Finite Group Databasebeta

← #33994530

Subgroups — #33994530

Order 18688.

11346 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989424C212yesmaximal, complemented
2#22623725C212yesmaximal, complemented
3#22623720C216yesmaximal, complemented
4#22623714C213yesmaximal, complemented
5#22623709C211yesmaximal, characteristic, complemented
6#22623704C213yesmaximal, complemented
7#22623701C214yesmaximal, complemented
8#22623689C2112yesmaximal, complemented
9D4×#11924029C214yesmaximal, complemented
10#22623418C2112yesmaximal, complemented
11#22623263C216yesmaximal, complemented
12C2×#17989138C213yesmaximal, complemented
13#532×D73C213yesmaximal, complemented
14C4×#41×D73C211yesmaximal, characteristic, complemented
15C73×#3499C211yesmaximal, characteristic, complemented
16#17989424—232no—
17C2×#14556639C2214yescomplemented
18C2×#14556639C2216yescomplemented
19C2×#14556637C22112yescomplemented
20C2×#14556637C2216yescomplemented
21C2×#14556637C2212yescomplemented
22C22×#11924029C2216yescomplemented
23C22×#11924029C2214yescomplemented
24C2×#41×D73C2211yescharacteristic
25C2×#41×D73C2216yescomplemented
26C2×#41×D73C22112yescomplemented
27#17989259C2214yescomplemented
28#17989258C22112yescomplemented
29#17989252C22112yescomplemented
30#17989248C2218yescomplemented
31#17989247C22124yescomplemented
32#17989240C22112yescomplemented
33#17989238C22124yescomplemented
34#17989229C22148yescomplemented
35#17989228C22124yescomplemented
36#17989225C22124yescomplemented
37D4×D292C22112yescomplemented
38D4×D292C22112yescomplemented
39#17989221C22124yescomplemented
40#17989167C22124yescomplemented
41#17989162C22112yescomplemented
42#17989161C2216yescomplemented
43#17989156C2216yescomplemented
44#17989155C22112yescomplemented
45#17989151C2216yescomplemented
46#17989148C22124yescomplemented
47#17989138C2216yescomplemented
48#17989138C22112yescomplemented
49#17989138C22112yescomplemented
50#17989138C2216yescomplemented
51#17989138C2213yescomplemented
52#17989138C2216yescomplemented
53#17989137C2213yescomplemented
54#17989136C2216yescomplemented
55#17989135C2211yescharacteristic, complemented
56#17989134C22112yescomplemented
57#17989133C2216yescomplemented
58#17989132C22112yescomplemented
59C4⋊Q8×D73C2213yescomplemented
60C2×#14556588C2213yescomplemented
61#127×D73C2213yescomplemented
62C2×#14556580C2216yescomplemented
63#124×D73C2216yescomplemented
64#17989100C22124yescomplemented
65#17989095C22124yescomplemented
66C2×#14556566C22112yescomplemented
67#121×D73C22112yescomplemented
68#41×Dic73C2211yescharacteristic, complemented
69C4×#11924029C2212yescomplemented
70C4×#11924028C2213yescomplemented
71#17989055C2213yescomplemented
72C4×#11924027C2216yescomplemented
73C4×Q8×D73C2212yescomplemented
74C2×#14556553C22112yescomplemented
75C4×D4×D73C2216yescomplemented
76C4×D4×D73C22112yescomplemented
77#117×D73C2213yescomplemented
78C2×C42×D73C2213yescomplemented
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—248no—
87#14556639—232no—
88#14556637—248no—
89#14556637—296no—
90#14556637—216no—
91C2×#11924029—232no—
92C2×#11924029—248no—
93C2×#11924029C2316yes—
94C2×#11924029C23112yes—
95C2×#11924029C23112yes—
96C2×#11924029C23112yes—
97C2×#11924029C23112yes—
98C2×#11924029C2314yes—
99C2×#11924029C2311yescharacteristic
100C2×#11924028C2316yes—
101C2×#11924028C23112yes—
102C2×#11924028C23124yes—
103C2×#11924028C23112yes—
104C2×#11924028C2313yes—
105C2×#11924027C23112yes—
106C2×#11924027C2312yes—
107C2×#11924027C2313yes—
108#41×D73—296no—
109#41×D73—248no—
110#41×D73D4116yescomplemented
111C2×Q8×D73C2316yes—
112C2×Q8×D73C23112yes—
113C2×Q8×D73C2311yescharacteristic
114C22×D292C2316yes—
115C22×D292C23112yes—
116C22×D292C23112yes—
117C22×D292C23112yes—
118C2×D4×D73C2316yes—
119C2×D4×D73C23112yes—
120C2×D4×D73C23124yes—
121C2×D4×D73C23112yes—
122C2×D4×D73C23112yes—
123C2×D4×D73C2313yes—
124C22×C4×D73C23112yes—
125C22×C4×D73C23112yes—
126C22×C4×D73C2316yes—
127C22×C4×D73C2313yes—
128#14556591C2311yescharacteristic
129#14556590C23112yes—
130#14556589C2316yes—
131#14556588C2313yes—
132#14556588C2316yes—
133#14556588C23112yes—
134#14556587C23112yes—
135#14556587C2316yes—
136#14556580C2316yes—
137#14556580C23112yes—
138#14556580C23124yes—
139#14556579C2316yes—
140#14556578C2312yes—
141#14556577C23124yes—
142#14556576C23148yes—
143#14556574C23124yes—
144#14556569C23148yes—
145#14556567C23124yes—
146#14556566C23112yes—
147#14556566C23124yes—
148#14556566C23124yes—
149#14556566C23124yes—
150#14556566C23124yes—
151#14556565C23112yes—
152#14556565C23124yes—
153#14556564C23124yes—
154#14556564C23148yes—
155#14556563C23124yes—
156#14556562C2314yes—
157#14556561C23148yes—
158#14556561C23124yes—
159#14556559C23124yes—
160Q8×Dic73C2312yes—
161C4×Dic146C2316yes—
162#14556556C2316yes—
163C4×D292C23112yes—
164C4×D292C2316yes—
165D4×Dic73C2314yes—
166D4×Dic73C2316yes—
167#14556553C23112yes—
168#14556553C23124yes—
169#14556553C23124yes—
170#14556553C23124yes—
171#14556553C2316yes—
172C4×C22⋊D73C23124yes—
173C4×C22⋊D73C23112yes—
174#14556551C23124yes—
175#14556551C23112yes—
176#14556550C2313yes—
177#14556549C2316yes—
178#14556548C2316yes—
179#14556547C2316yes—
180C4⋊C4×D73C23112yes—
181C4⋊C4×D73C2316yes—
182C2×#11924005C23124yes—
183C22⋊C4×D73C2316yes—
184C22⋊C4×D73C23124yes—
185C2×C4×Dic73C2316yes—
186C2×C4×Dic73C2313yes—
187C42×D73C2313yes—
188C42×D73C2316yes—
189C42×D73C2311yescharacteristic
190C42×D73C2313yes—
191C42×D73C2316yes—
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×D73C24112yes—
214C23×D73C24112yes—
215C23×D73C2413yes—
216#11924029—216no—
217#11924029—248no—
218#11924029—248no—
219#11924029—224no—
220#11924029—248no—
221#11924029—248no—
222#11924029C2×D418yescomplemented
223#11924028—224no—
224#11924028—296no—
225#11924028—248no—
226#11924028—248no—
227#11924028C2×D4124yescomplemented
228#11924027—248no—
229#11924027—28no—
230#11924027C2×D4124yescomplemented
231C2×Dic146C24112yes—
232C2×Dic146C2412yes—
233C2×Dic146C2413yes—
234Q8×D73—224no—
235Q8×D73—248no—
236Q8×D73C2×D418yescomplemented
237C2×D292—248no—
238C2×D292—224no—
239C2×D292—248no—
240C2×D292—424no—
241C2×D292C24112yes—
242C2×D292C24124yes—
243C2×D292C24112yes—
244C2×D292C24112yes—
245C2×D292C2416yes—
246C2×D292C24124yes—
247C2×D292C2413yes—
248C2×C22⋊D73C24112yes—
249C2×C22⋊D73C2414yes—
250C2×C22⋊D73C24112yes—
251C2×C22⋊D73C24124yes—
252C2×C22⋊D73C2416yes—
253D4×D73—248no—
254D4×D73—248no—
255D4×D73—296no—
256D4×D73—224no—
257D4×D73—424no—
258D4×D73C2×D4124yescomplemented
259C22×Dic73C2414yes—
260C22×Dic73C2416yes—
261C22×Dic73C2413yes—
262C2×C4×D73—248no—
263C2×C4×D73—248no—
264C2×C4×D73—412no—
265C2×C4×D73C2×D4124yescomplemented
266C2×C4×D73C2412yes—
267C2×C4×D73C2416yes—
268C2×C4×D73C24112yes—
269C2×C4×D73C24112yes—
270C2×C4×D73C24112yes—
271C2×C4×D73C24124yes—
272C2×C4×D73C2416yes—
273C2×C4×D73C2416yes—
274C2×C4×D73C2411yescharacteristic
275C2×C4×D73C2413yes—
276C2×C4×D73C2413yes—
277C2×C4×D73C2413yes—
278C4⋊Dic73C2414yes—
279C4⋊Dic73C2416yes—
280#11924007C24112yes—
281#11924007C24124yes—
282C22⋊Dic73C2418yes—
283C22⋊Dic73C2416yes—
284#11924005C24124yes—
285#11924005C24112yes—
286#11924005C24124yes—
287#11924005C24148yes—
288C4×Dic73C2412yes—
289C4×Dic73C2411yescharacteristic
290C4×Dic73C2416yes—
291C4×Dic73C2413yes—
292C4×Dic73C2416yes—
293C4×Dic73C2416yes—
294C4×Dic73C2416yes—
295#41×C73—248no—
296#41×C73—224no—
297#41×C73C2×D418yescomplemented
298C2×Q8×C73—216no—
299C2×Q8×C73—224no—
300C2×Q8×C73C24112yes—
301C2×Q8×C73C2416yes—
302C2×Q8×C73C2411yescharacteristic
303C2×D4×C73C2414yes—
304C2×D4×C73C24112yes—
305C2×D4×C73C2412yes—
306C2×D4×C73C2413yes—
307C22×C4×C73C2416yes—
308C22×C4×C73C24112yes—
309C22×C4×C73C24112yes—
310C22×C4×C73C2413yes—
311C4⋊C4×C73C24112yes—
312C4⋊C4×C73C24124yes—
313C4⋊C4×C73C2416yes—
314C22⋊C4×C73C2416yes—
315C22⋊C4×C73C24124yes—
316C42×C73C2411yescharacteristic
317C42×C73C2413yes—
318C42×C73C2416yes—
319C23×C73C2514yes—
320C23×C73C2513yes—
321C22×D73—224no—
322C22×D73—224no—
323C22×D73—46no—
324C22×D73—424no—
325C22×D73—424no—
326C22×D73C22×D4112yes—
327C22×D73C25112yes—
328C22×D73C2513yes—
329C22×D73C2511yescharacteristic
330Q8×C73—212no—
331Q8×C73—224no—
332Q8×C73C22×D414yes—
333D4×C73—224no—
334D4×C73—24no—
335D4×C73—28no—
336D4×C73C22×D4112yes—
337C2×C4×C73—224no—
338C2×C4×C73—224no—
339C2×C4×C73—212no—
340C2×C4×C73C22×D4112yes—
341C2×C4×C73C2516yes—
342C2×C4×C73C25112yes—
343C2×C4×C73C2511yescharacteristic
344C2×C4×C73C2513yes—
345C2×C4×C73C2512yes—
346C22⋊D73—224no—
347C22⋊D73—28no—
348C22⋊D73—224no—
349C22⋊D73—424no—
350C22⋊D73C22×D4124yes—
351C2×Dic73—28no—
352C2×Dic73—46no—
353C2×Dic73C22×D4112yes—
354C2×Dic73C2512yes—
355C2×Dic73C2516yes—
356C2×Dic73C2514yes—
357C2×Dic73C2511yescharacteristic
358C2×Dic73C2513yes—
359D292—248no—
360D292—224no—
361D292—212no—
362D292—224no—
363D292—224no—
364D292—424no—
365D292C22×D4112yes—
366C4×D73—224no—
367C4×D73—224no—
368C4×D73—24no—
369C4×D73—212no—
370C4×D73—224no—
371C4×D73—248no—
372C4×D73—46no—
373C4×D73—46no—
374C4×D73C22×D4112yes—
375C4×D73C22×D414yes—
376C4×D73C22×D4112yes—
377C4×D73C22×D4112yes—
378Dic146—24no—
379Dic146—224no—
380Dic146C22×D4112yes—
381C22×C73—26no—
382C22×C73—24no—
383C22×C73—28no—
384C22×C73C23×D416yes—
385C22×C73C2611yescharacteristic
386C2×D73—22no—
387C2×D73—26no—
388C2×D73—212no—
389C2×D73—224no—
390C2×D73—412no—
391C2×D73—824no—
392C2×D73—824no—
393C2×D73C23×D416yes—
394C2×D73C23×D412yes—
395C4×C73—212no—
396C4×C73—26no—
397C4×C73C23×D412yes—
398C4×C73C23×D416yes—
399C4×C73#58514yescomplemented
400Dic73—24no—
401Dic73—22no—
402Dic73—26no—
403Dic73C23×D416yes—
404Dic73C23×D412yes—
405#62812—731nomaximal, Sylow
406C2×C73—26no—
407C2×C73—44no—
408C2×C73C24×D411yescharacteristic
409C2×C73C2×#58512yes—
410D73—22no—
411D73—26no—
412D73—412no—
413C2×#585—732no—
414#3500—732no—
415#3500—736no—
416#3499—733no—
417#3499D7311yescharacteristic, complemented
418#3498—733no—
419#3498—731no—
420#3497—734no—
421#3496—7312no—
422D4×#41—734no—
423D4×#41—7312no—
424#3449—736no—
425C2×#532—733no—
426C2×#532—733no—
427C2×C4×#41—731no—
428C73#6281211yescharacteristic, complemented, Sylow
429#585—14632no—
430C2×2−1+4—734no—
431C2×2−1+4—736no—
432C2×2−1+4C2×D7312yescomplemented
433C2×H(5,𝔽2)—7312no—
434C2×H(5,𝔽2)—736no—
435C2×H(5,𝔽2)—732no—
436C22×#41—731no—
437C22×#41—736no—
438C22×#41—7312no—
439C22×#41—736no—
440C22×#41—734no—
441#550—734no—
442#550—7312no—
443D4×Q8—7312no—
444D4×Q8C2×D7314yescomplemented
445#548—738no—
446#548—7324no—
447#547—7312no—
448#547—7324no—
449#547C2×D73112yescomplemented
450#546—7324no—
451#546—7348no—
452#546—7324no—
453D42—7324no—
454D42—7312no—
455D42—7312no—
456#537—7324no—
457#536—736no—
458#536—7312no—
459#536C2×D7316yescomplemented
460#535—736no—
461#535—7312no—
462#535—736no—
463#534—7324no—
464#532—736no—
465#532—733no—
466#532—736no—
467#532—7312no—
468#532—7312no—
469#532—736no—
470#532—736no—
471#532—731no—
472#532—736no—
473#532—7312no—
474#532—7312no—
475#532—733no—
476#532C2×D7313yescomplemented
477C2×C4⋊Q8—733no—
478C2×C4⋊Q8C2×D7313yescomplemented
479C2×#127—733no—
480C2×#127—733no—
481C2×#124—736no—
482C2×#124—736no—
483#525—7324no—
484#525—7324no—
485C2×#121—7312no—
486C2×#121—7312no—
487C4×#41—731no—
488C4×#41—732no—
489C4×#41—736no—
490C4×#41—733no—
491C4×#41—733no—
492C4×#41C2×D7311yescharacteristic, complemented
493C2×C4×Q8—732no—
494C2×C4×D4—736no—
495C2×C4×D4—7312no—
496C2×C4×D4—7312no—
497C2×#117—733no—
498C22×C42—733no—
4992−1+4—216no—
5002−1+4—14632no—
5012−1+4—14648no—
502H(5,𝔽2)—14696no—
503H(5,𝔽2)—14648no—
504H(5,𝔽2)—14616no—
505C2×#41—7316no—
506C2×#41—731no—
507C2×#41—7312no—
508C2×#41—736no—
509C2×#41—7312no—
510C2×#41—7312no—
511C2×#41—7312no—
512C2×#41—734no—
513C2×#41—733no—
514C2×#41—7312no—
515C2×#41—732no—
516C2×#41—733no—
517C2×#41—736no—
518C2×#41—7312no—
519C2×#41—7324no—
520C2×#41—7312no—
521C2×#41—14648no—
522C2×#41—14648no—
523C2×#41—14632no—
524C2×#41—14696no—
525C2×#41C22×D7316yes—
526C2×#41C22×D73112yes—
527C2×#41C22×D7311yescharacteristic
528C22×Q8—731no—
529C22×Q8—736no—
530C22×Q8—7312no—
531C22×Q8C22×D7316yes—
532C22×Q8C22×D7314yes—
533C22×D4—7312no—
534C22×D4—733no—
535C22×D4—7312no—
536C22×D4—736no—
537C22×D4—7324no—
538C22×D4—7312no—
539C22×D4—7312no—
540C22×D4—7312no—
541C22×D4—736no—
542C22×D4—7312no—
543C23×C4—736no—
544C23×C4—733no—
545C23×C4—7312no—
546C23×C4—7312no—
547C4⋊Q8—736no—
548C4⋊Q8—7312no—
549C4⋊Q8—731no—
550C4⋊Q8C22×D7313yes—
551C4⋊Q8C22×D7316yes—
552C4⋊Q8C22×D73112yes—
553#127—736no—
554#127—7312no—
555#127—733no—
556#127—736no—
557#127—7312no—
558#127C22×D7311yescharacteristic
559#124—736no—
560#124—7312no—
561#124—7324no—
562#124—732no—
563#124—7324no—
564#124—736no—
565#124C22×D7316yes—
566#123—7324no—
567#123—7348no—
568#123C22×D73124yes—
569C22⋊Q8—7324no—
570C22⋊Q8—7348no—
571C22⋊Q8C22×D73124yes—
572#121—734no—
573#121—7324no—
574#121—7312no—
575#121—7324no—
576#121—7312no—
577#121—7324no—
578#121—7324no—
579#121—7324no—
580#121—7324no—
581#121—7324no—
582#121—7348no—
583#121C22×D73112yes—
584#120—7324no—
585#120—7348no—
586#120—7324no—
587C4×Q8—732no—
588C4×Q8—736no—
589C4×Q8—736no—
590C4×Q8C22×D7312yes—
591C4×D4—734no—
592C4×D4—736no—
593C4×D4—7312no—
594C4×D4—7324no—
595C4×D4—7312no—
596C4×D4—736no—
597C4×D4—7324no—
598C4×D4—7324no—
599C4×D4—7324no—
600C4×D4—7312no—
601C4×D4—7324no—
602C4×D4—736no—
603C4×D4—7312no—
604C4×D4C22×D7316yes—
605C4×D4C22×D73112yes—
606#117—733no—
607#117—736no—
608#117—736no—
609#117—736no—
610#117C22×D7313yes—
611C2×C4⋊C4—736no—
612C2×C4⋊C4—7312no—
613C2×C4⋊C4C22×D73112yes—
614C2×C22⋊C4—7324no—
615C2×C22⋊C4—736no—
616C2×C22⋊C4—7324no—
617C2×C42—736no—
618C2×C42—733no—
619C2×C42—733no—
620C2×C42—736no—
621C2×C42—736no—
622C2×C42—733no—
623C2×C42—733no—
624C2×C42—731no—
625C2×C42C22×D7313yes—
626C24—733no—
627C24—7312no—
628C24—7312no—
629#41—248no—
630#41—224no—
631#41—738no—
632#41—7324no—
633#41—7324no—
634#41—14648no—
635#41—14696no—
636#41—14648no—
637#41—14648no—
638#41—1468no—
639#41—14624no—
640#41—14648no—
641#41—14648no—
642#41—14648no—
643#41—14648no—
644#41—14616no—
645#41—14624no—
646#41D4×D7318yescomplemented
647C2×Q8—216no—
648C2×Q8—224no—
649C2×Q8—738no—
650C2×Q8—733no—
651C2×Q8—7312no—
652C2×Q8—732no—
653C2×Q8—14624no—
654C2×Q8—14648no—
655C2×Q8C23×D73112yes—
656C2×Q8C23×D7316yes—
657C2×Q8C23×D7311yescharacteristic
658C2×D4—29224no—
659C2×D4—29224no—
660C2×D4—7324no—
661C2×D4—736no—
662C2×D4—7324no—
663C2×D4—7312no—
664C2×D4—734no—
665C2×D4—7312no—
666C2×D4—7324no—
667C2×D4—733no—
668C2×D4—7312no—
669C2×D4—7324no—
670C2×D4—7312no—
671C2×D4—7312no—
672C2×D4—736no—
673C2×D4—14648no—
674C2×D4—14648no—
675C2×D4—14624no—
676C2×D4—14696no—
677C2×D4—14648no—
678C2×D4—14648no—
679C2×D4—14624no—
680C2×D4C23×D7314yes—
681C2×D4C23×D73112yes—
682C2×D4C23×D7312yes—
683C2×D4C23×D7313yes—
684C22×C4—29212no—
685C22×C4—736no—
686C22×C4—736no—
687C22×C4—736no—
688C22×C4—733no—
689C22×C4—7324no—
690C22×C4—731no—
691C22×C4—733no—
692C22×C4—733no—
693C22×C4—733no—
694C22×C4—734no—
695C22×C4—732no—
696C22×C4—736no—
697C22×C4—7312no—
698C22×C4—7312no—
699C22×C4—7324no—
700C22×C4—7312no—
701C22×C4—14648no—
702C22×C4—14648no—
703C22×C4C23×D7316yes—
704C22×C4C23×D73112yes—
705C22×C4C23×D73112yes—
706C22×C4C23×D7313yes—
707C4⋊C4—7312no—
708C4⋊C4—7324no—
709C4⋊C4—734no—
710C4⋊C4—736no—
711C4⋊C4C23×D73112yes—
712C4⋊C4C23×D7316yes—
713C4⋊C4C23×D73124yes—
714C22⋊C4—738no—
715C22⋊C4—736no—
716C22⋊C4—7324no—
717C22⋊C4—7312no—
718C22⋊C4—7348no—
719C22⋊C4—7324no—
720C22⋊C4C23×D7316yes—
721C22⋊C4C23×D73124yes—
722C42—732no—
723C42—731no—
724C42—736no—
725C42—733no—
726C42—736no—
727C42—736no—
728C42—736no—
729C42C23×D7311yescharacteristic
730C42C23×D7313yes—
731C42C23×D7316yes—
732C23—2926no—
733C23—29224no—
734C23—29224no—
735C23—7312no—
736C23—733no—
737C23—731no—
738C23—7312no—
739C23—14624no—
740C23—14624no—
741C23C24×D7314yes—
742C23C24×D7313yes—
743Q8—224no—
744Q8—212no—
745Q8—7312no—
746Q8—14624no—
747Q8—1464no—
748Q8C2×D4×D7314yes—
749D4—224no—
750D4—24no—
751D4—28no—
752D4—29224no—
753D4—29224no—
754D4—7324no—
755D4—7312no—
756D4—14624no—
757D4—14648no—
758D4—14624no—
759D4—1468no—
760D4—14624no—
761D4—14624no—
762D4—14612no—
763D4—14624no—
764D4C2×D4×D73112yes—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—212no—
768C2×C4—2926no—
769C2×C4—2926no—
770C2×C4—2926no—
771C2×C4—7312no—
772C2×C4—731no—
773C2×C4—733no—
774C2×C4—734no—
775C2×C4—7312no—
776C2×C4—7312no—
777C2×C4—7312no—
778C2×C4—732no—
779C2×C4—736no—
780C2×C4—734no—
781C2×C4—14624no—
782C2×C4—14648no—
783C2×C4—14624no—
784C2×C4—1468no—
785C2×C4—14624no—
786C2×C4—1464no—
787C2×C4—14612no—
788C2×C4C2×D4×D73112yes—
789C2×C4C24×D7316yes—
790C2×C4C24×D73112yes—
791C2×C4C24×D7311yescharacteristic
792C2×C4C24×D7313yes—
793C2×C4C24×D7312yes—
794C22—26no—
795C22—24no—
796C22—28no—
797C22—29212no—
798C22—58424no—
799C22—58424no—
800C22—732no—
801C22—736no—
802C22—14612no—
803C22—14624no—
804C22—1462no—
805C22—1466no—
806C22C22×D4×D7316yes—
807C22C25×D7311yescharacteristic
808C4—212no—
809C4—26no—
810C4—732no—
811C4—736no—
812C4—1464no—
813C4—1462no—
814C4—1466no—
815C4C22×D4×D7316yes—
816C4C22×D4×D7312yes—
817C4#1798942414yescomplemented
818C2—26no—
819C2—44no—
820C2—29212no—
821C2—1462no—
822C2—1466no—
823C2C23×D4×D7311yescharacteristic
824C2C2×#1798942412yes—
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3499C2
hypercenter#3499D73
hypocenterC73#62812
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×#17989424C2semidirect
2. #22623725C2semidirect
3. #22623720C2semidirect
4. #22623714C2semidirect
5. #22623709C2semidirect
6. #22623704C2semidirect
7. #22623701C2semidirect
8. #22623689C2semidirect
9. D4×#11924029C2semidirect
10. #22623418C2semidirect
11. #22623263C2semidirect
12. C2×#17989138C2semidirect
13. #532×D73C2semidirect
14. C4×#41×D73C2semidirect
15. C73×#3499C2semidirect
17. C2×#14556639C22semidirect
18. C2×#14556639C22semidirect
19. C2×#14556637C22semidirect
20. C2×#14556637C22semidirect
21. C2×#14556637C22semidirect
22. C22×#11924029C22semidirect
23. C22×#11924029C22semidirect
25. C2×#41×D73C22semidirect
26. C2×#41×D73C22semidirect
27. #17989259C22semidirect
28. #17989258C22semidirect
29. #17989252C22semidirect
30. #17989248C22semidirect
31. #17989247C22semidirect
32. #17989240C22semidirect
33. #17989238C22semidirect
34. #17989229C22semidirect
35. #17989228C22semidirect
36. #17989225C22semidirect
37. D4×D292C22semidirect
38. D4×D292C22semidirect
39. #17989221C22semidirect
40. #17989167C22semidirect
41. #17989162C22semidirect
42. #17989161C22semidirect
43. #17989156C22semidirect
44. #17989155C22semidirect
45. #17989151C22semidirect
46. #17989148C22semidirect
47. #17989138C22semidirect
48. #17989138C22semidirect
49. #17989138C22semidirect
50. #17989138C22semidirect
51. #17989138C22semidirect
52. #17989138C22semidirect
53. #17989137C22semidirect
54. #17989136C22semidirect
55. #17989135C22semidirect
56. #17989134C22semidirect
57. #17989133C22semidirect
58. #17989132C22semidirect
59. C4⋊Q8×D73C22semidirect
60. C2×#14556588C22semidirect
61. #127×D73C22semidirect
62. C2×#14556580C22semidirect
63. #124×D73C22semidirect
64. #17989100C22semidirect
65. #17989095C22semidirect
66. C2×#14556566C22semidirect
67. #121×D73C22semidirect
68. #41×Dic73C22semidirect
69. C4×#11924029C22semidirect
70. C4×#11924028C22semidirect
71. #17989055C22semidirect
72. C4×#11924027C22semidirect
73. C4×Q8×D73C22semidirect
74. C2×#14556553C22semidirect
75. C4×D4×D73C22semidirect
76. C4×D4×D73C22semidirect
77. #117×D73C22semidirect
78. C2×C42×D73C22semidirect
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
110. #41×D73D4semidirect
222. #11924029C2×D4semidirect
227. #11924028C2×D4semidirect
230. #11924027C2×D4semidirect
236. Q8×D73C2×D4semidirect
258. D4×D73C2×D4semidirect
265. C2×C4×D73C2×D4semidirect
297. #41×C73C2×D4semidirect
399. C4×C73#585semidirect
417. #3499D73semidirect
428. C73#62812semidirect
432. C2×2−1+4C2×D73semidirect
444. D4×Q8C2×D73semidirect
449. #547C2×D73semidirect
459. #536C2×D73semidirect
476. #532C2×D73semidirect
478. C2×C4⋊Q8C2×D73semidirect
492. C4×#41C2×D73semidirect
646. #41D4×D73semidirect
817. C4#17989424semidirect

Maximal subgroups

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

subgroupindex
C2×#179894242
#226237252
#226237202
#226237142
#226237092
#226237042
#226237012
#226236892
D4×#119240292
#226234182
#226232632
C2×#179891382
#532×D732
C4×#41×D732
C73×#34992
#6281273