Finite Group Databasebeta

← #3499×D73 #33994392

Subgroups — #3499×D73 #33994392

Order 18688.

11126 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D73C212yesmaximal, complemented
2#22623716C211yesmaximal, characteristic, complemented
3#22623715C214yesmaximal, complemented
4#22623714C213yesmaximal, complemented
5#22623713C216yesmaximal, complemented
6#22623712C212yesmaximal, complemented
7#22623711C213yesmaximal, complemented
8#22623710C2112yesmaximal, complemented
9D4×Q8×D73C214yesmaximal, complemented
10#547×D73C2112yesmaximal, complemented
11#536×D73C216yesmaximal, complemented
12#532×D73C213yesmaximal, complemented
13C2×C4⋊Q8×D73C213yesmaximal, complemented
14C4×#41×D73C211yesmaximal, characteristic, complemented
15C73×#3499C211yesmaximal, characteristic, complemented
16C2×#14556639C2216yescomplemented
17C2×#14556639C2214yescomplemented
18C2×#14556638C22112yescomplemented
19C2×#14556638C2216yescomplemented
20C2×#14556638C2212yescomplemented
212−1+4×D73—232no—
22C2×#41×D73C2216yes—
23C2×#41×D73C22112yes—
24C2×#41×D73C2211yescharacteristic
25C22×Q8×D73C2216yes—
26C22×Q8×D73C2214yes—
27Q8×D292C2214yescomplemented
28D4×Dic146C22112yescomplemented
29#17989252C22112yescomplemented
30Q8×C22⋊D73C2218yescomplemented
31#17989250C22124yescomplemented
32#17989242C22112yescomplemented
33#17989241C22112yescomplemented
34#17989240C22112yescomplemented
35#17989239C22124yescomplemented
36#17989238C22124yescomplemented
37#17989237C22124yescomplemented
38#17989236C22124yescomplemented
39#17989235C22148yescomplemented
40#17989163C2216yescomplemented
41#17989162C22112yescomplemented
42#17989161C2216yescomplemented
43#17989160C22124yescomplemented
44#17989159C22124yescomplemented
45#17989158C2216yescomplemented
46#17989157C22112yescomplemented
47#17989138C2213yescomplemented
48#17989137C2213yescomplemented
49#17989136C2216yescomplemented
50#17989135C2213yescomplemented
51#17989134C22112yescomplemented
52#17989133C2216yescomplemented
53#17989132C22112yescomplemented
54C2×#14556591C2213yescomplemented
55C2×#14556590C22112yescomplemented
56C2×#14556589C2216yescomplemented
57C4⋊Q8×D73C2216yes—
58C4⋊Q8×D73C22112yes—
59C4⋊Q8×D73C2213yes—
60C4⋊Q8×D73C22112yescomplemented
61C4⋊Q8×D73C2216yescomplemented
62C4⋊Q8×D73C2216yescomplemented
63#127×D73C2211yescharacteristic
64#124×D73C2216yes—
65#123×D73C22124yes—
66C22⋊Q8×D73C22124yes—
67#121×D73C22112yes—
68#41×Dic73C2211yescharacteristic, complemented
69C4×#11924029C2212yescomplemented
70C4×#11924028C2213yescomplemented
71#17989055C2213yescomplemented
72C4×#11924027C2216yescomplemented
73C4×Q8×D73C2212yes—
74C4×D4×D73C2216yes—
75C4×D4×D73C22112yes—
76#117×D73C2213yes—
77C2×C4⋊C4×D73C22112yes—
78C2×C42×D73C2213yes—
79C2×2−1+4×C73C2212yescomplemented
80D4×Q8×C73C2214yescomplemented
81#547×C73C22112yescomplemented
82#536×C73C2216yescomplemented
83#532×C73C2213yescomplemented
84C2×C4⋊Q8×C73C2213yescomplemented
85C4×#41×C73C2211yescharacteristic, complemented
86#14556639—232no—
87#14556639—248no—
88#14556638—248no—
89#14556638—296no—
90#14556638—216no—
91C2×#11924029C2316yes—
92C2×#11924029C23112yes—
93C2×#11924029C2311yescharacteristic
94C2×#11924028C2316yes—
95C2×#11924028C23112yes—
96C2×#11924028C23124yes—
97C2×#11924028C23112yes—
98C2×#11924028C2313yes—
99C2×#11924027C23112yes—
100C2×#11924027C2316yes—
101C2×#11924027C23124yes—
102C2×#11924027C23112yes—
103C2×#11924027C2313yes—
104#41×D73—296no—
105#41×D73—248no—
106#41×D73D4116yescomplemented
107C22×Dic146C2316yes—
108C22×Dic146C23112yes—
109C22×Dic146C23112yes—
110C2×Q8×D73—232no—
111C2×Q8×D73—248no—
112C2×Q8×D73C2316yes—
113C2×Q8×D73C23112yes—
114C2×Q8×D73C23112yes—
115C2×Q8×D73C23112yes—
116C2×Q8×D73C23112yes—
117C2×Q8×D73C2314yes—
118C2×Q8×D73C2311yescharacteristic
119C2×D4×D73C2312yes—
120C2×D4×D73C2314yes—
121C2×D4×D73C23112yes—
122C2×D4×D73C2313yes—
123C22×C4×D73C23112yes—
124C22×C4×D73C23112yes—
125C22×C4×D73C2316yes—
126C22×C4×D73C2313yes—
127#14556591C2313yes—
128#14556591C2316yes—
129#14556591C23112yes—
130#14556590C23112yes—
131#14556590C23124yes—
132#14556590C23124yes—
133#14556590C23124yes—
134#14556589C2316yes—
135#14556589C23112yes—
136#14556589C23124yes—
137#14556588C2311yescharacteristic
138#14556587C2314yes—
139#14556587C2312yes—
140#14556580C2316yes—
141#14556579C2316yes—
142#14556578C2316yes—
143#14556577C23124yes—
144#14556576C23148yes—
145#14556575C23124yes—
146#14556574C23124yes—
147#14556573C23148yes—
148#14556572C23124yes—
149#14556571C23124yes—
150#14556570C23124yes—
151#14556569C23148yes—
152#14556568C23148yes—
153#14556567C23124yes—
154#14556566C23112yes—
155#14556565C23112yes—
156#14556564C23124yes—
157#14556563C23124yes—
158#14556562C23112yes—
159Q8×Dic73C2312yes—
160C4×Dic146C2316yes—
161#14556556C2316yes—
162C4×D292C23112yes—
163C4×D292C2316yes—
164D4×Dic73C23112yes—
165D4×Dic73C2316yes—
166#14556553C23112yes—
167#14556553C2316yes—
168C4×C22⋊D73C23124yes—
169C4×C22⋊D73C23112yes—
170#14556551C23124yes—
171#14556551C23112yes—
172#14556550C2313yes—
173#14556549C2316yes—
174#14556548C2316yes—
175#14556547C2316yes—
176C2×C4⋊Dic73C23112yes—
177C2×#11924007C23124yes—
178C4⋊C4×D73C23112yes—
179C4⋊C4×D73C23124yes—
180C4⋊C4×D73C23124yes—
181C4⋊C4×D73C23124yes—
182C4⋊C4×D73C2316yes—
183C22⋊C4×D73C2316yes—
184C22⋊C4×D73C23124yes—
185C2×C4×Dic73C2313yes—
186C2×C4×Dic73C2316yes—
187C42×D73C2311yescharacteristic
188C42×D73C2313yes—
189C42×D73C2316yes—
190C42×D73C2316yes—
191C42×D73C2313yes—
192C42×D73C2313yes—
1932−1+4×C73—216no—
194C2×#41×C73C2316yes—
195C2×#41×C73C23112yes—
196C2×#41×C73C2311yescharacteristic
197C22×Q8×C73C2316yes—
198C22×Q8×C73C2314yes—
199C4⋊Q8×C73C2313yes—
200C4⋊Q8×C73C2316yes—
201C4⋊Q8×C73C23112yes—
202#127×C73C2311yescharacteristic
203#124×C73C2316yes—
204#123×C73C23124yes—
205C22⋊Q8×C73C23124yes—
206#121×C73C23112yes—
207C4×Q8×C73C2312yes—
208C4×D4×C73C23112yes—
209C4×D4×C73C2316yes—
210#117×C73C2313yes—
211C2×C4⋊C4×C73C23112yes—
212C2×C42×C73C2313yes—
213C23×D73C2414yes—
214C23×D73C2413yes—
215#11924029—248no—
216#11924029—224no—
217#11924029C2×D418yescomplemented
218#11924028—224no—
219#11924028—296no—
220#11924028—248no—
221#11924028—248no—
222#11924028C2×D4124yescomplemented
223#11924027—248no—
224#11924027—296no—
225#11924027—248no—
226#11924027—224no—
227#11924027C2×D4124yescomplemented
228C2×Dic146—224no—
229C2×Dic146—248no—
230C2×Dic146—248no—
231C2×Dic146C24124yes—
232C2×Dic146C24112yes—
233C2×Dic146C24112yes—
234C2×Dic146C2416yes—
235C2×Dic146C2413yes—
236Q8×D73—216no—
237Q8×D73—248no—
238Q8×D73—224no—
239Q8×D73—248no—
240Q8×D73—248no—
241Q8×D73—248no—
242Q8×D73C2×D418yes—
243C2×D292C2414yes—
244C2×D292C24112yes—
245C2×D292C2412yes—
246C2×D292C2413yes—
247C2×C22⋊D73C2418yes—
248C2×C22⋊D73C24112yes—
249C2×C22⋊D73C24112yes—
250C2×C22⋊D73C2414yes—
251C2×C22⋊D73C2416yes—
252D4×D73—248no—
253D4×D73—28no—
254D4×D73—216no—
255D4×D73C2×D4124yes—
256C22×Dic73C2416yes—
257C22×Dic73C24112yes—
258C22×Dic73C24112yes—
259C22×Dic73C2413yes—
260C2×C4×D73—248no—
261C2×C4×D73—248no—
262C2×C4×D73—224no—
263C2×C4×D73C2×D4124yes—
264C2×C4×D73C2416yes—
265C2×C4×D73C2416yes—
266C2×C4×D73C2416yes—
267C2×C4×D73C24112yes—
268C2×C4×D73C24124yes—
269C2×C4×D73C24112yes—
270C2×C4×D73C24112yes—
271C2×C4×D73C2411yescharacteristic
272C2×C4×D73C2413yes—
273C2×C4×D73C2413yes—
274C2×C4×D73C2413yes—
275C2×C4×D73C2412yes—
276C4⋊Dic73C24112yes—
277C4⋊Dic73C24124yes—
278C4⋊Dic73C2416yes—
279#11924007C24124yes—
280#11924007C24148yes—
281#11924007C24112yes—
282C22⋊Dic73C2416yes—
283C22⋊Dic73C24124yes—
284#11924005C24112yes—
285#11924005C24124yes—
286#11924005C24124yes—
287C4×Dic73C2411yescharacteristic
288C4×Dic73C2412yes—
289C4×Dic73C2416yes—
290C4×Dic73C2413yes—
291C4×Dic73C2416yes—
292C4×Dic73C2416yes—
293C4×Dic73C2416yes—
294#41×C73—248no—
295#41×C73—224no—
296#41×C73C2×D418yescomplemented
297C2×Q8×C73—216no—
298C2×Q8×C73—224no—
299C2×Q8×C73C24112yes—
300C2×Q8×C73C2416yes—
301C2×Q8×C73C2411yescharacteristic
302C2×D4×C73C2414yes—
303C2×D4×C73C24112yes—
304C2×D4×C73C2412yes—
305C2×D4×C73C2413yes—
306C22×C4×C73C2416yes—
307C22×C4×C73C24112yes—
308C22×C4×C73C24112yes—
309C22×C4×C73C2413yes—
310C4⋊C4×C73C24112yes—
311C4⋊C4×C73C24124yes—
312C4⋊C4×C73C2416yes—
313C22⋊C4×C73C2416yes—
314C22⋊C4×C73C24124yes—
315C42×C73C2411yescharacteristic
316C42×C73C2413yes—
317C42×C73C2416yes—
318C23×C73C2514yes—
319C23×C73C2513yes—
320C22×D73—212no—
321C22×D73—28no—
322C22×D73—216no—
323C22×D73C22×D4112yes—
324C22×D73C2514yes—
325C22×D73C2513yes—
326C22×D73C2511yescharacteristic
327Q8×C73—212no—
328Q8×C73—224no—
329Q8×C73C22×D414yes—
330D4×C73—224no—
331D4×C73—24no—
332D4×C73—28no—
333D4×C73C22×D4112yes—
334C2×C4×C73—224no—
335C2×C4×C73—224no—
336C2×C4×C73—212no—
337C2×C4×C73C22×D4112yes—
338C2×C4×C73C2516yes—
339C2×C4×C73C25112yes—
340C2×C4×C73C2511yescharacteristic
341C2×C4×C73C2513yes—
342C2×C4×C73C2512yes—
343C22⋊D73—224no—
344C22⋊D73—224no—
345C22⋊D73—28no—
346C22⋊D73—216no—
347C22⋊D73C22×D4124yes—
348C2×Dic73—224no—
349C2×Dic73—224no—
350C2×Dic73—212no—
351C2×Dic73C22×D4112yes—
352C2×Dic73C2516yes—
353C2×Dic73C25112yes—
354C2×Dic73C2511yescharacteristic
355C2×Dic73C2513yes—
356C2×Dic73C2512yes—
357D292—224no—
358D292—24no—
359D292—28no—
360D292C22×D4112yes—
361C4×D73—224no—
362C4×D73—248no—
363C4×D73—212no—
364C4×D73—224no—
365C4×D73—212no—
366C4×D73—224no—
367C4×D73—212no—
368C4×D73C22×D4112yes—
369C4×D73C22×D414yes—
370C4×D73C22×D4112yes—
371C4×D73C22×D4112yes—
372C4×D732−1+418yescomplemented
373Dic146—212no—
374Dic146—224no—
375Dic146—224no—
376Dic146—248no—
377Dic146C22×D4112yes—
378C22×C73—26no—
379C22×C73—24no—
380C22×C73—28no—
381C22×C73C23×D416yes—
382C22×C73C2611yescharacteristic
383C2×D73—26no—
384C2×D73—224no—
385C2×D73—24no—
386C2×D73—28no—
387C2×D73—416no—
388C2×D73C23×D416yes—
389C2×D73C23×D412yes—
390C2×D73C2×2−1+414yes—
391C4×C73—212no—
392C4×C73—26no—
393C4×C73C23×D412yes—
394C4×C73C23×D416yes—
395C4×C73C2×2−1+414yescomplemented
396Dic73—212no—
397Dic73—26no—
398Dic73C23×D412yes—
399Dic73C23×D416yes—
400Dic73C2×2−1+414yescomplemented
401C2×#3499—731nomaximal, Sylow
402C2×C73—26no—
403C2×C73—44no—
404C2×C73C24×D411yescharacteristic
405C2×C73C22×2−1+412yes—
406D73—26no—
407D73—44no—
408D73#349914yesdirect product factor
409C22×2−1+4—732no—
410#3499—732no—
411#3499—734no—
412#3499—7312no—
413#3499—736no—
414#3499—733no—
415#3499—733no—
416#3499—731no—
417#3499D7311yescharacteristic, direct product factor
418C2×D4×Q8—734no—
419C2×#547—7312no—
420C2×#536—736no—
421C2×#532—733no—
422C22×C4⋊Q8—733no—
423C2×C4×#41—731no—
424C73C2×#349911yescharacteristic, complemented, Sylow
425C2×2−1+4—736no—
426C2×2−1+4—7312no—
427C2×2−1+4—732no—
428C2×2−1+4—734no—
429C2×2−1+4—736no—
430C2×2−1+4—14632no—
431C2×2−1+4C2×D7312yescomplemented
432C22×#41—731no—
433C22×#41—736no—
434C22×#41—7312no—
435C23×Q8—736no—
436C23×Q8—734no—
437D4×Q8—738no—
438D4×Q8—7312no—
439D4×Q8—7324no—
440D4×Q8—734no—
441D4×Q8—7312no—
442D4×Q8C2×D7314yescomplemented
443#547—7324no—
444#547—7312no—
445#547—7348no—
446#547—7324no—
447#547—7324no—
448#547—7312no—
449#547—7312no—
450#547—7324no—
451#547C2×D73112yescomplemented
452#536—736no—
453#536—736no—
454#536—7312no—
455#536—7312no—
456#536—7324no—
457#536—7324no—
458#536—736no—
459#536C2×D7316yescomplemented
460#532—736no—
461#532—733no—
462#532—733no—
463#532—736no—
464#532—7312no—
465#532—7312no—
466#532—733no—
467#532C2×D7313yescomplemented
468C2×C4⋊Q8—736no—
469C2×C4⋊Q8—733no—
470C2×C4⋊Q8—736no—
471C2×C4⋊Q8—7312no—
472C2×C4⋊Q8—736no—
473C2×C4⋊Q8—736no—
474C2×C4⋊Q8—7312no—
475C2×C4⋊Q8—7312no—
476C2×C4⋊Q8—733no—
477C2×C4⋊Q8C2×D7313yescomplemented
478C2×#127—731no—
479C2×#124—736no—
480C2×#123—7324no—
481C2×C22⋊Q8—7324no—
482C2×#121—7312no—
483C4×#41—731no—
484C4×#41—732no—
485C4×#41—736no—
486C4×#41—733no—
487C4×#41—733no—
488C4×#41C2×D7311yescharacteristic, complemented
489C2×C4×Q8—732no—
490C2×C4×D4—736no—
491C2×C4×D4—7312no—
492C2×#117—733no—
493C22×C4⋊C4—7312no—
494C22×C42—733no—
4952−1+4—216no—
4962−1+4—14632no—
4972−1+4—14648no—
4982−1+4—14696no—
4992−1+4—14648no—
5002−1+4—14616no—
501C2×#41—7316no—
502C2×#41—731no—
503C2×#41—736no—
504C2×#41—7312no—
505C2×#41—733no—
506C2×#41—7312no—
507C2×#41—736no—
508C2×#41—7312no—
509C2×#41—7324no—
510C2×#41—733no—
511C2×#41—7312no—
512C2×#41—736no—
513C2×#41—7312no—
514C2×#41—7324no—
515C2×#41—14648no—
516C2×#41—14696no—
517C2×#41C22×D7316yes—
518C2×#41C22×D73112yes—
519C2×#41C22×D7311yescharacteristic
520C22×Q8—731no—
521C22×Q8—7312no—
522C22×Q8—736no—
523C22×Q8—7312no—
524C22×Q8—7312no—
525C22×Q8—7312no—
526C22×Q8—734no—
527C22×Q8—7312no—
528C22×Q8—736no—
529C22×Q8—7312no—
530C22×Q8—14648no—
531C22×Q8—14632no—
532C22×Q8C22×D7316yes—
533C22×Q8C22×D7314yes—
534C22×D4—733no—
535C22×D4—734no—
536C22×D4—7312no—
537C22×D4—732no—
538C23×C4—733no—
539C23×C4—736no—
540C23×C4—7312no—
541C23×C4—7312no—
542C4⋊Q8—736no—
543C4⋊Q8—7312no—
544C4⋊Q8—7324no—
545C4⋊Q8—7312no—
546C4⋊Q8—7324no—
547C4⋊Q8—7324no—
548C4⋊Q8—7324no—
549C4⋊Q8—733no—
550C4⋊Q8—736no—
551C4⋊Q8—7312no—
552C4⋊Q8C22×D7313yes—
553C4⋊Q8C22×D7316yes—
554C4⋊Q8C22×D73112yes—
555#127—732no—
556#127—734no—
557#127—731no—
558#127C22×D7311yescharacteristic
559#124—736no—
560#124—736no—
561#124—7324no—
562#124—736no—
563#124C22×D7316yes—
564#123—7324no—
565#123—7324no—
566#123—7348no—
567#123—7348no—
568#123—7324no—
569#123C22×D73124yes—
570C22⋊Q8—7324no—
571C22⋊Q8—7324no—
572C22⋊Q8—7348no—
573C22⋊Q8—7324no—
574C22⋊Q8—7348no—
575C22⋊Q8C22×D73124yes—
576#121—7312no—
577#121—7324no—
578#121—7312no—
579#121—7312no—
580#121—7324no—
581#121C22×D73112yes—
582C4×Q8—732no—
583C4×Q8—736no—
584C4×Q8—736no—
585C4×Q8C22×D7312yes—
586C4×D4—736no—
587C4×D4—7312no—
588C4×D4—7312no—
589C4×D4—7324no—
590C4×D4—736no—
591C4×D4—7312no—
592C4×D4—7312no—
593C4×D4—7324no—
594C4×D4—736no—
595C4×D4—7312no—
596C4×D4C22×D7316yes—
597C4×D4C22×D73112yes—
598#117—733no—
599#117—736no—
600#117—736no—
601#117—736no—
602#117C22×D7313yes—
603C2×C4⋊C4—7324no—
604C2×C4⋊C4—7312no—
605C2×C4⋊C4—7312no—
606C2×C4⋊C4—7324no—
607C2×C4⋊C4—7324no—
608C2×C4⋊C4—7324no—
609C2×C4⋊C4—736no—
610C2×C4⋊C4C22×D73112yes—
611C2×C22⋊C4—736no—
612C2×C22⋊C4—7324no—
613C2×C42—736no—
614C2×C42—733no—
615C2×C42—733no—
616C2×C42—736no—
617C2×C42—736no—
618C2×C42—733no—
619C2×C42—733no—
620C2×C42—731no—
621C2×C42C22×D7313yes—
622C24—733no—
623C24—734no—
624#41—248no—
625#41—224no—
626#41—738no—
627#41—7324no—
628#41—7324no—
629#41—14648no—
630#41—14696no—
631#41—14648no—
632#41—14648no—
633#41—14624no—
634#41—14624no—
635#41—14696no—
636#41—14648no—
637#41—14648no—
638#41—14624no—
639#41D4×D7318yescomplemented
640C2×Q8—216no—
641C2×Q8—224no—
642C2×Q8—738no—
643C2×Q8—733no—
644C2×Q8—7324no—
645C2×Q8—7312no—
646C2×Q8—7312no—
647C2×Q8—736no—
648C2×Q8—14648no—
649C2×Q8—14648no—
650C2×Q8—14624no—
651C2×Q8—14648no—
652C2×Q8—14648no—
653C2×Q8—14648no—
654C2×Q8—14648no—
655C2×Q8—14616no—
656C2×Q8—14624no—
657C2×Q8C23×D73112yes—
658C2×Q8C23×D7316yes—
659C2×Q8C23×D7311yescharacteristic
660C2×D4—736no—
661C2×D4—7324no—
662C2×D4—738no—
663C2×D4—7312no—
664C2×D4—7312no—
665C2×D4—734no—
666C2×D4—733no—
667C2×D4—734no—
668C2×D4—7312no—
669C2×D4—732no—
670C2×D4—14616no—
671C2×D4—1468no—
672C2×D4—14648no—
673C2×D4C23×D7314yes—
674C2×D4C23×D73112yes—
675C2×D4C23×D7312yes—
676C2×D4C23×D7313yes—
677C22×C4—733no—
678C22×C4—7324no—
679C22×C4—732no—
680C22×C4—731no—
681C22×C4—733no—
682C22×C4—733no—
683C22×C4—733no—
684C22×C4—736no—
685C22×C4—7312no—
686C22×C4—7312no—
687C22×C4—736no—
688C22×C4—736no—
689C22×C4—736no—
690C22×C4—7312no—
691C22×C4—7324no—
692C22×C4—7312no—
693C22×C4—7312no—
694C22×C4—14624no—
695C22×C4—14648no—
696C22×C4—14648no—
697C22×C4C23×D7316yes—
698C22×C4C23×D73112yes—
699C22×C4C23×D73112yes—
700C22×C4C23×D7313yes—
701C4⋊C4—7324no—
702C4⋊C4—7348no—
703C4⋊C4—7312no—
704C4⋊C4—7312no—
705C4⋊C4—7324no—
706C4⋊C4—736no—
707C4⋊C4C23×D73112yes—
708C4⋊C4C23×D73124yes—
709C4⋊C4C23×D7316yes—
710C22⋊C4—736no—
711C22⋊C4—7324no—
712C22⋊C4—7312no—
713C22⋊C4—7324no—
714C22⋊C4—7324no—
715C22⋊C4C23×D7316yes—
716C22⋊C4C23×D73124yes—
717C42—731no—
718C42—732no—
719C42—736no—
720C42—733no—
721C42—736no—
722C42—736no—
723C42—736no—
724C42C23×D7311yescharacteristic
725C42C23×D7313yes—
726C42C23×D7316yes—
727C23—731no—
728C23—7312no—
729C23—733no—
730C23—734no—
731C23—1468no—
732C23—14616no—
733C23—14612no—
734C23C24×D7314yes—
735C23C24×D7313yes—
736Q8—224no—
737Q8—212no—
738Q8—7312no—
739Q8—14624no—
740Q8—14648no—
741Q8—14624no—
742Q8—14612no—
743Q8C2×D4×D7314yes—
744D4—224no—
745D4—24no—
746D4—28no—
747D4—7324no—
748D4—7312no—
749D4—14624no—
750D4—1468no—
751D4—14616no—
752D4—14624no—
753D4—14624no—
754D4—1464no—
755D4—1468no—
756D4C2×D4×D73112yes—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—212no—
760C2×C4—7312no—
761C2×C4—732no—
762C2×C4—731no—
763C2×C4—733no—
764C2×C4—734no—
765C2×C4—7312no—
766C2×C4—7312no—
767C2×C4—7312no—
768C2×C4—738no—
769C2×C4—736no—
770C2×C4—7312no—
771C2×C4—14624no—
772C2×C4—14612no—
773C2×C4—14624no—
774C2×C4—14648no—
775C2×C4—14612no—
776C2×C4—14624no—
777C2×C4—14612no—
778C2×C4—14624no—
779C2×C4—14624no—
780C2×C4—14612no—
781C2×C4C2×D4×D73112yes—
782C2×C4C24×D7316yes—
783C2×C4C24×D73112yes—
784C2×C4C24×D7311yescharacteristic
785C2×C4C24×D7313yes—
786C2×C4C24×D7312yes—
787C22—26no—
788C22—24no—
789C22—28no—
790C22—29216no—
791C22—732no—
792C22—734no—
793C22—736no—
794C22—14624no—
795C22—1464no—
796C22—1468no—
797C22—1466no—
798C22C22×D4×D7316yes—
799C22C25×D7311yescharacteristic
800C4—212no—
801C4—26no—
802C4—732no—
803C4—736no—
804C4—734no—
805C4—14612no—
806C4—1466no—
807C4C22×D4×D7316yes—
808C4C22×D4×D7312yes—
809C42−1+4×D7314yescomplemented
810C2—26no—
811C2—44no—
812C2—2924no—
813C2—734no—
814C2—1466no—
815C2C23×D4×D7311yescharacteristic
816C2C2×2−1+4×D7312yes—
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3499C2
hypercenter#3499D73
hypocenterC73C2×#3499
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D73C2semidirect
2. #22623716C2semidirect
3. #22623715C2semidirect
4. #22623714C2semidirect
5. #22623713C2semidirect
6. #22623712C2semidirect
7. #22623711C2semidirect
8. #22623710C2semidirect
9. D4×Q8×D73C2semidirect
10. #547×D73C2semidirect
11. #536×D73C2semidirect
12. #532×D73C2semidirect
13. C2×C4⋊Q8×D73C2semidirect
14. C4×#41×D73C2semidirect
15. C73×#3499C2semidirect
16. C2×#14556639C22semidirect
17. C2×#14556639C22semidirect
18. C2×#14556638C22semidirect
19. C2×#14556638C22semidirect
20. C2×#14556638C22semidirect
27. Q8×D292C22semidirect
28. D4×Dic146C22semidirect
29. #17989252C22semidirect
30. Q8×C22⋊D73C22semidirect
31. #17989250C22semidirect
32. #17989242C22semidirect
33. #17989241C22semidirect
34. #17989240C22semidirect
35. #17989239C22semidirect
36. #17989238C22semidirect
37. #17989237C22semidirect
38. #17989236C22semidirect
39. #17989235C22semidirect
40. #17989163C22semidirect
41. #17989162C22semidirect
42. #17989161C22semidirect
43. #17989160C22semidirect
44. #17989159C22semidirect
45. #17989158C22semidirect
46. #17989157C22semidirect
47. #17989138C22semidirect
48. #17989137C22semidirect
49. #17989136C22semidirect
50. #17989135C22semidirect
51. #17989134C22semidirect
52. #17989133C22semidirect
53. #17989132C22semidirect
54. C2×#14556591C22semidirect
55. C2×#14556590C22semidirect
56. C2×#14556589C22semidirect
60. C4⋊Q8×D73C22semidirect
61. C4⋊Q8×D73C22semidirect
62. C4⋊Q8×D73C22semidirect
68. #41×Dic73C22semidirect
69. C4×#11924029C22semidirect
70. C4×#11924028C22semidirect
71. #17989055C22semidirect
72. C4×#11924027C22semidirect
79. C2×2−1+4×C73C22semidirect
80. D4×Q8×C73C22semidirect
81. #547×C73C22semidirect
82. #536×C73C22semidirect
83. #532×C73C22semidirect
84. C2×C4⋊Q8×C73C22semidirect
85. C4×#41×C73C22semidirect
106. #41×D73D4semidirect
217. #11924029C2×D4semidirect
222. #11924028C2×D4semidirect
227. #11924027C2×D4semidirect
296. #41×C73C2×D4semidirect
372. C4×D732−1+4semidirect
395. C4×C73C2×2−1+4semidirect
400. Dic73C2×2−1+4semidirect
408. D73#3499direct (N × H)
417. #3499D73direct (N × H)
424. C73C2×#3499semidirect
431. C2×2−1+4C2×D73semidirect
442. D4×Q8C2×D73semidirect
451. #547C2×D73semidirect
459. #536C2×D73semidirect
467. #532C2×D73semidirect
477. C2×C4⋊Q8C2×D73semidirect
488. C4×#41C2×D73semidirect
639. #41D4×D73semidirect
809. C42−1+4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D732
#226237162
#226237152
#226237142
#226237132
#226237122
#226237112
#226237102
D4×Q8×D732
#547×D732
#536×D732
#532×D732
C2×C4⋊Q8×D732
C4×#41×D732
C73×#34992
C2×#349973