Finite Group Databasebeta

← #33999721

Subgroups — #33999721

Order 18688.

6496 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624628C215yesmaximal, complemented
2#22624627C215yesmaximal, complemented
3#22624499C215yesmaximal, complemented
4#22624496C215yesmaximal, complemented
5#22624493C215yesmaximal, complemented
6#22624453C215yesmaximal, complemented
7#22624341C215yesmaximal, complemented
8#22624289C215yesmaximal, complemented
9#22624283C215yesmaximal, complemented
10#22624079C211yesmaximal, characteristic, complemented
11#22624079C211yesmaximal, characteristic, complemented
12#22623940C215yesmaximal, complemented
13#22623880C215yesmaximal, complemented
14#22623820C215yesmaximal, complemented
15C73×#3531C211yesmaximal, characteristic, complemented
16#17989341C2215yescomplemented
17#17989341C2215yescomplemented
18#17989341C2215yescomplemented
19#17989341C2215yescomplemented
20#17989341C2215yescomplemented
21#17989337C2215yescomplemented
22#17989335C2215yescomplemented
23#17989335C2215yescomplemented
24#17989335C2215yescomplemented
25#17989331C2215yescomplemented
26#17989329C2215yescomplemented
27#17989329C2215yescomplemented
28#17989321C22110yescomplemented
29#17989320C2215yescomplemented
30#17989317C2215yescomplemented
31#17989311C2215yescomplemented
32#17989309C22110yescomplemented
33#17989309C2215yescomplemented
34#17989308C22110yescomplemented
35#17989305C2215yescomplemented
36#17989305C2215yescomplemented
37#17989304C22110yescomplemented
38#17989304C22110yescomplemented
39#17989303C2215yescomplemented
40#17989300C2215yescomplemented
41#17989300C2215yescomplemented
42#17989266C22110yescomplemented
43#17989265C22110yescomplemented
44#17989264C22110yescomplemented
45#17989262C22110yescomplemented
46#17989262C22110yescomplemented
47#17989261C22110yescomplemented
48#17989261C22110yescomplemented
49#17989260C22110yescomplemented
50#17989252C2215yescomplemented
51#17989250C2215yescomplemented
52#17989250C22110yescomplemented
53#17989249C2215yescomplemented
54#17989247C22110yescomplemented
55#17989243C2215yescomplemented
56#17989232C2215yescomplemented
57#17989229C22110yescomplemented
58#17989228C2215yescomplemented
59#17989228C22110yescomplemented
60#17989226C22110yescomplemented
61#17989221C2215yescomplemented
62#17989212C22110yescomplemented
63#17989211C22110yescomplemented
64#17989210C2215yescomplemented
65#17989209C22110yescomplemented
66#17989209C2215yescomplemented
67#17989207C22110yescomplemented
68#17989207C22110yescomplemented
69#17989207C22110yescomplemented
70#17989205C22110yescomplemented
71#17989204C2215yescomplemented
72#17989203C22110yescomplemented
73#17989203C22110yescomplemented
74#17989202C2215yescomplemented
75#17989177C22110yescomplemented
76#17989176C22110yescomplemented
77#17989176C22110yescomplemented
78#17989173C22110yescomplemented
79#17989170C22110yescomplemented
80#17989169C22110yescomplemented
81#17989162C22110yescomplemented
82#17989160C2215yescomplemented
83#17989159C22110yescomplemented
84#17989153C2215yes—
85#17989148C22110yescomplemented
86#17989143C2215yescomplemented
87#17989143C2215yescomplemented
88#17989143C2215yescomplemented
89#17989136C2215yes—
90#17989122C2215yescomplemented
91#17989122C2215yescomplemented
92#17989122C2215yescomplemented
93#17989122C2215yescomplemented
94#17989122C2215yescomplemented
95#17989121C2215yescomplemented
96#17989121C2215yescomplemented
97#17989116C2215yescomplemented
98C2×#14556579C2215yescomplemented
99#124×D73C2215yescomplemented
100#124×D73C2215yescomplemented
101#17989063C2215yescomplemented
102#17989059C2215yescomplemented
103C4×#11924028C2215yescomplemented
104#564×C73C2211yescharacteristic, complemented
105#563×C73C2215yescomplemented
106#563×C73C2215yescomplemented
107#562×C73C2215yescomplemented
108#533×C73C2215yescomplemented
109#529×C73C2215yescomplemented
110#529×C73C2215yescomplemented
111C2×#11924029C2315yes—
112C2×#11924028C2315yes—
113C2×#11924027C2315yes—
114C22×Dic146C2315yes—
115C2×Q8×D73C2315yes—
116C2×Q8×D73C2315yes—
117C22×D292C2315yes—
118C2×D4×D73C2315yes—
119C2×D4×D73C2315yes—
120#14556590C2315yes—
121#14556590C2315yes—
122#14556590C2315yes—
123#14556590C2315yes—
124#14556590C2315yes—
125#14556590C2315yes—
126#14556590C23110yes—
127#14556589C2315yes—
128#14556589C23110yes—
129#14556587C2315yes—
130#14556586C23110yes—
131#14556586C23110yes—
132#14556586C23110yes—
133#14556586C23110yes—
134#14556586C23110yes—
135#14556586C23110yes—
136#14556586C23110yes—
137#14556585C23110yes—
138#14556585C23110yes—
139#14556584C23110yes—
140#14556584C23110yes—
141#14556584C23110yes—
142#14556583C2315yes—
143#14556583C2315yes—
144#14556580C23110yes—
145#14556580C2315yes—
146#14556580C23110yes—
147#14556580C2315yes—
148#14556579C2315yes—
149#14556579C2315yes—
150#14556579C2315yes—
151#14556579C2315yes—
152#14556579C23110yes—
153#14556579C23110yes—
154#14556579C2315yes—
155#14556579C2315yes—
156#14556578C2315yes—
157#14556578C2315yes—
158#14556577C23110yes—
159#14556577C23110yes—
160#14556577C23110yes—
161#14556577C23110yes—
162#14556577C23110yes—
163#14556577C23110yes—
164#14556577C23110yes—
165#14556577C23110yes—
166#14556576C23110yes—
167#14556576C23110yes—
168#14556576C23110yes—
169#14556576C23110yes—
170#14556576C23110yes—
171#14556576C23110yes—
172#14556576C23110yes—
173#14556576C23110yes—
174#14556575C23110yes—
175#14556574C23110yes—
176#14556574C23110yes—
177#14556573C23110yes—
178#14556573C23110yes—
179#14556572C23110yes—
180#14556571C2315yes—
181#14556571C2315yes—
182#14556571C2315yes—
183#14556571C2315yes—
184#14556571C2315yes—
185#14556571C23110yes—
186#14556570C2315yes—
187#14556570C2315yes—
188#14556569C23110yes—
189#14556569C23110yes—
190#14556569C23110yes—
191#14556569C23110yes—
192#14556569C23110yes—
193#14556569C23110yes—
194#14556569C23110yes—
195#14556569C23110yes—
196#14556569C23110yes—
197#14556568C23110yes—
198#14556568C23110yes—
199#14556568C23110yes—
200#14556567C2315yes—
201#14556567C23110yes—
202#14556566C2315yes—
203#14556566C2315yes—
204#14556566C2315yes—
205#14556566C2315yes—
206#14556566C2315yes—
207#14556566C23110yes—
208#14556566C23110yes—
209#14556565C2315yes—
210#14556565C2315yes—
211#14556564C23110yes—
212#14556564C23110yes—
213#14556564C23110yes—
214#14556563C23110yes—
215#14556562C2315yes—
216#14556561C23110yes—
217#14556561C23110yes—
218#14556561C23110yes—
219#14556561C23110yes—
220#14556559C23110yes—
221#14556559C23110yes—
222Q8×Dic73C2315yes—
223C4×Dic146C2315yes—
224C4×Dic146C2315yes—
225C4×Dic146C2315yes—
226C4×Dic146C2315yes—
227#14556556C2315yes—
228#14556556C2315yes—
229#14556556C2315yes—
230#14556556C2315yes—
231#14556556C2315yes—
232#14556556C23110yes—
233#14556556C23110yes—
234C4×D292C2315yes—
235C4×D292C2315yes—
236C4×D292C2315yes—
237C4×D292C2315yes—
238D4×Dic73C2315yes—
239#14556553C2315yes—
240#14556553C2315yes—
241#14556553C2315yes—
242#14556553C2315yes—
243#14556553C23110yes—
244#14556553C2315yes—
245C4×C22⋊D73C23110yes—
246C4×C22⋊D73C23110yes—
247C4×C22⋊D73C2315yes—
248C4×C22⋊D73C2315yes—
249C4×C22⋊D73C2315yes—
250C4×C22⋊D73C2315yes—
251#14556551C23110yes—
252#14556551C23110yes—
253#14556551C23110yes—
254#14556550C2315yes—
255#14556549C2315yes—
256#14556549C2315yes—
257#14556549C2315yes—
258#14556549C2315yes—
259#14556549C23110yes—
260#14556549C2315yes—
261#14556549C2315yes—
262#14556548C23110yes—
263#14556548C23110yes—
264#14556548C2315yes—
265#14556548C2315yes—
266#14556547C23110yes—
267C2×#11924005C23110yes—
268C2×#11924005C23110yes—
269C22⋊C4×D73C23110yes—
270C22⋊C4×D73C23110yes—
271C22⋊C4×D73C23110yes—
272C22⋊C4×D73C23110yes—
273C42×D73C2315yes—
274C42×D73C2315yes—
275C4⋊Q8×C73C2315yes—
276C4⋊Q8×C73C2315yes—
277#126×C73C23110yes—
278#126×C73C23110yes—
279#125×C73C2315yes—
280#125×C73C2315yes—
281#125×C73C2315yes—
282#125×C73C2315yes—
283#124×C73C2315yes—
284#124×C73C2315yes—
285#123×C73C23110yes—
286#123×C73C23110yes—
287C22⋊Q8×C73C2315yes—
288C22⋊Q8×C73C23110yes—
289C22⋊Q8×C73C2315yes—
290C22⋊Q8×C73C23110yes—
291#121×C73C2315yes—
292#121×C73C2315yes—
293C4×Q8×C73C2315yes—
294C4×Q8×C73C2315yes—
295C4×D4×C73C2315yes—
296C4×D4×C73C2315yes—
297#117×C73C2315yes—
298#117×C73C2315yes—
299C2×C42×C73C2315yes—
300C23×D73C24110yes—
301#11924029—85no—
302#11924028—410no—
303#11924027—85no—
304C2×Dic146—85no—
305C2×Dic146C2415yes—
306C2×Dic146C2415yes—
307C2×Dic146C2415yes—
308C2×Dic146C2415yes—
309C2×Dic146C24110yes—
310C2×Dic146C2415yes—
311Q8×D73—410no—
312Q8×D73—85no—
313C2×D292—85no—
314C2×D292C2415yes—
315C2×D292C2415yes—
316C2×D292C24110yes—
317C2×D292C2415yes—
318C2×D292C2415yes—
319C2×D292C2415yes—
320C2×C22⋊D73C2415yes—
321C2×C22⋊D73C24110yes—
322C2×C22⋊D73C2415yes—
323C2×C22⋊D73C24110yes—
324D4×D73—410no—
325D4×D73—85no—
326C22×Dic73C24110yes—
327C2×C4×D73C2415yes—
328C2×C4×D73C2415yes—
329C2×C4×D73C2415yes—
330C2×C4×D73C2415yes—
331C2×C4×D73C2415yes—
332C2×C4×D73C2415yes—
333C2×C4×D73C24110yes—
334C2×C4×D73C24110yes—
335C4⋊Dic73C2415yes—
336C4⋊Dic73C2415yes—
337C4⋊Dic73C2415yes—
338C4⋊Dic73C2415yes—
339C4⋊Dic73C2415yes—
340C4⋊Dic73C2415yes—
341#11924007C24110yes—
342#11924007C24110yes—
343#11924007C2411yescharacteristic
344#11924007C2415yes—
345#11924007C2415yes—
346#11924007C2415yes—
347#11924007C24110yes—
348#11924007C24110yes—
349#11924007C24110yes—
350#11924007C24110yes—
351C22⋊Dic73C2415yes—
352C22⋊Dic73C24110yes—
353C22⋊Dic73C24110yes—
354C22⋊Dic73C2415yes—
355#11924005C2415yes—
356#11924005C24110yes—
357#11924005C24110yes—
358#11924005C24110yes—
359#11924005C24110yes—
360#11924005C24110yes—
361#11924005C24110yes—
362#11924005C24110yes—
363#11924005C2415yes—
364#11924005C2415yes—
365#11924005C24110yes—
366#11924005C24110yes—
367#11924005C24110yes—
368#11924005C24110yes—
369#11924005C2415yes—
370#11924005C24110yes—
371C4×Dic73C2415yes—
372C4×Dic73C2415yes—
373C4×Dic73C2415yes—
374C4×Dic73C2415yes—
375C4×Dic73C2415yes—
376C4×Dic73C2415yes—
377C4×Dic73C24110yes—
378C4×Dic73C24110yes—
379C2×Q8×C73C2415yes—
380C2×Q8×C73C2415yes—
381C2×D4×C73C2415yes—
382C2×D4×C73C2415yes—
383C22×C4×C73C2415yes—
384C22×C4×C73C2415yes—
385C22×C4×C73C2415yes—
386C4⋊C4×C73C2415yes—
387C4⋊C4×C73C2415yes—
388C4⋊C4×C73C2415yes—
389C4⋊C4×C73C2415yes—
390C4⋊C4×C73C2415yes—
391C4⋊C4×C73C2415yes—
392C4⋊C4×C73C2415yes—
393C4⋊C4×C73C2415yes—
394C4⋊C4×C73C24110yes—
395C4⋊C4×C73C24110yes—
396C22⋊C4×C73C24110yes—
397C22⋊C4×C73C24110yes—
398C22⋊C4×C73C24110yes—
399C22⋊C4×C73C24110yes—
400C42×C73C2415yes—
401C42×C73C2415yes—
402C42×C73C2415yes—
403C42×C73C2415yes—
404C23×C73C2515yes—
405C22×D73—410no—
406C22×D73—410no—
407C22×D73—410no—
408C22×D73C2515yes—
409C22×D73C2515yes—
410Q8×C73—45no—
411Q8×C73—45no—
412D4×C73—45no—
413D4×C73—45no—
414C2×C4×C73—45no—
415C2×C4×C73—45no—
416C2×C4×C73—45no—
417C2×C4×C73C2511yescharacteristic
418C2×C4×C73C2515yes—
419C2×C4×C73C2515yes—
420C2×C4×C73C2515yes—
421C2×C4×C73C2515yes—
422C2×C4×C73C2515yes—
423C22⋊D73—210no—
424C22⋊D73—410no—
425C22⋊D73—410no—
426C22⋊D73—45no—
427C2×Dic73—410no—
428C2×Dic73C2511yescharacteristic
429C2×Dic73C2515yes—
430C2×Dic73C2515yes—
431C2×Dic73C2515yes—
432C2×Dic73C2515yes—
433C2×Dic73C2511yescharacteristic
434D292—45no—
435D292—45no—
436D292—45no—
437D292—410no—
438D292—45no—
439D292—45no—
440C4×D73—210no—
441C4×D73—45no—
442C4×D73—45no—
443C4×D73—45no—
444C4×D73—410no—
445C4×D73—410no—
446C4×D73—45no—
447C4×D73—45no—
448Dic146—210no—
449Dic146—45no—
450Dic146—45no—
451Dic146—410no—
452Dic146—45no—
453Dic146—45no—
454C22×C73—25no—
455C22×C73—25no—
456C22×C73—25no—
457C22×C73C2611yescharacteristic
458C2×D73—25no—
459C2×D73—25no—
460C2×D73—25no—
461C2×D73—25no—
462C2×D73—25no—
463C2×D73—25no—
464C2×D73—1610no—
465C4×C73—25no—
466C4×C73—25no—
467C4×C73—25no—
468C4×C73—25no—
469C4×C73—25no—
470C4×C73—21no—
471Dic73—25no—
472Dic73—25no—
473Dic73—25no—
474Dic73—25no—
475Dic73—21no—
476Dic73#58512yes—
477#63069—731nomaximal, Sylow
478C2×C73—45no—
479C2×C73C2×#58511yescharacteristic
480C2×C73H(7,𝔽2)11yescharacteristic
481C2×C732−1+611yescharacteristic
482D73—45no—
483D73—45no—
484#3568—735no—
485#3568—735no—
486#3561—735no—
487#3561—735no—
488#3561—735no—
489#3558—735no—
490#3550—735no—
491#3545—735no—
492#3545—735no—
493#3531—731no—
494#3531—731no—
495#3531D7311yescharacteristic, complemented
496#3518—735no—
497#3514—735no—
498#3510—735no—
499C73#6306911yescharacteristic, complemented, Sylow
500#564C2×D7311yescharacteristic, complemented
501#563—735no—
502#563—735no—
503#563—735no—
504#563—735no—
505#563—735no—
506#563—735no—
507#563C2×D7315yescomplemented
508#563C2×D7315yescomplemented
509#562—735no—
510#562—735no—
511#562—735no—
512#562—735no—
513#562C2×D7315yescomplemented
514H(3,𝔽4)—735no—
515H(3,𝔽4)—735no—
516#559—7310no—
517#559—735no—
518Q82—735no—
519#556—735no—
520#556—7310no—
521#556—7310no—
522#556—7310no—
523#556—735no—
524#556—7310no—
525#556—735no—
526#556—735no—
527#555—735no—
528#555—735no—
529#555—735no—
530#551—7310no—
531#551—7310no—
532#551—7310no—
533#551—7310no—
534#551—7310no—
535#551—7310no—
536#551—7310no—
537#551—7310no—
538D4×Q8—735no—
539D4×Q8—735no—
540D4×Q8—7310no—
541#548—7310no—
542#548—735no—
543#548—735no—
544#546—7310no—
545#546—735no—
546#546—7310no—
547#546—7310no—
548#546—735no—
549D42—735no—
550#543—7310no—
551#542—7310no—
552#542—7310no—
553#542—7310no—
554#542—7310no—
555#542—7310no—
556#542—7310no—
557#542—7310no—
558#542—735no—
559#542—735no—
560#542—735no—
561#542—7310no—
562#542—735no—
563#538—7310no—
564#538—7310no—
565#538—7310no—
566#538—7310no—
567#538—7310no—
568#538—7310no—
569#536—7310no—
570#536—7310no—
571#536—735no—
572#535—735no—
573#534—7310no—
574#533—735no—
575#533—735no—
576#533—735no—
577#533C2×D7315yescomplemented
578#532—735no—
579#529—735no—
580#529—735no—
581#529—735no—
582#529—735no—
583#529—735no—
584#529—735no—
585#529—735no—
586#529—735no—
587#529C2×D7315yescomplemented
588#529C2×D7315yescomplemented
589C2×#124—735no—
590C2×#124—735no—
591C2×#124—735no—
592#519—735no—
593#518—735no—
594C4×#41—735no—
595C2×#41—735no—
596C2×#41—735no—
597C2×#41—735no—
598C22×Q8—735no—
599C22×Q8—735no—
600C22×Q8—735no—
601C22×D4—735no—
602C22×D4—735no—
603C22×D4—735no—
604C4⋊Q8—735no—
605C4⋊Q8—7310no—
606C4⋊Q8—735no—
607C4⋊Q8—735no—
608C4⋊Q8—735no—
609C4⋊Q8—735no—
610C4⋊Q8—735no—
611C4⋊Q8—735no—
612C4⋊Q8—7310no—
613C4⋊Q8C22×D7315yes—
614C4⋊Q8C22×D7315yes—
615#127—735no—
616#126—7310no—
617#126—7310no—
618#126—7310no—
619#126—7310no—
620#126—7310no—
621#126—7310no—
622#126—7310no—
623#126—7310no—
624#126—7310no—
625#126—7310no—
626#126—7310no—
627#126—7310no—
628#126C22×D73110yes—
629#126C22×D73110yes—
630#125—735no—
631#125—735no—
632#125C22×D7315yes—
633#125C22×D7315yes—
634#125C22×D7315yes—
635#125C22×D7315yes—
636#124—735no—
637#124—735no—
638#124—7310no—
639#124—7310no—
640#124—735no—
641#124—735no—
642#124—7310no—
643#124—7310no—
644#124—7310no—
645#124—7310no—
646#124—7310no—
647#124—7310no—
648#124—7310no—
649#124—7310no—
650#124—735no—
651#124—735no—
652#124—735no—
653#124—7310no—
654#124—7310no—
655#124—735no—
656#124—735no—
657#124—735no—
658#124C22×D7315yes—
659#124C22×D7315yes—
660#123—7310no—
661#123—7310no—
662#123—7310no—
663#123—7310no—
664#123—7310no—
665#123—7310no—
666#123—7310no—
667#123—7310no—
668#123—7310no—
669#123—7310no—
670#123—7310no—
671#123—7310no—
672#123—7310no—
673#123—7310no—
674#123C22×D73110yes—
675#123C22×D73110yes—
676C22⋊Q8—735no—
677C22⋊Q8—7310no—
678C22⋊Q8—735no—
679C22⋊Q8—735no—
680C22⋊Q8—735no—
681C22⋊Q8—735no—
682C22⋊Q8—735no—
683C22⋊Q8—735no—
684C22⋊Q8—735no—
685C22⋊Q8—7310no—
686C22⋊Q8—7310no—
687C22⋊Q8—7310no—
688C22⋊Q8—7310no—
689C22⋊Q8—7310no—
690C22⋊Q8—7310no—
691C22⋊Q8—7310no—
692C22⋊Q8—7310no—
693C22⋊Q8—7310no—
694C22⋊Q8—7310no—
695C22⋊Q8—7310no—
696C22⋊Q8—7310no—
697C22⋊Q8—7310no—
698C22⋊Q8C22×D7315yes—
699C22⋊Q8C22×D7315yes—
700C22⋊Q8C22×D73110yes—
701C22⋊Q8C22×D73110yes—
702#121—735no—
703#121—7310no—
704#121—735no—
705#121—735no—
706#121—735no—
707#121—735no—
708#121—735no—
709#121—735no—
710#121—735no—
711#121—7310no—
712#121—7310no—
713#121—7310no—
714#121—7310no—
715#121—7310no—
716#121C22×D7315yes—
717#121C22×D7315yes—
718#120—7310no—
719#120—7310no—
720#120—7310no—
721#120—7310no—
722#120—7310no—
723#120—7310no—
724C4×Q8—735no—
725C4×Q8—735no—
726C4×Q8—7310no—
727C4×Q8—735no—
728C4×Q8—735no—
729C4×Q8—735no—
730C4×Q8—735no—
731C4×Q8—7310no—
732C4×Q8—735no—
733C4×Q8—735no—
734C4×Q8—735no—
735C4×Q8—735no—
736C4×Q8C22×D7315yes—
737C4×Q8C22×D7315yes—
738C4×D4—735no—
739C4×D4—735no—
740C4×D4—735no—
741C4×D4—735no—
742C4×D4—735no—
743C4×D4—7310no—
744C4×D4—7310no—
745C4×D4—735no—
746C4×D4—735no—
747C4×D4—735no—
748C4×D4—735no—
749C4×D4—735no—
750C4×D4—7310no—
751C4×D4—7310no—
752C4×D4—7310no—
753C4×D4—7310no—
754C4×D4—735no—
755C4×D4—735no—
756C4×D4—735no—
757C4×D4—735no—
758C4×D4C22×D7315yes—
759C4×D4C22×D7315yes—
760#117—735no—
761#117—735no—
762#117—735no—
763#117—7310no—
764#117—735no—
765#117—735no—
766#117—735no—
767#117—735no—
768#117—7310no—
769#117—735no—
770#117—735no—
771#117—7310no—
772#117—7310no—
773#117C22×D7315yes—
774#117C22×D7315yes—
775C2×C22⋊C4—7310no—
776C2×C22⋊C4—7310no—
777C2×C22⋊C4—7310no—
778C2×C22⋊C4—7310no—
779C2×C22⋊C4—7310no—
780C2×C22⋊C4—7310no—
781C2×C42—735no—
782C2×C42—735no—
783C2×C42C22×D7315yes—
784C24—7310no—
785#41—29210no—
786#41—5845no—
787#41—5845no—
788C2×Q8—29210no—
789C2×Q8—5845no—
790C2×Q8—5845no—
791C2×Q8—735no—
792C2×Q8—735no—
793C2×Q8—735no—
794C2×Q8—7310no—
795C2×Q8—735no—
796C2×Q8—735no—
797C2×Q8C23×D7315yes—
798C2×Q8C23×D7315yes—
799C2×D4—29210no—
800C2×D4—5845no—
801C2×D4—5845no—
802C2×D4—7310no—
803C2×D4—735no—
804C2×D4—7310no—
805C2×D4—735no—
806C2×D4—735no—
807C2×D4—735no—
808C2×D4—735no—
809C2×D4—7310no—
810C2×D4—735no—
811C2×D4—735no—
812C2×D4C23×D7315yes—
813C2×D4C23×D7315yes—
814C22×C4—7310no—
815C22×C4—735no—
816C22×C4—735no—
817C22×C4—735no—
818C22×C4—735no—
819C22×C4—735no—
820C22×C4—7310no—
821C22×C4—7310no—
822C22×C4—735no—
823C22×C4C23×D7315yes—
824C22×C4C23×D7315yes—
825C22×C4C23×D7315yes—
826C4⋊C4—731no—
827C4⋊C4—735no—
828C4⋊C4—7310no—
829C4⋊C4—7310no—
830C4⋊C4—735no—
831C4⋊C4—735no—
832C4⋊C4—7310no—
833C4⋊C4—7310no—
834C4⋊C4—7310no—
835C4⋊C4—7310no—
836C4⋊C4—735no—
837C4⋊C4—735no—
838C4⋊C4—735no—
839C4⋊C4—735no—
840C4⋊C4—735no—
841C4⋊C4—735no—
842C4⋊C4C23×D7315yes—
843C4⋊C4C23×D7315yes—
844C4⋊C4C23×D7315yes—
845C4⋊C4C23×D7315yes—
846C4⋊C4C23×D7315yes—
847C4⋊C4C23×D7315yes—
848C4⋊C4C23×D73110yes—
849C4⋊C4C23×D7315yes—
850C4⋊C4C23×D7315yes—
851C4⋊C4C23×D73110yes—
852C22⋊C4—735no—
853C22⋊C4—7310no—
854C22⋊C4—7310no—
855C22⋊C4—735no—
856C22⋊C4—735no—
857C22⋊C4—735no—
858C22⋊C4—735no—
859C22⋊C4—7310no—
860C22⋊C4—7310no—
861C22⋊C4—7310no—
862C22⋊C4—7310no—
863C22⋊C4—7310no—
864C22⋊C4—7310no—
865C22⋊C4—7310no—
866C22⋊C4—7310no—
867C22⋊C4—7310no—
868C22⋊C4—7310no—
869C22⋊C4—7310no—
870C22⋊C4—735no—
871C22⋊C4—7310no—
872C22⋊C4C23×D73110yes—
873C22⋊C4C23×D73110yes—
874C22⋊C4C23×D73110yes—
875C22⋊C4C23×D73110yes—
876C42—735no—
877C42—735no—
878C42—735no—
879C42—735no—
880C42—735no—
881C42—735no—
882C42—7310no—
883C42—7310no—
884C42C23×D7315yes—
885C42C23×D7315yes—
886C42C23×D7315yes—
887C42C23×D7315yes—
888C23—29210no—
889C23—29210no—
890C23—29210no—
891C23—735no—
892C23—735no—
893C23C24×D7315yes—
894Q8—45no—
895Q8—45no—
896Q8—2925no—
897Q8—2925no—
898Q8—29210no—
899Q8—2925no—
900Q8—2925no—
901Q8—14610no—
902D4—45no—
903D4—45no—
904D4—2925no—
905D4—2925no—
906D4—2925no—
907D4—29210no—
908D4—2925no—
909D4—2925no—
910D4—29210no—
911D4—2925no—
912D4—29210no—
913D4—14610no—
914C2×C4—45no—
915C2×C4—45no—
916C2×C4—45no—
917C2×C4—2925no—
918C2×C4—29210no—
919C2×C4—29210no—
920C2×C4—2925no—
921C2×C4—2925no—
922C2×C4—2925no—
923C2×C4—2925no—
924C2×C4—29210no—
925C2×C4—731no—
926C2×C4—731no—
927C2×C4—735no—
928C2×C4—735no—
929C2×C4—735no—
930C2×C4—735no—
931C2×C4—14610no—
932C2×C4C24×D7315yes—
933C2×C4C24×D7315yes—
934C2×C4C24×D7315yes—
935C2×C4C24×D7315yes—
936C2×C4C24×D7315yes—
937C2×C4C24×D7311yescharacteristic
938C22—25no—
939C22—25no—
940C22—25no—
941C22—116810no—
942C22—1465no—
943C22—1465no—
944C22—1465no—
945C22—1465no—
946C22—1465no—
947C22—1465no—
948C22C25×D7311yescharacteristic
949C4—25no—
950C4—25no—
951C4—25no—
952C4—25no—
953C4—21no—
954C4—25no—
955C4—732no—
956C4—1465no—
957C4—1465no—
958C4—1465no—
959C4—1461no—
960C4—1465no—
961C2—45no—
962C2—2925no—
963C2—2925no—
964C2#585×D7311yescharacteristic
965C2#2262474211yescharacteristic
966C2#2262474311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3531C2
hypercenter#3531D73
hypocenterC73#63069
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3531

Complements

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

NH ≅ G/Ntype
1. #22624628C2semidirect
2. #22624627C2semidirect
3. #22624499C2semidirect
4. #22624496C2semidirect
5. #22624493C2semidirect
6. #22624453C2semidirect
7. #22624341C2semidirect
8. #22624289C2semidirect
9. #22624283C2semidirect
10. #22624079C2semidirect
11. #22624079C2semidirect
12. #22623940C2semidirect
13. #22623880C2semidirect
14. #22623820C2semidirect
15. C73×#3531C2semidirect
16. #17989341C22semidirect
17. #17989341C22semidirect
18. #17989341C22semidirect
19. #17989341C22semidirect
20. #17989341C22semidirect
21. #17989337C22semidirect
22. #17989335C22semidirect
23. #17989335C22semidirect
24. #17989335C22semidirect
25. #17989331C22semidirect
26. #17989329C22semidirect
27. #17989329C22semidirect
28. #17989321C22semidirect
29. #17989320C22semidirect
30. #17989317C22semidirect
31. #17989311C22semidirect
32. #17989309C22semidirect
33. #17989309C22semidirect
34. #17989308C22semidirect
35. #17989305C22semidirect
36. #17989305C22semidirect
37. #17989304C22semidirect
38. #17989304C22semidirect
39. #17989303C22semidirect
40. #17989300C22semidirect
41. #17989300C22semidirect
42. #17989266C22semidirect
43. #17989265C22semidirect
44. #17989264C22semidirect
45. #17989262C22semidirect
46. #17989262C22semidirect
47. #17989261C22semidirect
48. #17989261C22semidirect
49. #17989260C22semidirect
50. #17989252C22semidirect
51. #17989250C22semidirect
52. #17989250C22semidirect
53. #17989249C22semidirect
54. #17989247C22semidirect
55. #17989243C22semidirect
56. #17989232C22semidirect
57. #17989229C22semidirect
58. #17989228C22semidirect
59. #17989228C22semidirect
60. #17989226C22semidirect
61. #17989221C22semidirect
62. #17989212C22semidirect
63. #17989211C22semidirect
64. #17989210C22semidirect
65. #17989209C22semidirect
66. #17989209C22semidirect
67. #17989207C22semidirect
68. #17989207C22semidirect
69. #17989207C22semidirect
70. #17989205C22semidirect
71. #17989204C22semidirect
72. #17989203C22semidirect
73. #17989203C22semidirect
74. #17989202C22semidirect
75. #17989177C22semidirect
76. #17989176C22semidirect
77. #17989176C22semidirect
78. #17989173C22semidirect
79. #17989170C22semidirect
80. #17989169C22semidirect
81. #17989162C22semidirect
82. #17989160C22semidirect
83. #17989159C22semidirect
85. #17989148C22semidirect
86. #17989143C22semidirect
87. #17989143C22semidirect
88. #17989143C22semidirect
90. #17989122C22semidirect
91. #17989122C22semidirect
92. #17989122C22semidirect
93. #17989122C22semidirect
94. #17989122C22semidirect
95. #17989121C22semidirect
96. #17989121C22semidirect
97. #17989116C22semidirect
98. C2×#14556579C22semidirect
99. #124×D73C22semidirect
100. #124×D73C22semidirect
101. #17989063C22semidirect
102. #17989059C22semidirect
103. C4×#11924028C22semidirect
104. #564×C73C22semidirect
105. #563×C73C22semidirect
106. #563×C73C22semidirect
107. #562×C73C22semidirect
108. #533×C73C22semidirect
109. #529×C73C22semidirect
110. #529×C73C22semidirect
495. #3531D73semidirect
499. C73#63069semidirect
500. #564C2×D73semidirect
507. #563C2×D73semidirect
508. #563C2×D73semidirect
513. #562C2×D73semidirect
577. #533C2×D73semidirect
587. #529C2×D73semidirect
588. #529C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226246282
#226246272
#226244992
#226244962
#226244932
#226244532
#226243412
#226242892
#226242832
#226240792
#226239402
#226238802
#226238202
C73×#35312
#6306973