Finite Group Databasebeta

← #33994528

Subgroups — #33994528

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×#17989422C212yesmaximal, complemented
2#22623723C216yesmaximal, complemented
3#22623719C212yesmaximal, complemented
4#22623716C211yesmaximal, characteristic, complemented
5#22623711C213yesmaximal, complemented
6#22623707C213yesmaximal, complemented
7#22623696C214yesmaximal, complemented
8#22623687C2112yesmaximal, complemented
9#22623421C214yesmaximal, complemented
10D4×#11924027C2112yesmaximal, complemented
11#22623262C216yesmaximal, complemented
12C2×#17989135C213yesmaximal, complemented
13#532×D73C213yesmaximal, complemented
14C4×#41×D73C211yesmaximal, characteristic, complemented
15C73×#3498C211yesmaximal, characteristic, complemented
16#17989422—232no—
17C2×#14556638C2214yescomplemented
18C2×#14556638C2216yescomplemented
19C2×#14556638C2212yescomplemented
20C2×#14556636C22112yescomplemented
21C2×#14556636C2216yescomplemented
22C22×#11924027C2216yescomplemented
23C22×#11924027C22112yescomplemented
24C2×#41×D73C2211yescharacteristic
25C2×#41×D73C2216yescomplemented
26C2×#41×D73C2214yescomplemented
27#17989257C22112yescomplemented
28Q8×D292C2214yescomplemented
29D4×Dic146C22112yescomplemented
30#17989244C2218yescomplemented
31#17989243C22124yescomplemented
32#17989242C22112yescomplemented
33#17989241C22112yescomplemented
34#17989237C22124yescomplemented
35#17989234C22124yescomplemented
36#17989231C22124yescomplemented
37#17989224C22148yescomplemented
38#17989222C22112yescomplemented
39D4×C22⋊D73C22124yescomplemented
40#17989166C22124yescomplemented
41#17989163C2216yescomplemented
42#17989158C2216yescomplemented
43#17989157C22112yescomplemented
44#17989154C2216yescomplemented
45#17989150C22112yescomplemented
46#17989147C22124yescomplemented
47#17989138C2211yescharacteristic, complemented
48#17989137C2213yescomplemented
49#17989136C2216yescomplemented
50#17989135C2216yescomplemented
51#17989135C22112yescomplemented
52#17989135C22112yescomplemented
53#17989135C2216yescomplemented
54#17989135C2213yescomplemented
55#17989135C2216yescomplemented
56#17989134C22112yescomplemented
57#17989133C2216yescomplemented
58#17989132C22112yescomplemented
59C2×#14556591C2213yescomplemented
60C4⋊Q8×D73C2213yescomplemented
61#127×D73C2213yescomplemented
62C2×#14556578C2216yescomplemented
63#124×D73C2216yescomplemented
64#17989097C22124yescomplemented
65#17989093C22124yescomplemented
66C2×#14556562C22112yescomplemented
67#121×D73C22112yescomplemented
68#41×Dic73C2211yescharacteristic, complemented
69C4×#11924029C2212yescomplemented
70C4×#11924028C2213yescomplemented
71#17989055C2213yescomplemented
72C4×#11924027C2216yescomplemented
73C4×Q8×D73C2212yescomplemented
74C2×D4×Dic73C22112yescomplemented
75C4×D4×D73C2216yescomplemented
76C4×D4×D73C22112yescomplemented
77#117×D73C2213yescomplemented
78C2×C42×D73C2213yescomplemented
79C2×H(5,𝔽2)×C73C2212yescomplemented
80#550×C73C2214yescomplemented
81D42×C73C22112yescomplemented
82#535×C73C2216yescomplemented
83#532×C73C2213yescomplemented
84C2×#127×C73C2213yescomplemented
85C4×#41×C73C2211yescharacteristic, complemented
86#14556638—248no—
87#14556638—232no—
88#14556638—216no—
89#14556636—248no—
90#14556636—296no—
91C2×#11924029C2312yes—
92C2×#11924029C2311yescharacteristic
93C2×#11924028C2316yes—
94C2×#11924028C23112yes—
95C2×#11924028C23112yes—
96C2×#11924028C2313yes—
97C2×#11924027—296no—
98C2×#11924027—248no—
99C2×#11924027C23112yes—
100C2×#11924027C2316yes—
101C2×#11924027C23112yes—
102C2×#11924027C23112yes—
103C2×#11924027C23112yes—
104C2×#11924027C23124yes—
105C2×#11924027C23112yes—
106C2×#11924027C23112yes—
107C2×#11924027C2313yes—
108#41×D73—232no—
109#41×D73—248no—
110#41×D73D4116yescomplemented
111C22×Dic146C2316yes—
112C22×Dic146C23112yes—
113C2×Q8×D73C2316yes—
114C2×Q8×D73C2314yes—
115C2×Q8×D73C2311yescharacteristic
116C22×C22⋊D73C23112yes—
117C22×C22⋊D73C23124yes—
118C2×D4×D73C2316yes—
119C2×D4×D73C23112yes—
120C2×D4×D73C23112yes—
121C2×D4×D73C23112yes—
122C2×D4×D73C2313yes—
123C23×Dic73C23112yes—
124C22×C4×D73C23112yes—
125C22×C4×D73C2316yes—
126C22×C4×D73C2313yes—
127#14556591C2313yes—
128#14556591C2316yes—
129#14556591C23112yes—
130#14556590C23112yes—
131#14556589C2316yes—
132#14556588C2311yescharacteristic
133#14556587C23112yes—
134#14556587C2316yes—
135#14556580C2312yes—
136#14556579C2316yes—
137#14556578C2316yes—
138#14556578C23112yes—
139#14556578C23124yes—
140#14556577C23124yes—
141#14556575C23124yes—
142#14556573C23148yes—
143#14556572C23124yes—
144#14556571C23124yes—
145#14556570C23124yes—
146#14556568C23148yes—
147#14556566C2314yes—
148#14556565C23112yes—
149#14556564C23124yes—
150#14556563C23124yes—
151#14556563C23148yes—
152#14556562C23112yes—
153#14556562C23124yes—
154#14556562C23124yes—
155#14556562C23124yes—
156#14556562C23124yes—
157#14556560C23124yes—
158#14556559C23148yes—
159Q8×Dic73C2312yes—
160C4×Dic146C2316yes—
161#14556556C2316yes—
162C4×D292C23112yes—
163C4×D292C2316yes—
164D4×Dic73C23112yes—
165D4×Dic73C23124yes—
166D4×Dic73C23124yes—
167D4×Dic73C23124yes—
168D4×Dic73C2316yes—
169#14556553C2314yes—
170#14556553C2316yes—
171C4×C22⋊D73C23124yes—
172C4×C22⋊D73C23112yes—
173#14556551C23124yes—
174#14556551C23112yes—
175#14556550C2313yes—
176#14556549C2316yes—
177#14556548C2316yes—
178#14556547C2316yes—
179C2×C4⋊Dic73C23112yes—
180C4⋊C4×D73C23112yes—
181C4⋊C4×D73C2316yes—
182C2×C22⋊Dic73C23124yes—
183C22⋊C4×D73C2316yes—
184C22⋊C4×D73C23124yes—
185C2×C4×Dic73C2316yes—
186C2×C4×Dic73C2313yes—
187C42×D73C2313yes—
188C42×D73C2316yes—
189C42×D73C2311yescharacteristic
190C42×D73C2313yes—
191C42×D73C2316yes—
192C42×D73C2313yes—
193H(5,𝔽2)×C73—216no—
194C2×#41×C73C2316yes—
195C2×#41×C73C2314yes—
196C2×#41×C73C2311yescharacteristic
197C22×D4×C73C2316yes—
198C22×D4×C73C23112yes—
199C22×D4×C73C23112yes—
200C4⋊Q8×C73C2311yescharacteristic
201#127×C73C2313yes—
202#127×C73C2316yes—
203#127×C73C23112yes—
204#124×C73C2316yes—
205#121×C73C23112yes—
206#121×C73C23124yes—
207#120×C73C23124yes—
208C4×Q8×C73C2312yes—
209C4×D4×C73C23112yes—
210C4×D4×C73C2316yes—
211#117×C73C2313yes—
212C2×C42×C73C2313yes—
213C23×D73C24112yes—
214C23×D73C2413yes—
215#11924029—28no—
216#11924029C2×D418yescomplemented
217#11924028—224no—
218#11924028—248no—
219#11924028—248no—
220#11924028C2×D4124yescomplemented
221#11924027—248no—
222#11924027—296no—
223#11924027—248no—
224#11924027—248no—
225#11924027—224no—
226#11924027—248no—
227#11924027—248no—
228#11924027—248no—
229#11924027C2×D4124yescomplemented
230C2×Dic146—224no—
231C2×Dic146—248no—
232C2×Dic146C24112yes—
233C2×Dic146C24112yes—
234C2×Dic146C2416yes—
235C2×Dic146C2413yes—
236Q8×D73—216no—
237Q8×D73—224no—
238Q8×D73C2×D418yescomplemented
239C2×D292C2414yes—
240C2×D292C2414yes—
241C2×D292C2412yes—
242C2×D292C2413yes—
243C2×C22⋊D73—248no—
244C2×C22⋊D73—296no—
245C2×C22⋊D73C24124yes—
246C2×C22⋊D73C24112yes—
247C2×C22⋊D73C24112yes—
248C2×C22⋊D73C24112yes—
249C2×C22⋊D73C24124yes—
250C2×C22⋊D73C2416yes—
251D4×D73—248no—
252D4×D73—248no—
253D4×D73—224no—
254D4×D73—424no—
255D4×D73C2×D4124yescomplemented
256C22×Dic73—248no—
257C22×Dic73C24112yes—
258C22×Dic73C24112yes—
259C22×Dic73C24124yes—
260C22×Dic73C2416yes—
261C22×Dic73C2413yes—
262C2×C4×D73—248no—
263C2×C4×D73—412no—
264C2×C4×D73C2×D4124yescomplemented
265C2×C4×D73C2412yes—
266C2×C4×D73C2416yes—
267C2×C4×D73C24112yes—
268C2×C4×D73C2414yes—
269C2×C4×D73C24112yes—
270C2×C4×D73C2416yes—
271C2×C4×D73C2416yes—
272C2×C4×D73C2411yescharacteristic
273C2×C4×D73C2413yes—
274C2×C4×D73C2413yes—
275C2×C4×D73C2413yes—
276C4⋊Dic73C24112yes—
277C4⋊Dic73C2416yes—
278C4⋊Dic73C24124yes—
279#11924007C24112yes—
280#11924007C24124yes—
281C22⋊Dic73C24124yes—
282C22⋊Dic73C2416yes—
283C22⋊Dic73C24148yes—
284#11924005C2418yes—
285#11924005C24112yes—
286#11924005C24124yes—
287C4×Dic73C2412yes—
288C4×Dic73C2411yescharacteristic
289C4×Dic73C2416yes—
290C4×Dic73C2413yes—
291C4×Dic73C2416yes—
292C4×Dic73C2416yes—
293C4×Dic73C2416yes—
294C24×C73C24112yes—
295#41×C73—216no—
296#41×C73—224no—
297#41×C73C2×D418yescomplemented
298C2×Q8×C73C2412yes—
299C2×Q8×C73C2411yescharacteristic
300C2×D4×C73—248no—
301C2×D4×C73—224no—
302C2×D4×C73—424no—
303C2×D4×C73C24112yes—
304C2×D4×C73C24112yes—
305C2×D4×C73C24112yes—
306C2×D4×C73C2416yes—
307C2×D4×C73C24124yes—
308C2×D4×C73C2413yes—
309C22×C4×C73C2416yes—
310C22×C4×C73C24112yes—
311C22×C4×C73C2413yes—
312C4⋊C4×C73C2416yes—
313C4⋊C4×C73C2414yes—
314C22⋊C4×C73C2416yes—
315C22⋊C4×C73C24124yes—
316C42×C73C2411yescharacteristic
317C42×C73C2413yes—
318C42×C73C2416yes—
319C23×C73—224no—
320C23×C73—424no—
321C23×C73C25112yes—
322C23×C73C2513yes—
323C22×D73—224no—
324C22×D73—46no—
325C22×D73—424no—
326C22×D73C22×D4112yes—
327C22×D73C2514yes—
328C22×D73C2513yes—
329C22×D73C2511yescharacteristic
330Q8×C73—24no—
331Q8×C73C22×D414yes—
332D4×C73—224no—
333D4×C73—212no—
334D4×C73—224no—
335D4×C73—224no—
336D4×C73—424no—
337D4×C73C22×D4112yes—
338C2×C4×C73—224no—
339C2×C4×C73—212no—
340C2×C4×C73C22×D4112yes—
341C2×C4×C73C2516yes—
342C2×C4×C73C2514yes—
343C2×C4×C73C2511yescharacteristic
344C2×C4×C73C2513yes—
345C2×C4×C73C2512yes—
346C22⋊D73—224no—
347C22⋊D73—248no—
348C22⋊D73—224no—
349C22⋊D73—224no—
350C22⋊D73—424no—
351C22⋊D73C22×D4124yes—
352C2×Dic73—224no—
353C2×Dic73—224no—
354C2×Dic73—248no—
355C2×Dic73—46no—
356C2×Dic73C22×D4112yes—
357C2×Dic73C2512yes—
358C2×Dic73C2516yes—
359C2×Dic73C25112yes—
360C2×Dic73C2511yescharacteristic
361C2×Dic73C2513yes—
362D292—28no—
363D292—24no—
364D292—28no—
365D292C22×D4112yes—
366C4×D73—224no—
367C4×D73—224no—
368C4×D73—24no—
369C4×D73—212no—
370C4×D73—28no—
371C4×D73—46no—
372C4×D73—46no—
373C4×D73C22×D4112yes—
374C4×D73C22×D414yes—
375C4×D73C22×D4112yes—
376C4×D73C22×D4112yes—
377Dic146—212no—
378Dic146—224no—
379Dic146—224no—
380Dic146C22×D4112yes—
381C22×C73—26no—
382C22×C73—212no—
383C22×C73—224no—
384C22×C73—824no—
385C22×C73C23×D416yes—
386C22×C73C2611yescharacteristic
387C2×D73—22no—
388C2×D73—26no—
389C2×D73—24no—
390C2×D73—28no—
391C2×D73—412no—
392C2×D73—824no—
393C2×D73C23×D416yes—
394C2×D73C23×D412yes—
395C4×C73—24no—
396C4×C73—26no—
397C4×C73C23×D412yes—
398C4×C73C23×D416yes—
399C4×C73#58514yescomplemented
400Dic73—212no—
401Dic73—22no—
402Dic73—26no—
403Dic73C23×D416yes—
404Dic73C23×D412yes—
405#62812—731nomaximal, Sylow
406C2×C73—26no—
407C2×C73—412no—
408C2×C73C24×D411yescharacteristic
409C2×C73C2×#58512yes—
410D73—22no—
411D73—26no—
412D73—44no—
413C2×#585—732no—
414#3500—732no—
415#3500—736no—
416#3499—733no—
417#3499—731no—
418#3498—733no—
419#3498D7311yescharacteristic, complemented
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+4—732no—
433C2×H(5,𝔽2)—7312no—
434C2×H(5,𝔽2)—736no—
435C2×H(5,𝔽2)C2×D7312yescomplemented
436C22×#41—731no—
437C22×#41—736no—
438C22×#41—734no—
439C22×#41—736no—
440C22×#41—7312no—
441#550—7312no—
442#550C2×D7314yescomplemented
443D4×Q8—734no—
444D4×Q8—7312no—
445#548—738no—
446#548—7324no—
447#547—7324no—
448#547—7312no—
449#547—7312no—
450#546—7324no—
451#546—7324no—
452#546—7348no—
453D42—7324no—
454D42—7312no—
455D42C2×D73112yescomplemented
456#537—7324no—
457#536—736no—
458#536—7312no—
459#536—736no—
460#535—736no—
461#535—7312no—
462#535C2×D7316yescomplemented
463#534—7324no—
464#532—736no—
465#532—731no—
466#532—733no—
467#532—736no—
468#532—7312no—
469#532—7312no—
470#532—736no—
471#532—736no—
472#532—736no—
473#532—7312no—
474#532—7312no—
475#532—733no—
476#532C2×D7313yescomplemented
477C2×C4⋊Q8—733no—
478C2×C4⋊Q8—733no—
479C2×#127—733no—
480C2×#127C2×D7313yescomplemented
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—7312no—
495C2×C4×D4—736no—
496C2×C4×D4—7312no—
497C2×#117—733no—
498C22×C42—733no—
4992−1+4—14632no—
5002−1+4—14648no—
5012−1+4—14616no—
502H(5,𝔽2)—216no—
503H(5,𝔽2)—14696no—
504H(5,𝔽2)—14648no—
505C2×#41—7316no—
506C2×#41—731no—
507C2×#41—732no—
508C2×#41—733no—
509C2×#41—7312no—
510C2×#41—7312no—
511C2×#41—736no—
512C2×#41—7312no—
513C2×#41—7312no—
514C2×#41—7312no—
515C2×#41—7324no—
516C2×#41—7312no—
517C2×#41—733no—
518C2×#41—736no—
519C2×#41—7312no—
520C2×#41—7312no—
521C2×#41—14648no—
522C2×#41—14648no—
523C2×#41—14696no—
524C2×#41—14632no—
525C2×#41C22×D7316yes—
526C2×#41C22×D7314yes—
527C2×#41C22×D7311yescharacteristic
528C22×Q8—731no—
529C22×Q8—736no—
530C22×Q8—734no—
531C22×Q8—736no—
532C22×Q8—7312no—
533C22×D4—7312no—
534C22×D4—733no—
535C22×D4—7312no—
536C22×D4—7324no—
537C22×D4—7312no—
538C22×D4—736no—
539C22×D4—7312no—
540C22×D4C22×D7316yes—
541C22×D4C22×D73112yes—
542C22×D4C22×D73112yes—
543C23×C4—736no—
544C23×C4—733no—
545C23×C4—7312no—
546C23×C4—7312no—
547C4⋊Q8—736no—
548C4⋊Q8—7312no—
549C4⋊Q8—733no—
550C4⋊Q8—736no—
551C4⋊Q8—7312no—
552C4⋊Q8C22×D7311yescharacteristic
553#127—736no—
554#127—7312no—
555#127—731no—
556#127C22×D7313yes—
557#127C22×D7316yes—
558#127C22×D73112yes—
559#124—732no—
560#124—736no—
561#124—7312no—
562#124—7324no—
563#124—7324no—
564#124—736no—
565#124C22×D7316yes—
566#123—7324no—
567#123—7348no—
568#123—7324no—
569C22⋊Q8—7324no—
570C22⋊Q8—7324no—
571C22⋊Q8—7348no—
572#121—7312no—
573#121—7324no—
574#121—7324no—
575#121—7324no—
576#121—7324no—
577#121—7324no—
578#121—7348no—
579#121—7312no—
580#121—734no—
581#121—7324no—
582#121C22×D73112yes—
583#121C22×D73124yes—
584#120—7324no—
585#120—7348no—
586#120C22×D73124yes—
587C4×Q8—732no—
588C4×Q8—736no—
589C4×Q8—736no—
590C4×Q8C22×D7312yes—
591C4×D4—7312no—
592C4×D4—736no—
593C4×D4—7324no—
594C4×D4—7324no—
595C4×D4—7324no—
596C4×D4—7312no—
597C4×D4—7324no—
598C4×D4—734no—
599C4×D4—736no—
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—7312no—
612C2×C4⋊C4—736no—
613C2×C4⋊C4—7312no—
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—
628C24C23×D73112yes—
629#41—216no—
630#41—224no—
631#41—738no—
632#41—7324no—
633#41—7324no—
634#41—14648no—
635#41—14648no—
636#41—14648no—
637#41—14624no—
638#41—14648no—
639#41—14648no—
640#41—14648no—
641#41—1468no—
642#41—14696no—
643#41—14648no—
644#41—14648no—
645#41—14624no—
646#41D4×D7318yescomplemented
647C2×Q8—738no—
648C2×Q8—733no—
649C2×Q8—7312no—
650C2×Q8—7312no—
651C2×Q8—736no—
652C2×Q8—14648no—
653C2×Q8—14624no—
654C2×Q8—14616no—
655C2×Q8—14624no—
656C2×Q8C23×D7312yes—
657C2×Q8C23×D7311yescharacteristic
658C2×D4—248no—
659C2×D4—224no—
660C2×D4—424no—
661C2×D4—29224no—
662C2×D4—7324no—
663C2×D4—736no—
664C2×D4—7324no—
665C2×D4—7324no—
666C2×D4—7312no—
667C2×D4—7312no—
668C2×D4—7312no—
669C2×D4—733no—
670C2×D4—734no—
671C2×D4—734no—
672C2×D4—732no—
673C2×D4—14624no—
674C2×D4—14648no—
675C2×D4—14648no—
676C2×D4—14696no—
677C2×D4—14648no—
678C2×D4C23×D73112yes—
679C2×D4C23×D73112yes—
680C2×D4C23×D73112yes—
681C2×D4C23×D7316yes—
682C2×D4C23×D73124yes—
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—7312no—
695C22×C4—7312no—
696C22×C4—7324no—
697C22×C4—732no—
698C22×C4—736no—
699C22×C4—7312no—
700C22×C4—734no—
701C22×C4—7312no—
702C22×C4—14648no—
703C22×C4—14648no—
704C22×C4C23×D7316yes—
705C22×C4C23×D73112yes—
706C22×C4C23×D7313yes—
707C4⋊C4—7312no—
708C4⋊C4—7324no—
709C4⋊C4—7312no—
710C4⋊C4—736no—
711C4⋊C4—7324no—
712C4⋊C4C23×D7314yes—
713C4⋊C4C23×D7316yes—
714C22⋊C4—7324no—
715C22⋊C4—736no—
716C22⋊C4—7348no—
717C22⋊C4—738no—
718C22⋊C4—7312no—
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—224no—
733C23—424no—
734C23—2926no—
735C23—29224no—
736C23—7312no—
737C23—733no—
738C23—731no—
739C23—734no—
740C23—14624no—
741C23C24×D73112yes—
742C23C24×D7313yes—
743Q8—24no—
744Q8—7312no—
745Q8—14624no—
746Q8—14624no—
747Q8—14612no—
748Q8C2×D4×D7314yes—
749D4—224no—
750D4—224no—
751D4—212no—
752D4—224no—
753D4—424no—
754D4—29224no—
755D4—7324no—
756D4—7312no—
757D4—1468no—
758D4—14624no—
759D4—14624no—
760D4—14648no—
761D4—14624no—
762D4—1464no—
763D4—1468no—
764D4C2×D4×D73112yes—
765C2×C4—224no—
766C2×C4—212no—
767C2×C4—2926no—
768C2×C4—2926no—
769C2×C4—2926no—
770C2×C4—7312no—
771C2×C4—731no—
772C2×C4—733no—
773C2×C4—734no—
774C2×C4—7312no—
775C2×C4—7312no—
776C2×C4—7312no—
777C2×C4—732no—
778C2×C4—736no—
779C2×C4—7312no—
780C2×C4—1468no—
781C2×C4—14624no—
782C2×C4—14624no—
783C2×C4—14648no—
784C2×C4—14624no—
785C2×C4—14624no—
786C2×C4—1464no—
787C2×C4—14612no—
788C2×C4C2×D4×D73112yes—
789C2×C4C24×D7316yes—
790C2×C4C24×D7314yes—
791C2×C4C24×D7311yescharacteristic
792C2×C4C24×D7313yes—
793C2×C4C24×D7312yes—
794C22—26no—
795C22—212no—
796C22—224no—
797C22—824no—
798C22—29212no—
799C22—58424no—
800C22—732no—
801C22—736no—
802C22—1464no—
803C22—1468no—
804C22—1462no—
805C22—1466no—
806C22C22×D4×D7316yes—
807C22C25×D7311yescharacteristic
808C4—24no—
809C4—26no—
810C4—732no—
811C4—736no—
812C4—14612no—
813C4—1462no—
814C4—1466no—
815C4C22×D4×D7316yes—
816C4C22×D4×D7312yes—
817C4#1798942214yescomplemented
818C2—26no—
819C2—412no—
820C2—2924no—
821C2—1462no—
822C2—1466no—
823C2C23×D4×D7311yescharacteristic
824C2C2×#1798942212yes—
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3498C2
hypercenter#3498D73
hypocenterC73#62812
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. C2×#17989422C2semidirect
2. #22623723C2semidirect
3. #22623719C2semidirect
4. #22623716C2semidirect
5. #22623711C2semidirect
6. #22623707C2semidirect
7. #22623696C2semidirect
8. #22623687C2semidirect
9. #22623421C2semidirect
10. D4×#11924027C2semidirect
11. #22623262C2semidirect
12. C2×#17989135C2semidirect
13. #532×D73C2semidirect
14. C4×#41×D73C2semidirect
15. C73×#3498C2semidirect
17. C2×#14556638C22semidirect
18. C2×#14556638C22semidirect
19. C2×#14556638C22semidirect
20. C2×#14556636C22semidirect
21. C2×#14556636C22semidirect
22. C22×#11924027C22semidirect
23. C22×#11924027C22semidirect
25. C2×#41×D73C22semidirect
26. C2×#41×D73C22semidirect
27. #17989257C22semidirect
28. Q8×D292C22semidirect
29. D4×Dic146C22semidirect
30. #17989244C22semidirect
31. #17989243C22semidirect
32. #17989242C22semidirect
33. #17989241C22semidirect
34. #17989237C22semidirect
35. #17989234C22semidirect
36. #17989231C22semidirect
37. #17989224C22semidirect
38. #17989222C22semidirect
39. D4×C22⋊D73C22semidirect
40. #17989166C22semidirect
41. #17989163C22semidirect
42. #17989158C22semidirect
43. #17989157C22semidirect
44. #17989154C22semidirect
45. #17989150C22semidirect
46. #17989147C22semidirect
47. #17989138C22semidirect
48. #17989137C22semidirect
49. #17989136C22semidirect
50. #17989135C22semidirect
51. #17989135C22semidirect
52. #17989135C22semidirect
53. #17989135C22semidirect
54. #17989135C22semidirect
55. #17989135C22semidirect
56. #17989134C22semidirect
57. #17989133C22semidirect
58. #17989132C22semidirect
59. C2×#14556591C22semidirect
60. C4⋊Q8×D73C22semidirect
61. #127×D73C22semidirect
62. C2×#14556578C22semidirect
63. #124×D73C22semidirect
64. #17989097C22semidirect
65. #17989093C22semidirect
66. C2×#14556562C22semidirect
67. #121×D73C22semidirect
68. #41×Dic73C22semidirect
69. C4×#11924029C22semidirect
70. C4×#11924028C22semidirect
71. #17989055C22semidirect
72. C4×#11924027C22semidirect
73. C4×Q8×D73C22semidirect
74. C2×D4×Dic73C22semidirect
75. C4×D4×D73C22semidirect
76. C4×D4×D73C22semidirect
77. #117×D73C22semidirect
78. C2×C42×D73C22semidirect
79. C2×H(5,𝔽2)×C73C22semidirect
80. #550×C73C22semidirect
81. D42×C73C22semidirect
82. #535×C73C22semidirect
83. #532×C73C22semidirect
84. C2×#127×C73C22semidirect
85. C4×#41×C73C22semidirect
110. #41×D73D4semidirect
216. #11924029C2×D4semidirect
220. #11924028C2×D4semidirect
229. #11924027C2×D4semidirect
238. Q8×D73C2×D4semidirect
255. D4×D73C2×D4semidirect
264. C2×C4×D73C2×D4semidirect
297. #41×C73C2×D4semidirect
399. C4×C73#585semidirect
419. #3498D73semidirect
428. C73#62812semidirect
435. C2×H(5,𝔽2)C2×D73semidirect
442. #550C2×D73semidirect
455. D42C2×D73semidirect
462. #535C2×D73semidirect
476. #532C2×D73semidirect
480. C2×#127C2×D73semidirect
492. C4×#41C2×D73semidirect
646. #41D4×D73semidirect
817. C4#17989422semidirect

Maximal subgroups

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

subgroupindex
C2×#179894222
#226237232
#226237192
#226237162
#226237112
#226237072
#226236962
#226236872
#226234212
D4×#119240272
#226232622
C2×#179891352
#532×D732
C4×#41×D732
C73×#34982
#6281273