Finite Group Databasebeta

← C2×#22624010 #33994191

Subgroups — C2×#22624010 #33994191

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#22624010C2132yesmaximal, direct product factor
2C2×#17989320C213yesmaximal, complemented
3C2×Q8×Dic146C211yesmaximal, characteristic, complemented
4C2×#17989292C213yesmaximal, complemented
5C2×#17989256C211yesmaximal, characteristic, complemented
6C2×#17989249C211yesmaximal, characteristic, complemented
7C2×#17989244C211yesmaximal, characteristic, complemented
8C2×#17989242C213yesmaximal, complemented
9C2×#17989238C213yesmaximal, complemented
10C2×#17989208C213yesmaximal, complemented
11C2×#17989202C213yesmaximal, complemented
12C2×#17989134C213yesmaximal, complemented
13C2×#17989115C213yesmaximal, complemented
14C2×#17989069C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D73C211yesmaximal, characteristic, complemented
16C2×#520×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×#11924028C2216yes—
19C22×Q8×D73C2211yescharacteristic
20#17989320C22148yescomplemented
21Q8×Dic146C22116yescomplemented
22#17989292C22148yescomplemented
23#17989256C22116yescomplemented
24#17989249C22116yescomplemented
25#17989244C22116yescomplemented
26#17989242C22148yescomplemented
27#17989238C22148yescomplemented
28#17989208C22148yescomplemented
29#17989202C22148yescomplemented
30#17989134C22148yescomplemented
31C2×#14556591C2213yes—
32C2×#14556590C2213yes—
33C2×#14556590C2213yes—
34C2×#14556587C2213yes—
35#17989115C22148yescomplemented
36C2×#14556586C2213yes—
37C2×#14556584C2213yes—
38C2×#14556581C2213yes—
39C2×#14556579C2213yes—
40C2×#14556578C2213yes—
41C2×#14556577C2213yes—
42C2×#14556577C2216yes—
43C2×#14556576C2213yes—
44C2×#14556574C2216yes—
45C2×#14556573C2216yes—
46C2×#14556573C2213yes—
47C2×#14556571C2213yes—
48C2×#14556570C2216yes—
49C2×#14556570C2213yes—
50C2×#14556569C2216yes—
51C2×#14556569C2211yescharacteristic
52C2×#14556566C2213yes—
53C2×#14556565C2213yes—
54C2×#14556564C2213yes—
55C2×#14556562C2213yes—
56C2×#14556562C2213yes—
57#17989069C22116yescomplemented
58C2×Q8×Dic73C2211yescharacteristic
59C2×Q8×Dic73C2211yescharacteristic
60C2×C4×Dic146C2213yes—
61C2×C4×Dic146C2213yes—
62C2×#14556556C2213yes—
63C4×Q8×D73C22116yescomplemented
64C2×C4×D292C2213yes—
65C2×C4×D292C2213yes—
66C2×#14556553C2213yes—
67C2×C4×C22⋊D73C2216yes—
68C2×C4×C22⋊D73C2213yes—
69C2×C4×C22⋊D73C2213yes—
70C2×#14556548C2213yes—
71C2×C4⋊C4×D73C2213yes—
72C2×C4⋊C4×D73C2213yes—
73C2×C42×D73C2213yes—
74C22×#41×C73C2211yescharacteristic
75#520×C73C22116yescomplemented
76C2×C4×Q8×C73C2211yescharacteristic
77C2×C4×Q8×C73C2211yescharacteristic
78C2×C4×D4×C73C2213yes—
79C2×C4×D4×C73C2213yes—
80C2×#117×C73C2213yes—
81C22×C4⋊C4×C73C2213yes—
82C2×#11924029—28no—
83C2×#11924029C2318yes—
84C2×#11924028—424no—
85C2×#11924028C23148yes—
86C22×Dic146C2313yes—
87C22×Dic146C2311yescharacteristic
88C22×Dic146C2316yes—
89C2×Q8×D73—28no—
90C2×Q8×D73C2318yes—
91C22×D292C2313yes—
92C22×D292C2313yes—
93C22×C22⋊D73C2313yes—
94C22×C22⋊D73C2313yes—
95C22×C22⋊D73C2316yes—
96C22×C4×D73C2313yes—
97C22×C4×D73C2313yes—
98C22×C4×D73C2313yes—
99C22×C4×D73C2311yescharacteristic
100C22×C4×D73C2316yes—
101#14556591C23124yes—
102#14556590C23124yes—
103#14556590C23124yes—
104#14556587C23124yes—
105#14556586C23124yes—
106#14556584C23124yes—
107#14556581C23124yes—
108#14556579C23124yes—
109#14556578C23124yes—
110#14556577C23148yes—
111#14556577C23124yes—
112#14556576C23124yes—
113#14556574C23148yes—
114#14556573C23148yes—
115#14556573C23124yes—
116#14556571C23124yes—
117#14556570C23148yes—
118#14556570C23124yes—
119#14556569C23148yes—
120#14556569C2318yes—
121#14556566C23124yes—
122#14556565C23124yes—
123#14556564C23124yes—
124#14556562C23124yes—
125#14556562C23124yes—
126Q8×Dic73C2318yes—
127Q8×Dic73C2318yes—
128C4×Dic146C23124yes—
129C4×Dic146C23124yes—
130#14556556C23124yes—
131C4×D292C23124yes—
132C4×D292C23124yes—
133#14556553C23124yes—
134C4×C22⋊D73C23148yes—
135C4×C22⋊D73C23124yes—
136C4×C22⋊D73C23124yes—
137#14556548C23124yes—
138C2×C4⋊Dic73C2313yes—
139C2×C4⋊Dic73C2313yes—
140C2×C4⋊Dic73C2313yes—
141C2×C4⋊Dic73C2313yes—
142C2×#11924007C2313yes—
143C2×#11924007C2313yes—
144C2×#11924007C2313yes—
145C2×#11924007C2316yes—
146C2×#11924007C2311yescharacteristic
147C2×#11924007C2311yescharacteristic
148C2×#11924007C2313yes—
149C4⋊C4×D73C23124yes—
150C4⋊C4×D73C23124yes—
151C2×C22⋊Dic73C2313yes—
152C2×C22⋊Dic73C2316yes—
153C2×C22⋊Dic73C2313yes—
154C2×#11924005C2313yes—
155C2×#11924005C2313yes—
156C2×#11924005C2311yescharacteristic
157C2×#11924005C2313yes—
158C2×#11924005C2316yes—
159C2×#11924005C2311yescharacteristic
160C2×#11924005C2313yes—
161C2×C4×Dic73C2313yes—
162C2×C4×Dic73C2313yes—
163C2×C4×Dic73C2313yes—
164C2×C4×Dic73C2313yes—
165C42×D73C23124yes—
166C2×#41×C73—28no—
167C2×#41×C73C2318yes—
168C22×Q8×C73C2311yescharacteristic
169C22×D4×C73C2313yes—
170C23×C4×C73C2313yes—
171C23×C4×C73C2316yes—
172C4×Q8×C73C2318yes—
173C4×Q8×C73C2318yes—
174C4×D4×C73C23124yes—
175C4×D4×C73C23124yes—
176#117×C73C23124yes—
177C2×C4⋊C4×C73C2313yes—
178C2×C4⋊C4×C73C23124yes—
179C2×C4⋊C4×C73C2313yes—
180C2×C4⋊C4×C73C2313yes—
181C2×C4⋊C4×C73C2311yescharacteristic
182C2×C22⋊C4×C73C2313yes—
183C2×C22⋊C4×C73C2313yes—
184C2×C42×C73C2313yes—
185C2×C42×C73C2313yes—
186C23×D73C2413yes—
187C23×D73C2411yescharacteristic
188#11924029—232no—
189#11924028—496no—
190C2×Dic146—212no—
191C2×Dic146—24no—
192C2×Dic146—412no—
193C2×Dic146C24112yes—
194C2×Dic146C2414yes—
195C2×Dic146C24124yes—
196Q8×D73—232no—
197C2×D292—212no—
198C2×D292—212no—
199C2×D292C24112yes—
200C2×D292C24112yes—
201C2×C22⋊D73—212no—
202C2×C22⋊D73—212no—
203C2×C22⋊D73—412no—
204C2×C22⋊D73C24112yes—
205C2×C22⋊D73C24112yes—
206C2×C22⋊D73C24124yes—
207C22×Dic73C2411yescharacteristic
208C22×Dic73C2413yes—
209C22×Dic73C2413yes—
210C22×Dic73C2413yes—
211C22×Dic73C2411yescharacteristic
212C22×Dic73C2411yescharacteristic
213C2×C4×D73—212no—
214C2×C4×D73—212no—
215C2×C4×D73—212no—
216C2×C4×D73—24no—
217C2×C4×D73—412no—
218C2×C4×D73C2414yes—
219C2×C4×D73C24112yes—
220C2×C4×D73C24112yes—
221C2×C4×D73C24112yes—
222C2×C4×D73C24124yes—
223C4⋊Dic73C24112yes—
224C4⋊Dic73C24112yes—
225C4⋊Dic73C24112yes—
226C4⋊Dic73C24112yes—
227#11924007C24112yes—
228#11924007C24124yes—
229#11924007C2414yes—
230#11924007C2414yes—
231#11924007C24112yes—
232#11924007C24112yes—
233#11924007C24112yes—
234C22⋊Dic73C24112yes—
235C22⋊Dic73C24124yes—
236C22⋊Dic73C24112yes—
237#11924005C24112yes—
238#11924005C24112yes—
239#11924005C2414yes—
240#11924005C24112yes—
241#11924005C24124yes—
242#11924005C2414yes—
243#11924005C24112yes—
244C4×Dic73C24112yes—
245C4×Dic73C24112yes—
246C4×Dic73C24112yes—
247C4×Dic73C24112yes—
248C24×C73C2413yes—
249#41×C73—232no—
250C2×Q8×C73#4118yescomplemented
251C2×Q8×C73C2414yes—
252C2×D4×C73—212no—
253C2×D4×C73C24112yes—
254C22×C4×C73—212no—
255C22×C4×C73—412no—
256C22×C4×C73C2411yescharacteristic
257C22×C4×C73C2411yescharacteristic
258C22×C4×C73C2413yes—
259C22×C4×C73C2413yes—
260C22×C4×C73C2411yescharacteristic
261C22×C4×C73C24112yes—
262C22×C4×C73C24124yes—
263C22×C4×C73C2413yes—
264C4⋊C4×C73C24112yes—
265C4⋊C4×C73C24112yes—
266C4⋊C4×C73C24112yes—
267C4⋊C4×C73C2414yes—
268C22⋊C4×C73C24112yes—
269C22⋊C4×C73C24112yes—
270C42×C73C24112yes—
271C42×C73C24112yes—
272C23×C73—26no—
273C23×C73—26no—
274C23×C73—26no—
275C23×C73C2516yes—
276C23×C73C2511yescharacteristic
277C22×D73—22no—
278C22×D73—22no—
279C22×D73—26no—
280C22×D73—26no—
281C22×D73—26no—
282C22×D73H(5,𝔽2)14yes—
283C22×D73C2516yes—
284C22×D73C2512yes—
285Q8×C73C2×#41116yescomplemented
286D4×C73—224no—
287C2×C4×C73—22no—
288C2×C4×C73—26no—
289C2×C4×C73—26no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—224no—
293C2×C4×C73—424no—
294C2×C4×C73C2×#41112yes—
295C2×C4×C73C2512yes—
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—26no—
308C2×Dic73—22no—
309C2×Dic732−1+414yes—
310C2×Dic73C2512yes—
311C2×Dic73C2516yes—
312C2×Dic73C2516yes—
313C2×Dic73C2516yes—
314C2×Dic73C2512yes—
315C2×Dic73C2512yes—
316D292—224no—
317D292—224no—
318C4×D73—224no—
319C4×D73—224no—
320C4×D73—224no—
321C4×D73—28no—
322C4×D73—424no—
323Dic146—224no—
324Dic146—28no—
325Dic146—424no—
326C22×C73—26no—
327C22×C73—26no—
328C22×C73—26no—
329C22×C73—412no—
330C22×C73C22×#4112yes—
331C22×C73C2×H(5,𝔽2)12yes—
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×D73C2×H(5,𝔽2)14yes—
342C4×C73—22no—
343C4×C73—26no—
344C4×C73—26no—
345C4×C73—22no—
346C4×C73—22no—
347C4×C73C22×#41112yes—
348Dic73—26no—
349Dic73—22no—
350Dic73—26no—
351Dic73—26no—
352Dic73—22no—
353Dic73C2×2−1+414yes—
354C2×#3522—731nomaximal, Sylow
355C2×C73—46no—
356C2×C73#352214yescomplemented
357C2×C73C23×#4111yescharacteristic
358C2×C73C22×H(5,𝔽2)11yescharacteristic
359C2×C73C22×2−1+411yescharacteristic
360D73—24no—
361D73—46no—
362#3522—7332no—
363C2×#559—733no—
364C2×Q82—731no—
365C2×#554—733no—
366C2×#550—731no—
367C2×#548—731no—
368C2×#548—731no—
369C2×#547—733no—
370C2×#547—733no—
371C2×#542—733no—
372C2×#542—733no—
373C2×#532—733no—
374C2×#529—733no—
375C2×#520—731no—
376C2×#520D7311yescharacteristic, complemented
377C22×C4×Q8—731no—
378C73C2×#352211yescharacteristic, complemented, Sylow
379C22×#41—731no—
380C22×#41—736no—
381C22×#41C2×D7311yescharacteristic
382C23×Q8—731no—
383#559—7348no—
384Q82—7316no—
385#554—7348no—
386#550—7316no—
387#548—7316no—
388#548—7316no—
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×#124—733no—
406C2×#123—736no—
407C2×#123—733no—
408C2×#123—733no—
409C2×#123—736no—
410C2×C22⋊Q8—736no—
411C2×C22⋊Q8—733no—
412C2×C22⋊Q8—731no—
413C2×C22⋊Q8—736no—
414C2×C22⋊Q8—733no—
415C2×#121—733no—
416C2×#121—733no—
417C2×#121—733no—
418C2×#121—733no—
419C2×#121—733no—
420#520—7316no—
421#520C2×D73116yescomplemented
422C2×C4×Q8—731no—
423C2×C4×Q8—731no—
424C2×C4×Q8—7316no—
425C2×C4×Q8—733no—
426C2×C4×Q8—733no—
427C2×C4×Q8—733no—
428C2×C4×Q8C2×D7311yescharacteristic
429C2×C4×Q8C2×D7311yescharacteristic
430C2×C4×D4—733no—
431C2×C4×D4—733no—
432C2×C4×D4—736no—
433C2×C4×D4—733no—
434C2×C4×D4—733no—
435C2×C4×D4—733no—
436C2×C4×D4C2×D7313yes—
437C2×C4×D4C2×D7313yes—
438C2×#117—733no—
439C2×#117C2×D7313yes—
440C22×C4⋊C4—733no—
441C22×C4⋊C4—733no—
442C22×C4⋊C4C2×D7313yes—
443C22×C42—733no—
444C2×#41—28no—
445C2×#41—29224no—
446C2×#41—738no—
447C2×#41—7348no—
448C2×#41—1468no—
449C2×#41C22×D7318yes—
450C22×Q8—738no—
451C22×Q8—736no—
452C22×Q8—731no—
453C22×Q8—733no—
454C22×Q8—1468no—
455C22×Q8C22×D7311yescharacteristic
456C22×D4—736no—
457C22×D4—733no—
458C22×D4—733no—
459C22×D4—733no—
460C22×D4—733no—
461C22×D4C22×D7313yes—
462C23×C4—736no—
463C23×C4—733no—
464C23×C4—733no—
465C23×C4—733no—
466C23×C4—731no—
467C23×C4C22×D7313yes—
468C23×C4C22×D7316yes—
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#124—7324no—
480#123—7348no—
481#123—7324no—
482#123—7324no—
483#123—7348no—
484C22⋊Q8—7348no—
485C22⋊Q8—7324no—
486C22⋊Q8—738no—
487C22⋊Q8—7348no—
488C22⋊Q8—7324no—
489#121—7324no—
490#121—7324no—
491#121—7324no—
492#121—7324no—
493#121—7324no—
494C4×Q8—738no—
495C4×Q8—738no—
496C4×Q8—7324no—
497C4×Q8—7324no—
498C4×Q8—7324no—
499C4×Q8C22×D7318yes—
500C4×Q8C22×D7318yes—
501C4×D4—7324no—
502C4×D4—7324no—
503C4×D4—7348no—
504C4×D4—7324no—
505C4×D4—7324no—
506C4×D4—7324no—
507C4×D4C22×D73124yes—
508C4×D4C22×D73124yes—
509#117—7324no—
510#117C22×D73124yes—
511C2×C4⋊C4—733no—
512C2×C4⋊C4—733no—
513C2×C4⋊C4—733no—
514C2×C4⋊C4—736no—
515C2×C4⋊C4—731no—
516C2×C4⋊C4—731no—
517C2×C4⋊C4—733no—
518C2×C4⋊C4—733no—
519C2×C4⋊C4—733no—
520C2×C4⋊C4—733no—
521C2×C4⋊C4—733no—
522C2×C4⋊C4—7324no—
523C2×C4⋊C4—7324no—
524C2×C4⋊C4C22×D7313yes—
525C2×C4⋊C4C22×D7313yes—
526C2×C4⋊C4C22×D7313yes—
527C2×C4⋊C4C22×D73124yes—
528C2×C4⋊C4C22×D7311yescharacteristic
529C2×C22⋊C4—733no—
530C2×C22⋊C4—736no—
531C2×C22⋊C4—733no—
532C2×C22⋊C4—733no—
533C2×C22⋊C4—733no—
534C2×C22⋊C4—731no—
535C2×C22⋊C4—731no—
536C2×C22⋊C4—733no—
537C2×C22⋊C4—736no—
538C2×C22⋊C4—733no—
539C2×C22⋊C4C22×D7313yes—
540C2×C22⋊C4C22×D7313yes—
541C2×C42—733no—
542C2×C42—733no—
543C2×C42—733no—
544C2×C42—733no—
545C2×C42—7324no—
546C2×C42C22×D7313yes—
547C2×C42C22×D7313yes—
548C24—731no—
549C24—733no—
550C24C23×D7313yes—
551#41—232no—
552#41—29296no—
553#41—14632no—
554C2×Q8—29212no—
555C2×Q8—7324no—
556C2×Q8—734no—
557C2×Q8—7312no—
558C2×Q8—1464no—
559C2×Q8—14632no—
560C2×Q8—14612no—
561C2×Q8#1192402818yescomplemented
562C2×Q8C23×D7314yes—
563C2×D4—212no—
564C2×D4—29212no—
565C2×D4—7324no—
566C2×D4—7312no—
567C2×D4—7312no—
568C2×D4—7312no—
569C2×D4—7312no—
570C2×D4—14612no—
571C2×D4—14612no—
572C2×D4—14612no—
573C2×D4—14612no—
574C2×D4C23×D73112yes—
575C22×C4—212no—
576C22×C4—412no—
577C22×C4—29212no—
578C22×C4—7324no—
579C22×C4—731no—
580C22×C4—731no—
581C22×C4—733no—
582C22×C4—733no—
583C22×C4—733no—
584C22×C4—731no—
585C22×C4—734no—
586C22×C4—7312no—
587C22×C4—7312no—
588C22×C4—7312no—
589C22×C4—1464no—
590C22×C4—14612no—
591C22×C4—14612no—
592C22×C4—14612no—
593C22×C4C23×D73112yes—
594C22×C4C23×D7311yescharacteristic
595C22×C4C23×D7313yes—
596C22×C4C23×D7311yescharacteristic
597C22×C4C23×D7313yes—
598C22×C4C23×D7311yescharacteristic
599C22×C4C23×D73124yes—
600C22×C4C23×D7313yes—
601C4⋊C4—7312no—
602C4⋊C4—7324no—
603C4⋊C4—734no—
604C4⋊C4—734no—
605C4⋊C4—7312no—
606C4⋊C4—7312no—
607C4⋊C4—7312no—
608C4⋊C4—7312no—
609C4⋊C4—7312no—
610C4⋊C4—7312no—
611C4⋊C4—7312no—
612C4⋊C4C23×D73112yes—
613C4⋊C4C23×D73112yes—
614C4⋊C4C23×D73112yes—
615C4⋊C4C23×D7314yes—
616C22⋊C4—7312no—
617C22⋊C4—7324no—
618C22⋊C4—7312no—
619C22⋊C4—7312no—
620C22⋊C4—7312no—
621C22⋊C4—734no—
622C22⋊C4—734no—
623C22⋊C4—7312no—
624C22⋊C4—7324no—
625C22⋊C4—7312no—
626C22⋊C4C23×D73112yes—
627C22⋊C4C23×D73112yes—
628C42—7312no—
629C42—7312no—
630C42—7312no—
631C42—7312no—
632C42C23×D73112yes—
633C42C23×D73112yes—
634C23—26no—
635C23—26no—
636C23—26no—
637C23—734no—
638C23—732no—
639C23—736no—
640C23—1466no—
641C23—1466no—
642C23—1466no—
643C23—1462no—
644C23—1462no—
645C23C24×D7316yes—
646C23C24×D7311yescharacteristic
647Q8—29224no—
648Q8—1468no—
649Q8—14624no—
650Q8C2×#11924028116yescomplemented
651D4—224no—
652D4—29224no—
653D4—14624no—
654D4—14624no—
655D4—14624no—
656D4—14624no—
657C2×C4—22no—
658C2×C4—26no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—224no—
663C2×C4—424no—
664C2×C4—29224no—
665C2×C4—734no—
666C2×C4—732no—
667C2×C4—732no—
668C2×C4—736no—
669C2×C4—736no—
670C2×C4—736no—
671C2×C4—732no—
672C2×C4—1468no—
673C2×C4—14624no—
674C2×C4—1462no—
675C2×C4—1466no—
676C2×C4—1466no—
677C2×C4—1466no—
678C2×C4—1462no—
679C2×C4—14624no—
680C2×C4—14624no—
681C2×C4C2×#11924028112yes—
682C2×C4C24×D7312yes—
683C2×C4C24×D7316yes—
684C2×C4C24×D7312yes—
685C2×C4C24×D7316yes—
686C2×C4C24×D7312yes—
687C2×C4C24×D7316yes—
688C22—26no—
689C22—26no—
690C22—26no—
691C22—412no—
692C22—29212no—
693C22—734no—
694C22—1466no—
695C22—1466no—
696C22—1466no—
697C22—1468no—
698C22—1462no—
699C22—1462no—
700C22C22×#1192402812yes—
701C22H(5,𝔽2)×D7312yes—
702C222−1+4×D7312yes—
703C22C25×D7311yescharacteristic
704C4—22no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—22no—
709C4—734no—
710C4—1462no—
711C4—1466no—
712C4—1466no—
713C4—1466no—
714C4—1462no—
715C4C22×#11924028112yes—
716C2—46no—
717C2—2926no—
718C2—1464no—
719C2#2262401014yesdirect product factor
720C2C23×#1192402811yescharacteristic
721C2C2×H(5,𝔽2)×D7311yescharacteristic
722C2C2×2−1+4×D7311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#520×C73C2
socleC23×C73C25
hypercenterC2×#520D73
hypocenterC73C2×#3522
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #22624010C2direct (N × H)
2. C2×#17989320C2semidirect
3. C2×Q8×Dic146C2semidirect
4. C2×#17989292C2semidirect
5. C2×#17989256C2semidirect
6. C2×#17989249C2semidirect
7. C2×#17989244C2semidirect
8. C2×#17989242C2semidirect
9. C2×#17989238C2semidirect
10. C2×#17989208C2semidirect
11. C2×#17989202C2semidirect
12. C2×#17989134C2semidirect
13. C2×#17989115C2semidirect
14. C2×#17989069C2semidirect
15. C2×C4×Q8×D73C2semidirect
16. C2×#520×C73C2semidirect
20. #17989320C22semidirect
21. Q8×Dic146C22semidirect
22. #17989292C22semidirect
23. #17989256C22semidirect
24. #17989249C22semidirect
25. #17989244C22semidirect
26. #17989242C22semidirect
27. #17989238C22semidirect
28. #17989208C22semidirect
29. #17989202C22semidirect
30. #17989134C22semidirect
35. #17989115C22semidirect
57. #17989069C22semidirect
63. C4×Q8×D73C22semidirect
75. #520×C73C22semidirect
250. C2×Q8×C73#41semidirect
285. Q8×C73C2×#41semidirect
356. C2×C73#3522semidirect
376. C2×#520D73semidirect
378. C73C2×#3522semidirect
421. #520C2×D73semidirect
561. C2×Q8#11924028semidirect
650. Q8C2×#11924028semidirect
719. C2#22624010direct (N × H)

Maximal subgroups

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

subgroupindex
#226240102
C2×#179893202
C2×Q8×Dic1462
C2×#179892922
C2×#179892562
C2×#179892492
C2×#179892442
C2×#179892422
C2×#179892382
C2×#179892082
C2×#179892022
C2×#179891342
C2×#179891152
C2×#179890692
C2×C4×Q8×D732
C2×#520×C732
C2×#352273