C4—732no—
665C2×C4—732no—
666C2×C4—736no—
667C2×C4—736no—
668C2×C4—736no—
669C2×C4—14624no—
670C2×C4—14624no—
671C2×C4—1466no—
672C2×C4—1462no—
673C2×C4—1466no—
674C2×C4—1462no—
675C2×C4—1466no—
676C2×C4—14624no—
677C2×C4—14624no—
678C2×C4—14624no—
679C2×C4—1468no—
680C2×C4C2×#11924028112yes—
681C2×C4#1455663914yes—
682C2×C4C24×D7316yes—
683C2×C4C24×D7312yes—
684C2×C4C24×D7316yes—
685C2×C4C24×D7316yes—
686C2×C4C24×D7316yes—
687C2×C4C24×D7312yes—
688C22—28no—
689C22—22no—
690C22—22no—
691C22—29212no—
692C22—734no—
693C22—1466no—
694C22—1466no—
695C22—1466no—
696C22—1468no—
697C22—1462no—
698C22—1462no—
699C22C2×#41×D7314yes—
700C22C2×#41×D7312yes—
701C22C22×#1192402812yes—
702C22C2×#1455663912yes—
703C22C25×D7311yescharacteristic
704C4—26no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—734no—
709C4—1466no—
710C4—1462no—
711C4—1466no—
712C4—1462no—
713C4—1466no—
714C4C22×#11924028112yes—
715C4C2×#1455663914yes—
716C2—24no—
717C2—2926no—
718C2—1464no—
719C2#2262354814yesdirect product factor
720C2C22×#41×D7311yescharacteristic
721C2C23×#1192402811yescharacteristic
722C2C22×#1455663911yescharacteristic
subgroupG/H
centerC22×C4C23×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC22×C4×Q8×C73C2
socleC23×C73C25
hypercenterC22×C4×Q8D73
hypocenterC73C2×#3482
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #22623548C2direct (N × H)
2. C2×#17989313C2semidirect
3. C2×#17989309C2semidirect
4. C2×#17989278C2semidirect
5. C2×#17989272C2semidirect
6. C2×Q8×C22⋊D73C2semidirect
7. C2×#17989249C2semidirect
8. C2×#17989248C2semidirect
9. C2×#17989238C2semidirect
10. C2×#17989141C2semidirect
11. C2×#17989124C2semidirect
12. C2×#17989121C2semidirect
13. C2×C4×#11924029C2semidirect
14. C2×C4×#11924028C2semidirect
15. C2×C4×Q8×D73C2semidirect
16. C22×C4×Q8×C73C2semidirect
20. #17989313C22semidirect
21. #17989309C22semidirect
22. #17989278C22semidirect
23. #17989272C22semidirect
24. Q8×C22⋊D73C22semidirect
25. #17989249C22semidirect
26. #17989248C22semidirect
27. #17989238C22semidirect
28. #17989141C22semidirect
31. #17989124C22semidirect
32. #17989121C22semidirect
49. C4×#11924029C22semidirect
50. C4×#11924028C22semidirect
57. C4×Q8×D73C22semidirect
79. C2×C4×Q8×C73C22semidirect
200. C2×C22⋊D73#41semidirect
250. C2×Q8×C73#41semidirect
286. Q8×C73C2×#41semidirect
303. C22⋊D73C2×#41semidirect
356. C2×C73#3482semidirect
377. C22×C4×Q8D73semidirect
378. C73C2×#3482semidirect
425. C2×C4×Q8C2×D73semidirect
560. C2×Q8#11924028semidirect
650. Q8C2×#11924028semidirect
719. C2#22623548direct (N × H)

Maximal subgroups

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

subgroupindex
#226235482
C2×#179893132
C2×#179893092
C2×#179892782
C2×#179892722
C2×Q8×C22⋊D732
C2×#179892492
C2×#179892482
C2×#179892382
C2×#179891412
C2×#179891242
C2×#179891212
C2×C4×#119240292
C2×C4×#119240282
C2×C4×Q8×D732
C22×C4×Q8×C732
C2×#348273