Finite Group Databasebeta

← C2×#22624007 #33994192

Subgroups — C2×#22624007 #33994192

Order 18688.

7758 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#22624007C2132yesmaximal, direct product factor
2C2×#17989319C213yesmaximal, complemented
3C2×Q8×Dic146C211yesmaximal, characteristic, complemented
4C2×#17989295C213yesmaximal, complemented
5C2×#17989256C211yesmaximal, characteristic, complemented
6C2×#17989248C211yesmaximal, characteristic, complemented
7C2×#17989241C213yesmaximal, complemented
8C2×#17989237C213yesmaximal, complemented
9C2×#17989210C213yesmaximal, complemented
10C2×#17989206C213yesmaximal, complemented
11C2×#17989132C213yesmaximal, complemented
12C2×#17989117C213yesmaximal, complemented
13C2×#17989070C211yesmaximal, characteristic, complemented
14C2×#17989069C211yesmaximal, characteristic, complemented
15C22×Q8×Dic73C211yesmaximal, characteristic, complemented
16C2×#548×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×#11924027C2216yes—
19#17989319C22148yescomplemented
20Q8×Dic146C22116yescomplemented
21#17989295C22148yescomplemented
22#17989256C22116yescomplemented
23#17989248C22116yescomplemented
24#17989241C22148yescomplemented
25#17989237C22148yescomplemented
26#17989210C22148yescomplemented
27#17989206C22148yescomplemented
28#17989132C22148yescomplemented
29C2×#14556591C2213yes—
30C2×#14556590C2213yes—
31C2×#14556590C2213yes—
32C2×#14556587C2213yes—
33#17989117C22148yescomplemented
34C2×#14556586C2213yes—
35C2×#14556584C2213yes—
36C2×#14556581C2213yes—
37C2×#14556580C2213yes—
38C2×#14556577C2213yes—
39C2×#14556577C2216yes—
40C2×#14556575C2216yes—
41C2×#14556575C2213yes—
42C2×#14556573C2216yes—
43C2×#14556572C2213yes—
44C2×#14556571C2216yes—
45C2×#14556568C2216yes—
46C2×#14556568C2211yescharacteristic
47C2×#14556567C2213yes—
48C2×#14556565C2213yes—
49C2×#14556565C2213yes—
50C2×#14556563C2213yes—
51C2×#14556562C2213yes—
52#17989070C22116yescomplemented
53#17989069C22116yescomplemented
54C2×Q8×Dic73C2211yescharacteristic
55C2×Q8×Dic73C2211yescharacteristic
56C2×Q8×Dic73C2213yes—
57C2×Q8×Dic73C2213yes—
58C2×Q8×Dic73C2211yescharacteristic
59C2×Q8×Dic73C22116yescomplemented
60C2×C4×Dic146C2213yes—
61C2×C4×D292C2213yes—
62C2×D4×Dic73C2213yes—
63C2×D4×Dic73C2213yes—
64C2×#14556553C2213yes—
65C2×C4×C22⋊D73C2213yes—
66C2×C4×C22⋊D73C2213yes—
67C2×#14556551C2216yes—
68C2×#14556550C2213yes—
69C2×#14556548C2213yes—
70C22×C4⋊Dic73C2213yes—
71C22×C4⋊Dic73C2213yes—
72C2×C4⋊C4×D73C2213yes—
73C22×C4×Dic73C2213yes—
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×#11924029—28no—
83C2×#11924029C2318yes—
84C2×#11924027—424no—
85C2×#11924027C23148yes—
86C22×Dic146C2311yescharacteristic
87C22×Dic146C2316yes—
88C22×D292C2313yes—
89C22×C22⋊D73C2313yes—
90C22×C22⋊D73C2313yes—
91C22×C22⋊D73C2316yes—
92C23×Dic73C2313yes—
93C23×Dic73C2311yescharacteristic
94C23×Dic73C2316yes—
95C22×C4×D73C2313yes—
96C22×C4×D73C2316yes—
97#14556591C23124yes—
98#14556590C23124yes—
99#14556590C23124yes—
100#14556587C23124yes—
101#14556586C23124yes—
102#14556584C23124yes—
103#14556581C23124yes—
104#14556580C23124yes—
105#14556577C23148yes—
106#14556577C23124yes—
107#14556575C23148yes—
108#14556575C23124yes—
109#14556573C23148yes—
110#14556572C23124yes—
111#14556571C23148yes—
112#14556568C23148yes—
113#14556568C2318yes—
114#14556567C23124yes—
115#14556565C23124yes—
116#14556565C23124yes—
117#14556563C23124yes—
118#14556562C23124yes—
119Q8×Dic73C23124yes—
120Q8×Dic73C2318yes—
121Q8×Dic73C2318yes—
122Q8×Dic73C23124yes—
123Q8×Dic73C2318yes—
124C4×Dic146C23124yes—
125C4×D292C23124yes—
126D4×Dic73C23124yes—
127D4×Dic73C23124yes—
128#14556553C23124yes—
129C4×C22⋊D73C23124yes—
130C4×C22⋊D73C23124yes—
131#14556551C23148yes—
132#14556550C23124yes—
133#14556548C23124yes—
134C2×C4⋊Dic73C2313yes—
135C2×C4⋊Dic73C2313yes—
136C2×C4⋊Dic73C2313yes—
137C2×C4⋊Dic73C23124yes—
138C2×C4⋊Dic73C23124yes—
139C2×C4⋊Dic73C2313yes—
140C2×C4⋊Dic73C2313yes—
141C2×C4⋊Dic73C2316yes—
142C2×C4⋊Dic73C2311yescharacteristic
143C2×#11924007C2313yes—
144C2×#11924007C2313yes—
145C2×#11924007C2313yes—
146C2×#11924007C2311yescharacteristic
147C2×#11924007C2311yescharacteristic
148C2×#11924007C2313yes—
149C4⋊C4×D73C23124yes—
150C2×C22⋊Dic73C2313yes—
151C2×C22⋊Dic73C2313yes—
152C2×C22⋊Dic73C2311yescharacteristic
153C2×C22⋊Dic73C2313yes—
154C2×#11924005C2313yes—
155C2×#11924005C2313yes—
156C2×#11924005C2316yes—
157C2×#11924005C2313yes—
158C2×#11924005C2313yes—
159C2×C4×Dic73C2313yes—
160C2×C4×Dic73C2313yes—
161C2×C4×Dic73C23124yes—
162C2×C4×Dic73C2313yes—
163C2×C4×Dic73C2313yes—
164C2×C4×Dic73C2313yes—
165C2×#41×C73—28no—
166C2×#41×C73C2318yes—
167C22×Q8×C73—28no—
168C22×Q8×C73C2318yes—
169C22×Q8×C73C2313yes—
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×D73C2413yes—
187#11924029—232no—
188#11924027—496no—
189C2×Dic146—24no—
190C2×Dic146—412no—
191C2×Dic146C2414yes—
192C2×Dic146C24124yes—
193C2×D292—212no—
194C2×D292C24112yes—
195C2×C22⋊D73—212no—
196C2×C22⋊D73—212no—
197C2×C22⋊D73—412no—
198C2×C22⋊D73C24112yes—
199C2×C22⋊D73C24112yes—
200C2×C22⋊D73C24124yes—
201C22×Dic73—212no—
202C22×Dic73—24no—
203C22×Dic73—412no—
204C22×Dic73C2411yescharacteristic
205C22×Dic73C2414yes—
206C22×Dic73C2411yescharacteristic
207C22×Dic73C2413yes—
208C22×Dic73C2413yes—
209C22×Dic73C24112yes—
210C22×Dic73C2413yes—
211C22×Dic73C2411yescharacteristic
212C22×Dic73C24124yes—
213C22×Dic73C2411yescharacteristic
214C2×C4×D73—212no—
215C2×C4×D73—412no—
216C2×C4×D73C24112yes—
217C2×C4×D73C24124yes—
218C4⋊Dic73C24112yes—
219C4⋊Dic73C24112yes—
220C4⋊Dic73C24112yes—
221C4⋊Dic73C24112yes—
222C4⋊Dic73C24124yes—
223C4⋊Dic73C2414yes—
224C4⋊Dic73C24112yes—
225#11924007C24112yes—
226#11924007C2414yes—
227#11924007C24112yes—
228#11924007C2414yes—
229#11924007C24112yes—
230#11924007C24112yes—
231C22⋊Dic73C24112yes—
232C22⋊Dic73C24112yes—
233C22⋊Dic73C2414yes—
234C22⋊Dic73C24112yes—
235#11924005C24112yes—
236#11924005C24112yes—
237#11924005C24124yes—
238#11924005C24112yes—
239#11924005C24112yes—
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×C73H(5,𝔽2)14yes—
278C23×C73C2516yes—
279C23×C73C2512yes—
280C23×C73C2511yescharacteristic
281C22×D73—26no—
282C22×D73—26no—
283C22×D73—26no—
284C22×D73C2516yes—
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⋊D73—224no—
303C22⋊D73—424no—
304C2×Dic73—22no—
305C2×Dic73—26no—
306C2×Dic73—26no—
307C2×Dic73—224no—
308C2×Dic73—26no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—28no—
312C2×Dic73—424no—
313C2×Dic732−1+414yes—
314C2×Dic73C2512yes—
315C2×Dic73C2512yes—
316C2×Dic73C2516yes—
317C2×Dic73C2516yes—
318C2×Dic73C2516yes—
319C2×Dic73C2512yes—
320C2×Dic73C2512yes—
321D292—224no—
322C4×D73—224no—
323C4×D73—424no—
324Dic146—28no—
325Dic146—424no—
326C22×C73—22no—
327C22×C73—22no—
328C22×C73—28no—
329C22×C73—26no—
330C22×C73—26no—
331C22×C73—26no—
332C22×C73—412no—
333C22×C73C22×#4112yes—
334C22×C73C2×H(5,𝔽2)14yes—
335C22×C73C2×H(5,𝔽2)12yes—
336C22×C73C2×2−1+412yes—
337C22×C73C2611yescharacteristic
338C2×D73—26no—
339C2×D73—26no—
340C2×D73—26no—
341C2×D73—412no—
342C4×C73—22no—
343C4×C73—26no—
344C4×C73—26no—
345C4×C73—22no—
346C4×C73C22×#41112yes—
347Dic73—22no—
348Dic73—26no—
349Dic73—26no—
350Dic73—26no—
351Dic73—22no—
352Dic73—22no—
353Dic73C2×2−1+414yes—
354C2×#3522—731nomaximal, Sylow
355C2×C73—24no—
356C2×C73—46no—
357C2×C73#352214yescomplemented
358C2×C73C23×#4111yescharacteristic
359C2×C73C22×H(5,𝔽2)11yescharacteristic
360C2×C73C22×2−1+411yescharacteristic
361D73—46no—
362#3522—7332no—
363C2×#559—733no—
364C2×Q82—731no—
365C2×#554—733no—
366C2×#550—731no—
367C2×#548—731no—
368C2×#548D7311yescharacteristic, complemented
369C2×#547—733no—
370C2×#547—733no—
371C2×#542—733no—
372C2×#542—733no—
373C2×#532—733no—
374C2×#529—733no—
375C2×#520—731no—
376C2×#520—731no—
377C22×C4×Q8—731no—
378C73C2×#352211yescharacteristic, complemented, Sylow
379C22×#41—731no—
380C22×#41—736no—
381C22×#41C2×D7311yescharacteristic
382C23×Q8C2×D7311yescharacteristic
383#559—7348no—
384Q82—7316no—
385#554—7348no—
386#550—7316no—
387#548—7316no—
388#548C2×D73116yescomplemented
389#547—7348no—
390#547—7348no—
391#542—7348no—
392#542—7348no—
393#532—7348no—
394C2×C4⋊Q8—733no—
395C2×C4⋊Q8—733no—
396C2×C4⋊Q8—733no—
397C2×#127—733no—
398#529—7348no—
399C2×#126—733no—
400C2×#126—733no—
401C2×#125—733no—
402C2×#124—733no—
403C2×#124—733no—
404C2×#124—736no—
405C2×#124C2×D7313yes—
406C2×#123—733no—
407C2×#123—733no—
408C2×#123—736no—
409C2×#123—736no—
410C2×C22⋊Q8—733no—
411C2×C22⋊Q8—736no—
412C2×C22⋊Q8—731no—
413C2×C22⋊Q8—736no—
414C2×C22⋊Q8C2×D7313yes—
415C2×#121—733no—
416C2×#121—733no—
417C2×#121—733no—
418C2×#121—733no—
419C2×#121C2×D7313yes—
420#520—7316no—
421#520—7316no—
422C2×C4×Q8—731no—
423C2×C4×Q8—733no—
424C2×C4×Q8—731no—
425C2×C4×Q8—733no—
426C2×C4×Q8—7316no—
427C2×C4×Q8—731no—
428C2×C4×Q8—733no—
429C2×C4×Q8C2×D7311yescharacteristic
430C2×C4×D4—733no—
431C2×C4×D4—733no—
432C2×C4×D4—733no—
433C2×C4×D4—733no—
434C2×C4×D4—733no—
435C2×C4×D4—736no—
436C2×C4×D4—733no—
437C2×C4×D4C2×D7313yes—
438C2×#117—733no—
439C2×#117—733no—
440C22×C4⋊C4—733no—
441C22×C4⋊C4—733no—
442C22×C4⋊C4—733no—
443C22×C42—733no—
444C2×#41—28no—
445C2×#41—29224no—
446C2×#41—738no—
447C2×#41—7348no—
448C2×#41—1468no—
449C2×#41C22×D7318yes—
450C22×Q8—28no—
451C22×Q8—736no—
452C22×Q8—731no—
453C22×Q8C22×D7313yes—
454C22×Q8C22×D7318yes—
455C22×Q8C22×D7311yescharacteristic
456C22×D4—736no—
457C22×D4—733no—
458C22×D4—733no—
459C22×D4—733no—
460C22×D4C22×D7313yes—
461C22×D4C22×D7313yes—
462C23×C4—736no—
463C23×C4—736no—
464C23×C4—733no—
465C23×C4—731no—
466C23×C4—733no—
467C23×C4C22×D7313yes—
468C23×C4C22×D7313yes—
469C4⋊Q8—7324no—
470C4⋊Q8—7324no—
471C4⋊Q8—7324no—
472#127—7324no—
473#126—7324no—
474#126—7324no—
475#125—7324no—
476#124—7324no—
477#124—7324no—
478#124—7348no—
479#124C22×D73124yes—
480#123—7324no—
481#123—7324no—
482#123—7348no—
483#123—7348no—
484C22⋊Q8—7324no—
485C22⋊Q8—7348no—
486C22⋊Q8—738no—
487C22⋊Q8—7348no—
488C22⋊Q8C22×D73124yes—
489#121—7324no—
490#121—7324no—
491#121—7324no—
492#121—7324no—
493#121C22×D73124yes—
494C4×Q8—738no—
495C4×Q8—7324no—
496C4×Q8—738no—
497C4×Q8—7324no—
498C4×Q8—738no—
499C4×Q8—7324no—
500C4×Q8C22×D7318yes—
501C4×D4—7324no—
502C4×D4—7324no—
503C4×D4—7324no—
504C4×D4—7324no—
505C4×D4—7324no—
506C4×D4—7348no—
507C4×D4—7324no—
508C4×D4C22×D73124yes—
509#117—7324no—
510#117—7324no—
511C2×C4⋊C4—733no—
512C2×C4⋊C4—733no—
513C2×C4⋊C4—733no—
514C2×C4⋊C4—733no—
515C2×C4⋊C4—733no—
516C2×C4⋊C4—736no—
517C2×C4⋊C4—7324no—
518C2×C4⋊C4—7324no—
519C2×C4⋊C4—731no—
520C2×C4⋊C4—731no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—733no—
523C2×C4⋊C4—733no—
524C2×C4⋊C4—733no—
525C2×C4⋊C4—733no—
526C2×C4⋊C4—7324no—
527C2×C4⋊C4C22×D7313yes—
528C2×C4⋊C4C22×D7313yes—
529C2×C22⋊C4—733no—
530C2×C22⋊C4—733no—
531C2×C22⋊C4—731no—
532C2×C22⋊C4—733no—
533C2×C22⋊C4—733no—
534C2×C22⋊C4—733no—
535C2×C22⋊C4—733no—
536C2×C22⋊C4—736no—
537C2×C22⋊C4—733no—
538C2×C22⋊C4C22×D7316yes—
539C2×C22⋊C4C22×D7311yescharacteristic
540C2×C22⋊C4C22×D7313yes—
541C2×C42—733no—
542C2×C42—733no—
543C2×C42—733no—
544C2×C42—733no—
545C2×C42—733no—
546C2×C42—7324no—
547C2×C42C22×D7313yes—
548C24—733no—
549C24C23×D7313yes—
550C24C23×D7311yescharacteristic
551#41—232no—
552#41—29296no—
553#41—14632no—
554C2×Q8—232no—
555C2×Q8—212no—
556C2×Q8—29212no—
557C2×Q8—7324no—
558C2×Q8—734no—
559C2×Q8—1464no—
560C2×Q8#1192402718yescomplemented
561C2×Q8C23×D73112yes—
562C2×Q8C23×D7314yes—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—29212no—
566C2×D4—7324no—
567C2×D4—7312no—
568C2×D4—7312no—
569C2×D4—7312no—
570C2×D4—14612no—
571C2×D4—14612no—
572C2×D4—14612no—
573C2×D4C23×D73112yes—
574C2×D4C23×D73112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—29212no—
578C22×C4—29212no—
579C22×C4—7324no—
580C22×C4—7324no—
581C22×C4—731no—
582C22×C4—734no—
583C22×C4—7312no—
584C22×C4—731no—
585C22×C4—731no—
586C22×C4—733no—
587C22×C4—733no—
588C22×C4—733no—
589C22×C4—731no—
590C22×C4—7312no—
591C22×C4—1464no—
592C22×C4—14612no—
593C22×C4—14612no—
594C22×C4C23×D73112yes—
595C22×C4C23×D73112yes—
596C22×C4C23×D7313yes—
597C22×C4C23×D7311yescharacteristic
598C22×C4C23×D7313yes—
599C22×C4C23×D7311yescharacteristic
600C22×C4C23×D7313yes—
601C4⋊C4—7312no—
602C4⋊C4—734no—
603C4⋊C4—734no—
604C4⋊C4—7312no—
605C4⋊C4—7312no—
606C4⋊C4—7312no—
607C4⋊C4—7312no—
608C4⋊C4—7312no—
609C4⋊C4—7312no—
610C4⋊C4—7312no—
611C4⋊C4—7324no—
612C4⋊C4—734no—
613C4⋊C4—7312no—
614C4⋊C4C23×D73112yes—
615C4⋊C4C23×D73112yes—
616C22⋊C4—7312no—
617C22⋊C4—7312no—
618C22⋊C4—734no—
619C22⋊C4—7312no—
620C22⋊C4—7312no—
621C22⋊C4—7312no—
622C22⋊C4—7312no—
623C22⋊C4—7324no—
624C22⋊C4—7312no—
625C22⋊C4C23×D73124yes—
626C22⋊C4C23×D7314yes—
627C22⋊C4C23×D73112yes—
628C42—7312no—
629C42—7312no—
630C42—7312no—
631C42—7312no—
632C42—7312no—
633C42C23×D73112yes—
634C23—22no—
635C23—22no—
636C23—26no—
637C23—26no—
638C23—26no—
639C23—736no—
640C23—1466no—
641C23—1466no—
642C23—1466no—
643C23#1455663714yes—
644C23C24×D7316yes—
645C23C24×D7312yes—
646C23C24×D7311yescharacteristic
647Q8—224no—
648Q8—29224no—
649Q8—1468no—
650Q8C2×#11924027116yescomplemented
651D4—224no—
652D4—224no—
653D4—29224no—
654D4—14624no—
655D4—14624no—
656D4—14624no—
657C2×C4—22no—
658C2×C4—26no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—224no—
662C2×C4—224no—
663C2×C4—29224no—
664C2×C4—29224no—
665C2×C4—734no—
666C2×C4—732no—
667C2×C4—732no—
668C2×C4—732no—
669C2×C4—736no—
670C2×C4—736no—
671C2×C4—736no—
672C2×C4—732no—
673C2×C4—1468no—
674C2×C4—1462no—
675C2×C4—1466no—
676C2×C4—1466no—
677C2×C4—1466no—
678C2×C4—14624no—
679C2×C4—1462no—
680C2×C4—1462no—
681C2×C4—14624no—
682C2×C4C2×#11924027112yes—
683C2×C4C24×D7316yes—
684C2×C4C24×D7312yes—
685C2×C4C24×D7316yes—
686C2×C4C24×D7312yes—
687C2×C4C24×D7316yes—
688C22—28no—
689C22—22no—
690C22—22no—
691C22—26no—
692C22—26no—
693C22—26no—
694C22—412no—
695C22—29212no—
696C22—1466no—
697C22—1466no—
698C22—1466no—
699C22C22×#1192402712yes—
700C22C2×#1455663714yes—
701C22C2×#1455663712yes—
702C222−1+4×D7312yes—
703C22C25×D7311yescharacteristic
704C4—22no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—734no—
709C4—1462no—
710C4—1466no—
711C4—1466no—
712C4—1466no—
713C4—1462no—
714C4—1462no—
715C4C22×#11924027112yes—
716C2—24no—
717C2—46no—
718C2—2926no—
719C2#2262400714yesdirect product factor
720C2C23×#1192402711yescharacteristic
721C2C22×#1455663711yescharacteristic
722C2C2×2−1+4×D7311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#548×C73C2
socleC23×C73C25
hypercenterC2×#548D73
hypocenterC73C2×#3522
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #22624007C2direct (N × H)
2. C2×#17989319C2semidirect
3. C2×Q8×Dic146C2semidirect
4. C2×#17989295C2semidirect
5. C2×#17989256C2semidirect
6. C2×#17989248C2semidirect
7. C2×#17989241C2semidirect
8. C2×#17989237C2semidirect
9. C2×#17989210C2semidirect
10. C2×#17989206C2semidirect
11. C2×#17989132C2semidirect
12. C2×#17989117C2semidirect
13. C2×#17989070C2semidirect
14. C2×#17989069C2semidirect
15. C22×Q8×Dic73C2semidirect
16. C2×#548×C73C2semidirect
19. #17989319C22semidirect
20. Q8×Dic146C22semidirect
21. #17989295C22semidirect
22. #17989256C22semidirect
23. #17989248C22semidirect
24. #17989241C22semidirect
25. #17989237C22semidirect
26. #17989210C22semidirect
27. #17989206C22semidirect
28. #17989132C22semidirect
33. #17989117C22semidirect
52. #17989070C22semidirect
53. #17989069C22semidirect
59. C2×Q8×Dic73C22semidirect
76. #548×C73C22semidirect
250. C2×Q8×C73#41semidirect
286. Q8×C73C2×#41semidirect
357. C2×C73#3522semidirect
368. C2×#548D73semidirect
378. C73C2×#3522semidirect
388. #548C2×D73semidirect
560. C2×Q8#11924027semidirect
650. Q8C2×#11924027semidirect
719. C2#22624007direct (N × H)

Maximal subgroups

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

subgroupindex
#226240072
C2×#179893192
C2×Q8×Dic1462
C2×#179892952
C2×#179892562
C2×#179892482
C2×#179892412
C2×#179892372
C2×#179892102
C2×#179892062
C2×#179891322
C2×#179891172
C2×#179890702
C2×#179890692
C22×Q8×Dic732
C2×#548×C732
C2×#352273