Finite Group Databasebeta

← #33999734

Subgroups — #33999734

Order 18688.

6588 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624469C212yesmaximal, complemented
2#22624466C214yesmaximal, complemented
3#22624461C214yesmaximal, complemented
4#22624459C214yesmaximal, complemented
5#22624458C218yesmaximal, complemented
6#22624456C218yesmaximal, complemented
7#22624327C212yesmaximal, complemented
8#22624326C218yesmaximal, complemented
9#22624324C214yesmaximal, complemented
10#22624078C211yesmaximal, characteristic, complemented
11#22624075C212yesmaximal, complemented
12#22623934C214yesmaximal, complemented
13#22623933C214yesmaximal, complemented
14#22623929C212yesmaximal, complemented
15#22623752C211yesmaximal, characteristic, complemented
16#22623751C214yesmaximal, complemented
17C73×#3548C211yesmaximal, characteristic, complemented
18C73⋊#564C2211yescharacteristic
19#17989341C2212yes—
20#17989340C2218yes—
21#17989338C2218yes—
22#17989338C2214yes—
23#17989337C2214yes—
24#17989336C2214yes—
25#17989335C2211yescharacteristic
26#17989333C2214yes—
27#17989333C2218yes—
28#17989332C2218yes—
29#17989332C2218yes—
30#17989332C2218yes—
31#17989331C2214yes—
32#17989315C2214yes—
33#17989314C2214yes—
34#17989312C2212yes—
35#17989297C2214yes—
36#17989296C2214yes—
37#17989296C2214yes—
38#17989295C2218yes—
39#17989294C2214yes—
40#17989292C2218yes—
41#17989291C2218yes—
42#17989291C2218yes—
43#17989291C2218yes—
44#17989290C2214yes—
45#17989289C2214yes—
46#17989287C2214yes—
47#17989287C2214yes—
48#17989286C2218yes—
49#17989284C2214yes—
50#17989282C2218yes—
51#17989280C2218yes—
52#17989280C2218yes—
53#17989280C2218yes—
54#17989257C2212yes—
55#17989257C2214yes—
56#17989257C2212yes—
57#17989257C2214yes—
58#17989256C2214yes—
59#17989255C2218yes—
60#17989255C2218yes—
61#17989255C2214yes—
62#17989242C2214yes—
63#17989240C2212yes—
64#17989239C2218yes—
65#17989238C2218yes—
66#17989237C2218yes—
67#17989237C2218yes—
68#17989237C2214yes—
69#17989236C2218yes—
70#17989236C2218yes—
71#17989236C2214yes—
72#17989236C2218yes—
73#17989235C2218yes—
74#17989235C2218yes—
75#17989217C2214yes—
76#17989216C2218yes—
77#17989216C2218yes—
78#17989215C2212yes—
79#17989214C2214yes—
80#17989214C2214yes—
81#17989191C2214yes—
82#17989191C2214yes—
83#17989189C2218yes—
84#17989188C2214yes—
85#17989188C2214yes—
86#17989187C2218yes—
87#17989187C2218yes—
88#17989187C2218yes—
89#17989187C2218yes—
90#17989184C2218yes—
91#17989183C2218yes—
92#17989183C2218yes—
93#17989182C2218yes—
94#17989182C2214yes—
95#17989181C2218yes—
96#17989180C2218yes—
97#17989179C2218yes—
98#17989167C2218yes—
99#17989166C2218yes—
100#17989166C2218yes—
101#17989165C2218yes—
102#17989164C2218yes—
103#17989164C2218yes—
104#17989164C2214yes—
105#17989143C2212yes—
106#17989141C2214yes—
107#17989139C2218yes—
108#17989136C2214yes—
109#17989135C2214yes—
110#17989134C2214yes—
111#17989133C2218yes—
112#17989132C2218yes—
113#17989124C2214yes—
114#17989121C2212yes—
115#17989118C2218yes—
116#17989116C2214yes—
117#17989115C2214yes—
118#17989114C2218yes—
119C2×#14556583C2211yescharacteristic
120C2×#14556581C2218yes—
121#125×D73C2214yes—
122#125×D73C2212yes—
123#17989067C2212yes—
124#17989066C2214yes—
125#17989066C2214yes—
126C4×#11924028C2211yescharacteristic
127C4×#11924027C2214yes—
128#562×C73C2212yes—
129#562×C73C2212yes—
130#554×C73C2214yes—
131#550×C73C2214yes—
132#547×C73C2214yes—
133#540×C73C2214yes—
134#537×C73C2218yes—
135#533×C73C2211yescharacteristic
136#532×C73C2212yes—
137C2×#11924029C2314yes—
138C2×#11924028C2311yescharacteristic
139C2×#11924028C2318yes—
140C2×#11924028C2318yes—
141C2×#11924027C2314yes—
142C2×#11924027C2318yes—
143C2×#11924027C2318yes—
144C2×#11924027C2318yes—
145C2×#11924027C2314yes—
146#14556591C2314yes—
147#14556590C2318yes—
148#14556590C2314yes—
149#14556590C2318yes—
150#14556590C2314yes—
151#14556590C2314yes—
152#14556589C2318yes—
153#14556589C2314yes—
154#14556589C2318yes—
155#14556589C2314yes—
156#14556587C2318yes—
157#14556587C2318yes—
158#14556587C2314yes—
159#14556587C2314yes—
160#14556586C2314yes—
161#14556586C2314yes—
162#14556586C2314yes—
163#14556586C2318yes—
164#14556585C2314yes—
165#14556584C2318yes—
166#14556584C2318yes—
167#14556584C2314yes—
168#14556584C2318yes—
169#14556584C2318yes—
170#14556583C2312yes—
171#14556583C2312yes—
172#14556583C2312yes—
173#14556583C2314yes—
174#14556583C2314yes—
175#14556582C2314yes—
176#14556582C2314yes—
177#14556582C2314yes—
178#14556582C2314yes—
179#14556581C2314yes—
180#14556581C2318yes—
181#14556581C2314yes—
182#14556581C2318yes—
183#14556581C2318yes—
184#14556581C2318yes—
185#14556581C2318yes—
186#14556581C2318yes—
187#14556581C2318yes—
188#14556581C2318yes—
189#14556581C2318yes—
190#14556581C2314yes—
191#14556580C2314yes—
192#14556579C2312yes—
193#14556578C2318yes—
194#14556577C2314yes—
195#14556577C2318yes—
196#14556576C2314yes—
197#14556576C2314yes—
198#14556576C2318yes—
199#14556576C2318yes—
200#14556576C2314yes—
201#14556575C2318yes—
202#14556574C2314yes—
203#14556574C2318yes—
204#14556574C2318yes—
205#14556574C2318yes—
206#14556574C2318yes—
207#14556573C2318yes—
208#14556573C2318yes—
209#14556573C2318yes—
210#14556573C2318yes—
211#14556573C2314yes—
212#14556573C2318yes—
213#14556572C2318yes—
214#14556572C2318yes—
215#14556572C2318yes—
216#14556572C2318yes—
217#14556572C2318yes—
218#14556572C2318yes—
219#14556571C2314yes—
220#14556571C2318yes—
221#14556570C2312yes—
222#14556570C2318yes—
223#14556570C2318yes—
224#14556570C2318yes—
225#14556570C2318yes—
226#14556569C2314yes—
227#14556569C2314yes—
228#14556569C2318yes—
229#14556569C2318yes—
230#14556569C2318yes—
231#14556569C2318yes—
232#14556569C2314yes—
233#14556568C2318yes—
234#14556568C2318yes—
235#14556568C2318yes—
236#14556568C2318yes—
237#14556568C2318yes—
238#14556568C2318yes—
239#14556568C2318yes—
240#14556568C2318yes—
241#14556567C2314yes—
242#14556567C2314yes—
243#14556567C2318yes—
244#14556567C2318yes—
245#14556567C2314yes—
246#14556566C2314yes—
247#14556566C2314yes—
248#14556566C2318yes—
249#14556565C2312yes—
250#14556565C2318yes—
251#14556565C2318yes—
252#14556564C2318yes—
253#14556564C2318yes—
254#14556564C2318yes—
255#14556564C2318yes—
256#14556564C2318yes—
257#14556564C2314yes—
258#14556564C2318yes—
259#14556563C2318yes—
260#14556563C2318yes—
261#14556563C2318yes—
262#14556563C2318yes—
263#14556563C2318yes—
264#14556563C2318yes—
265#14556563C2318yes—
266#14556563C2318yes—
267#14556563C2318yes—
268#14556563C2318yes—
269#14556563C2318yes—
270#14556563C2318yes—
271#14556562C2314yes—
272#14556562C2318yes—
273#14556562C2314yes—
274#14556562C2314yes—
275#14556562C2318yes—
276#14556562C2318yes—
277#14556562C2314yes—
278Q8×Dic73C2314yes—
279C4×Dic146C2312yes—
280C4×Dic146C2314yes—
281C4×Dic146C2314yes—
282C4×Dic146C2312yes—
283#14556556C2318yes—
284#14556556C2318yes—
285#14556556C2314yes—
286C4×D292C2312yes—
287C4×D292C2314yes—
288C4×D292C2314yes—
289C4×D292C2312yes—
290D4×Dic73C2318yes—
291D4×Dic73C2318yes—
292D4×Dic73C2314yes—
293D4×Dic73C2314yes—
294D4×Dic73C2314yes—
295D4×Dic73C2318yes—
296D4×Dic73C2314yes—
297#14556553C2318yes—
298C4×C22⋊D73C2314yes—
299C4×C22⋊D73C2318yes—
300C4×C22⋊D73C2318yes—
301C4×C22⋊D73C2318yes—
302C4×C22⋊D73C2318yes—
303C4×C22⋊D73C2318yes—
304C4×C22⋊D73C2314yes—
305C4×C22⋊D73C2318yes—
306#14556551C2318yes—
307#14556551C2318yes—
308#14556551C2318yes—
309#14556551C2318yes—
310#14556551C2318yes—
311#14556551C2318yes—
312#14556550C2311yescharacteristic
313#14556549C2314yes—
314#14556549C2314yes—
315#14556548C2314yes—
316#14556548C2314yes—
317#14556548C2312yes—
318#14556547C2318yes—
319#14556547C2318yes—
320#14556547C2318yes—
321C2×C4⋊Dic73C2318yes—
322C2×C4⋊Dic73C2312yes—
323C2×#11924007C2318yes—
324C2×#11924007C2318yes—
325C2×#11924007C2314yes—
326C2×#11924007C2318yes—
327C2×#11924007C2318yes—
328C4⋊C4×D73C2318yes—
329C4⋊C4×D73C2318yes—
330C4⋊C4×D73C2318yes—
331C4⋊C4×D73C2314yes—
332C4⋊C4×D73C2314yes—
333C4⋊C4×D73C2314yes—
334C2×C4×Dic73C2318yes—
335C42×D73C2314yes—
336C42×D73C2312yes—
337C2×#41×C73C2318yes—
338C2×#41×C73C2314yes—
339C4⋊Q8×C73C2312yes—
340C4⋊Q8×C73C2312yes—
341#127×C73C2314yes—
342#127×C73C2312yes—
343#125×C73C2311yescharacteristic
344#125×C73C2314yes—
345#125×C73C2311yescharacteristic
346#124×C73C2314yes—
347#123×C73C2318yes—
348#123×C73C2318yes—
349C22⋊Q8×C73C2318yes—
350C22⋊Q8×C73C2318yes—
351C22⋊Q8×C73C2318yes—
352C22⋊Q8×C73C2314yes—
353#121×C73C2318yes—
354#121×C73C2314yes—
355#121×C73C2318yes—
356#121×C73C2318yes—
357#121×C73C2318yes—
358#121×C73C2314yes—
359#121×C73C2318yes—
360C4×Q8×C73C2314yes—
361C4×D4×C73C2314yes—
362C4×D4×C73C2314yes—
363C4×D4×C73C2314yes—
364C4×D4×C73C2314yes—
365#117×C73C2312yes—
366C2×C4⋊C4×C73C2318yes—
367C2×C42×C73C2311yescharacteristic
368#11924029—84no—
369#11924028—24no—
370#11924028—88no—
371#11924028—88no—
372#11924027—216no—
373#11924027—88no—
374#11924027—84no—
375#11924027—88no—
376#11924027—88no—
377C2×Dic146C2418yes—
378C2×Dic146C2418yes—
379C2×Dic146C2412yes—
380C2×Dic146C2414yes—
381C2×Dic146C2411yescharacteristic
382C2×D292C2411yescharacteristic
383C2×D292C2418yes—
384C2×D292C2412yes—
385C2×D292C2414yes—
386C2×C22⋊D73C2412yes—
387C2×C22⋊D73C2418yes—
388C2×C22⋊D73C2418yes—
389C2×C22⋊D73C2418yes—
390C2×C22⋊D73C2418yes—
391C2×C22⋊D73C2414yes—
392C2×C22⋊D73C2418yes—
393C2×C22⋊D73C2418yes—
394C22×Dic73C2418yes—
395C22×Dic73C2418yes—
396C22×Dic73C2418yes—
397C22×Dic73C2418yes—
398C22×Dic73C2414yes—
399C2×C4×D73C2414yes—
400C2×C4×D73C2412yes—
401C2×C4×D73C2414yes—
402C2×C4×D73C2414yes—
403C2×C4×D73C2414yes—
404C2×C4×D73C2418yes—
405C2×C4×D73C2418yes—
406C2×C4×D73C2418yes—
407C4⋊Dic73C2412yes—
408C4⋊Dic73C2414yes—
409C4⋊Dic73C2414yes—
410C4⋊Dic73C2418yes—
411C4⋊Dic73C2418yes—
412C4⋊Dic73C2418yes—
413C4⋊Dic73C2414yes—
414C4⋊Dic73C2412yes—
415C4⋊Dic73C2414yes—
416C4⋊Dic73C2412yes—
417#11924007C2418yes—
418#11924007C2418yes—
419#11924007C2418yes—
420#11924007C2418yes—
421#11924007C2418yes—
422#11924007C2418yes—
423#11924007C2418yes—
424#11924007C2418yes—
425#11924007C2418yes—
426#11924007C2414yes—
427#11924007C2414yes—
428#11924007C2414yes—
429#11924007C2418yes—
430#11924007C2418yes—
431#11924007C2414yes—
432#11924007C2414yes—
433#11924007C2414yes—
434#11924007C2414yes—
435#11924007C2414yes—
436#11924007C2414yes—
437C22⋊Dic73C2418yes—
438C22⋊Dic73C2418yes—
439C22⋊Dic73C2418yes—
440C22⋊Dic73C2412yes—
441C22⋊Dic73C2418yes—
442C22⋊Dic73C2418yes—
443C22⋊Dic73C2418yes—
444C22⋊Dic73C2414yes—
445#11924005C2414yes—
446#11924005C2414yes—
447#11924005C2414yes—
448#11924005C2414yes—
449#11924005C2414yes—
450#11924005C2418yes—
451#11924005C2418yes—
452#11924005C2414yes—
453#11924005C2418yes—
454#11924005C2414yes—
455#11924005C2414yes—
456#11924005C2414yes—
457C4×Dic73C2414yes—
458C4×Dic73C2414yes—
459C4×Dic73C2414yes—
460C4×Dic73C2414yes—
461C4×Dic73C2412yes—
462C4×Dic73C2418yes—
463C4×Dic73C2418yes—
464C4×Dic73C2418yes—
465#41×C73—84no—
466#41×C73—88no—
467C2×Q8×C73C2414yes—
468C2×Q8×C73C2414yes—
469C2×D4×C73C2414yes—
470C2×D4×C73C2414yes—
471C2×D4×C73C2418yes—
472C2×D4×C73C2418yes—
473C2×D4×C73C2418yes—
474C2×D4×C73C2414yes—
475C22×C4×C73C2411yescharacteristic
476C22×C4×C73C2412yes—
477C22×C4×C73C2418yes—
478C22×C4×C73C2418yes—
479C22×C4×C73C2418yes—
480C4⋊C4×C73C2414yes—
481C4⋊C4×C73C2414yes—
482C4⋊C4×C73C2418yes—
483C4⋊C4×C73C2418yes—
484C4⋊C4×C73C2412yes—
485C4⋊C4×C73C2412yes—
486C4⋊C4×C73C2414yes—
487C4⋊C4×C73C2414yes—
488C4⋊C4×C73C2414yes—
489C22⋊C4×C73C2414yes—
490C22⋊C4×C73C2418yes—
491C22⋊C4×C73C2418yes—
492C22⋊C4×C73C2418yes—
493C22⋊C4×C73C2418yes—
494C42×C73C2411yescharacteristic
495C42×C73C2412yes—
496C42×C73C2411yescharacteristic
497C42×C73C2414yes—
498C23×C73C2518yes—
499C23×C73C2511yescharacteristic
500C22×D73C2512yes—
501C22×D73C2514yes—
502Q8×C73—44no—
503Q8×C73—44no—
504D4×C73—28no—
505D4×C73—44no—
506D4×C73—48no—
507D4×C73—48no—
508D4×C73—48no—
509D4×C73—44no—
510C2×C4×C73—22no—
511C2×C4×C73—48no—
512C2×C4×C73—42no—
513C2×C4×C73—48no—
514C2×C4×C73—48no—
515C2×C4×C73C2511yescharacteristic
516C2×C4×C73C2512yes—
517C2×C4×C73C2512yes—
518C2×C4×C73C2514yes—
519C2×C4×C73C2514yes—
520C2×C4×C73C2518yes—
521C2×C4×C73C2511yescharacteristic
522C22⋊D73—216no—
523C22⋊D73—24no—
524C22⋊D73—44no—
525C22⋊D73—48no—
526C22⋊D73—48no—
527C22⋊D73—48no—
528C22⋊D73—48no—
529C22⋊D73—48no—
530C2×Dic73—216no—
531C2×Dic73—48no—
532C2×Dic73—48no—
533C2×Dic73—44no—
534C2×Dic73—48no—
535C2×Dic73C2514yes—
536C2×Dic73C2514yes—
537C2×Dic73C2514yes—
538C2×Dic73C2518yes—
539C2×Dic73C2514yes—
540C2×Dic73C2512yes—
541D292—22no—
542D292—44no—
543D292—48no—
544D292—42no—
545C4×D73—28no—
546C4×D73—24no—
547C4×D73—44no—
548C4×D73—48no—
549C4×D73—48no—
550C4×D73—44no—
551C4×D73—44no—
552C4×D73—48no—
553Dic146—44no—
554Dic146—42no—
555Dic146—48no—
556Dic146—48no—
557Dic1462−1+414yes—
558C22×C73—28no—
559C22×C73—21no—
560C22×C73—28no—
561C22×C73—22no—
562C22×C73—28no—
563C22×C73C2611yescharacteristic
564C2×D73—22no—
565C2×D73—24no—
566C2×D73—24no—
567C2×D73—24no—
568C2×D73—24no—
569C4×C73—21no—
570C4×C73—24no—
571C4×C73—24no—
572C4×C73—28no—
573C4×C73—22no—
574C4×C73—22no—
575C4×C73C2×2−1+412yes—
576Dic73—24no—
577Dic73—24no—
578Dic73—24no—
579Dic73—28no—
580Dic73—24no—
581Dic73C2×2−1+414yes—
582#63070—731nomaximal, Sylow
583C2×C73—48no—
584C2×C73—41no—
585C2×C73C22×2−1+411yescharacteristic
586C2×C73H(7,𝔽2)12yes—
587D73—42no—
588D73—44no—
589#3559—734no—
590#3559—734no—
591#3559—738no—
592#3559—734no—
593#3559—738no—
594#3559—732no—
595#3548—732no—
596#3548—734no—
597#3548—738no—
598#3548D7311yescharacteristic, complemented
599#3531—732no—
600#3531—731no—
601#3517—734no—
602#3517—734no—
603#3517—732no—
604#3504—734no—
605#3504—731no—
606C73#6307011yescharacteristic, complemented, Sylow
607#564—731no—
608#563—734no—
609#563—732no—
610#563—734no—
611#563—738no—
612#563—738no—
613#563—734no—
614#562—731no—
615#562—734no—
616#562—734no—
617#562—738no—
618#562—738no—
619#562—738no—
620#562—738no—
621#562C2×D7312yes—
622#562C2×D7312yes—
623#557—732no—
624#557—734no—
625#557—734no—
626#554—738no—
627#554—738no—
628#554—738no—
629#554—738no—
630#554—734no—
631#554—734no—
632#554—734no—
633#554—734no—
634#554—738no—
635#554C2×D7314yes—
636#553—734no—
637#553—738no—
638#553—738no—
639#553—738no—
640#553—738no—
641#553—734no—
642#553—734no—
643#553—738no—
644#553—734no—
645#553—734no—
646#550—734no—
647#550—734no—
648#550—732no—
649#550—734no—
650#550—732no—
651#550—734no—
652#550—738no—
653#550—738no—
654#550C2×D7314yes—
655#547—738no—
656#547—734no—
657#547—738no—
658#547—738no—
659#547—732no—
660#547—738no—
661#547—738no—
662#547—738no—
663#547—734no—
664#547—738no—
665#547—738no—
666#547—734no—
667#547—738no—
668#547C2×D7314yes—
669#544—734no—
670#544—734no—
671#544—734no—
672#544—738no—
673#544—738no—
674#544—732no—
675#540—734no—
676#540—734no—
677#540—738no—
678#540—738no—
679#540—738no—
680#540—738no—
681#540—738no—
682#540—734no—
683#540—734no—
684#540C2×D7314yes—
685#539—738no—
686#539—738no—
687#539—738no—
688#539—738no—
689#539—738no—
690#539—734no—
691#539—738no—
692#539—738no—
693#537—738no—
694#537—738no—
695#537—738no—
696#537—734no—
697#537—738no—
698#537—738no—
699#537—738no—
700#537C2×D7318yes—
701#533—732no—
702#533—738no—
703#533—734no—
704#533C2×D7311yescharacteristic
705#532—738no—
706#532—734no—
707#532—734no—
708#532—738no—
709#532—734no—
710#532C2×D7312yes—
711#529—734no—
712#529—738no—
713#529—738no—
714#529—734no—
715#529—734no—
716#529—732no—
717C2×#125—734no—
718C2×#125—732no—
719C2×#125—738no—
720C2×#125—731no—
721#520—734no—
722#520—734no—
723#520—732no—
724C4×#41—734no—
725C4×#41—731no—
726C2×#41—734no—
727C2×#41—738no—
728C2×#41—738no—
729C2×#41—734no—
730C2×#41—738no—
731C2×#41—734no—
732C2×#41—738no—
733C2×#41—738no—
734C2×#41—731no—
735C2×#41C22×D7318yes—
736C2×#41C22×D7314yes—
737C4⋊Q8—734no—
738C4⋊Q8—738no—
739C4⋊Q8—738no—
740C4⋊Q8—734no—
741C4⋊Q8—738no—
742C4⋊Q8—734no—
743C4⋊Q8—734no—
744C4⋊Q8—738no—
745C4⋊Q8—734no—
746C4⋊Q8—734no—
747C4⋊Q8C22×D7312yes—
748C4⋊Q8C22×D7312yes—
749#127—734no—
750#127—734no—
751#127—738no—
752#127—738no—
753#127C22×D7314yes—
754#127C22×D7312yes—
755#126—734no—
756#126—738no—
757#126—734no—
758#126—734no—
759#126—738no—
760#126—738no—
761#126—738no—
762#126—738no—
763#126—734no—
764#126—734no—
765#125—738no—
766#125—734no—
767#125—738no—
768#125—738no—
769#125—738no—
770#125—734no—
771#125—738no—
772#125—738no—
773#125—738no—
774#125—738no—
775#125—738no—
776#125—734no—
777#125—734no—
778#125—734no—
779#125—734no—
780#125—734no—
781#125—732no—
782#125—732no—
783#125—734no—
784#125—734no—
785#125—732no—
786#125C22×D7311yescharacteristic
787#125C22×D7314yes—
788#125C22×D7311yescharacteristic
789#124—734no—
790#124—738no—
791#124—738no—
792#124—734no—
793#124—732no—
794#124C22×D7314yes—
795#123—738no—
796#123—738no—
797#123—738no—
798#123—738no—
799#123—738no—
800#123—738no—
801#123—738no—
802#123—734no—
803#123—738no—
804#123—738no—
805#123—738no—
806#123—734no—
807#123—734no—
808#123—734no—
809#123—738no—
810#123—738no—
811#123—738no—
812#123—734no—
813#123—738no—
814#123—738no—
815#123—738no—
816#123—738no—
817#123—738no—
818#123C22×D7318yes—
819#123C22×D7318yes—
820C22⋊Q8—734no—
821C22⋊Q8—734no—
822C22⋊Q8—734no—
823C22⋊Q8—738no—
824C22⋊Q8—738no—
825C22⋊Q8—738no—
826C22⋊Q8—732no—
827C22⋊Q8—738no—
828C22⋊Q8—738no—
829C22⋊Q8—738no—
830C22⋊Q8—734no—
831C22⋊Q8—738no—
832C22⋊Q8—734no—
833C22⋊Q8—734no—
834C22⋊Q8—734no—
835C22⋊Q8—738no—
836C22⋊Q8—738no—
837C22⋊Q8—738no—
838C22⋊Q8—738no—
839C22⋊Q8—738no—
840C22⋊Q8—738no—
841C22⋊Q8—738no—
842C22⋊Q8—738no—
843C22⋊Q8—738no—
844C22⋊Q8—738no—
845C22⋊Q8—738no—
846C22⋊Q8—738no—
847C22⋊Q8C22×D7318yes—
848C22⋊Q8C22×D7314yes—
849C22⋊Q8C22×D7318yes—
850C22⋊Q8C22×D7318yes—
851#121—734no—
852#121—738no—
853#121—738no—
854#121—738no—
855#121—738no—
856#121—734no—
857#121—734no—
858#121—734no—
859#121—738no—
860#121—738no—
861#121—738no—
862#121—738no—
863#121—738no—
864#121—738no—
865#121—738no—
866#121—738no—
867#121—738no—
868#121—738no—
869#121—738no—
870#121—732no—
871#121—738no—
872#121—738no—
873#121—734no—
874#121—734no—
875#121—738no—
876#121—734no—
877#121—738no—
878#121—738no—
879#121—738no—
880#121—738no—
881#121—738no—
882#121—738no—
883#121C22×D7318yes—
884#121C22×D7318yes—
885#121C22×D7314yes—
886#121C22×D7314yes—
887#121C22×D7318yes—
888#121C22×D7318yes—
889#121C22×D7318yes—
890C4×Q8—734no—
891C4×Q8—734no—
892C4×Q8—738no—
893C4×Q8—738no—
894C4×Q8—734no—
895C4×Q8—732no—
896C4×Q8—734no—
897C4×Q8—732no—
898C4×Q8C22×D7314yes—
899C4×D4—734no—
900C4×D4—734no—
901C4×D4—734no—
902C4×D4—734no—
903C4×D4—738no—
904C4×D4—738no—
905C4×D4—738no—
906C4×D4—738no—
907C4×D4—734no—
908C4×D4—738no—
909C4×D4—738no—
910C4×D4—734no—
911C4×D4—738no—
912C4×D4—738no—
913C4×D4—738no—
914C4×D4—738no—
915C4×D4—738no—
916C4×D4—738no—
917C4×D4—738no—
918C4×D4—738no—
919C4×D4—738no—
920C4×D4—738no—
921C4×D4—732no—
922C4×D4—734no—
923C4×D4—734no—
924C4×D4—732no—
925C4×D4C22×D7314yes—
926C4×D4C22×D7314yes—
927C4×D4C22×D7314yes—
928C4×D4C22×D7314yes—
929#117—731no—
930#117—734no—
931#117—734no—
932#117—738no—
933#117—738no—
934#117—738no—
935#117—732no—
936#117—734no—
937#117—734no—
938#117C22×D7312yes—
939C2×C4⋊C4—738no—
940C2×C4⋊C4—738no—
941C2×C4⋊C4—732no—
942C2×C4⋊C4—738no—
943C2×C4⋊C4—738no—
944C2×C4⋊C4—734no—
945C2×C4⋊C4—738no—
946C2×C4⋊C4—734no—
947C2×C4⋊C4—734no—
948C2×C4⋊C4—734no—
949C2×C4⋊C4—738no—
950C2×C4⋊C4—738no—
951C2×C4⋊C4—738no—
952C2×C4⋊C4C22×D7318yes—
953C2×C42—738no—
954C2×C42—734no—
955C2×C42—732no—
956C2×C42C22×D7311yescharacteristic
957#41—84no—
958#41—88no—
959#41—5848no—
960#41—5848no—
961#41—5848no—
962#41—5848no—
963#41—5848no—
964#41—5844no—
965#41—5844no—
966#41—1464no—
967#41—14616no—
968C2×Q8—738no—
969C2×Q8—734no—
970C2×Q8—738no—
971C2×Q8—732no—
972C2×Q8—731no—
973C2×Q8C23×D7314yes—
974C2×Q8C23×D7314yes—
975C2×D4—738no—
976C2×D4—738no—
977C2×D4—738no—
978C2×D4—738no—
979C2×D4—738no—
980C2×D4—734no—
981C2×D4—732no—
982C2×D4—738no—
983C2×D4—738no—
984C2×D4—734no—
985C2×D4—732no—
986C2×D4—731no—
987C2×D4C23×D7314yes—
988C2×D4C23×D7318yes—
989C2×D4C23×D7318yes—
990C2×D4C23×D7314yes—
991C2×D4C23×D7318yes—
992C2×D4C23×D7314yes—
993C22×C4—738no—
994C22×C4—738no—
995C22×C4—738no—
996C22×C4—734no—
997C22×C4—734no—
998C22×C4—734no—
999C22×C4—734no—
1000C22×C4—738no—
1001C22×C4—738no—
1002C22×C4—738no—
1003C22×C4—738no—
1004C22×C4—732no—
1005C22×C4—734no—
1006C22×C4C23×D7311yescharacteristic
1007C22×C4C23×D7318yes—
1008C22×C4C23×D7312yes—
1009C22×C4C23×D7318yes—
1010C22×C4C23×D7318yes—
1011C4⋊C4—738no—
1012C4⋊C4—738no—
1013C4⋊C4—734no—
1014C4⋊C4—738no—
1015C4⋊C4—738no—
1016C4⋊C4—734no—
1017C4⋊C4—734no—
1018C4⋊C4—738no—
1019C4⋊C4—738no—
1020C4⋊C4—738no—
1021C4⋊C4—738no—
1022C4⋊C4—738no—
1023C4⋊C4—734no—
1024C4⋊C4—738no—
1025C4⋊C4—734no—
1026C4⋊C4—738no—
1027C4⋊C4—734no—
1028C4⋊C4—734no—
1029C4⋊C4—734no—
1030C4⋊C4—734no—
1031C4⋊C4—732no—
1032C4⋊C4—734no—
1033C4⋊C4—734no—
1034C4⋊C4—738no—
1035C4⋊C4—738no—
1036C4⋊C4—738no—
1037C4⋊C4—734no—
1038C4⋊C4—734no—
1039C4⋊C4—732no—
1040C4⋊C4—732no—
1041C4⋊C4C23×D7314yes—
1042C4⋊C4C23×D7312yes—
1043C4⋊C4C23×D7314yes—
1044C4⋊C4C23×D7318yes—
1045C4⋊C4C23×D7318yes—
1046C4⋊C4C23×D7314yes—
1047C4⋊C4C23×D7314yes—
1048C4⋊C4C23×D7312yes—
1049C4⋊C4C23×D7314yes—
1050C22⋊C4—738no—
1051C22⋊C4—738no—
1052C22⋊C4—738no—
1053C22⋊C4—732no—
1054C22⋊C4—738no—
1055C22⋊C4—738no—
1056C22⋊C4—738no—
1057C22⋊C4—734no—
1058C22⋊C4—734no—
1059C22⋊C4—734no—
1060C22⋊C4—734no—
1061C22⋊C4—738no—
1062C22⋊C4—734no—
1063C22⋊C4—738no—
1064C22⋊C4—734no—
1065C22⋊C4—738no—
1066C22⋊C4—734no—
1067C22⋊C4—734no—
1068C22⋊C4—734no—
1069C22⋊C4—734no—
1070C22⋊C4C23×D7318yes—
1071C22⋊C4C23×D7318yes—
1072C22⋊C4C23×D7318yes—
1073C22⋊C4C23×D7314yes—
1074C22⋊C4C23×D7318yes—
1075C42—734no—
1076C42—738no—
1077C42—738no—
1078C42—734no—
1079C42—734no—
1080C42—738no—
1081C42—734no—
1082C42—732no—
1083C42C23×D7311yescharacteristic
1084C42C23×D7314yes—
1085C42C23×D7312yes—
1086C42C23×D7311yescharacteristic
1087C23—734no—
1088C23—732no—
1089C23C24×D7311yescharacteristic
1090C23C24×D7318yes—
1091Q8—44no—
1092Q8—44no—
1093Q8—2928no—
1094Q8—2924no—
1095Q8—2928no—
1096Q8—2922no—
1097Q8—734no—
1098D4—28no—
1099D4—44no—
1100D4—48no—
1101D4—48no—
1102D4—48no—
1103D4—44no—
1104D4—2928no—
1105D4—2924no—
1106D4—2922no—
1107D4—2928no—
1108D4—2928no—
1109D4—2928no—
1110D4—2928no—
1111D4—2928no—
1112D4—2924no—
1113D4—1464no—
1114D4—14616no—
1115D4—1462no—
1116C2×C4—22no—
1117C2×C4—48no—
1118C2×C4—42no—
1119C2×C4—48no—
1120C2×C4—48no—
1121C2×C4—2928no—
1122C2×C4—2928no—
1123C2×C4—2928no—
1124C2×C4—2924no—
1125C2×C4—2924no—
1126C2×C4—2924no—
1127C2×C4—2928no—
1128C2×C4—2928no—
1129C2×C4—2924no—
1130C2×C4—2928no—
1131C2×C4—732no—
1132C2×C4—734no—
1133C2×C4—734no—
1134C2×C4—734no—
1135C2×C4—738no—
1136C2×C4—734no—
1137C2×C4—1464no—
1138C2×C4—14616no—
1139C2×C4—1468no—
1140C2×C4C24×D7314yes—
1141C2×C4C24×D7311yescharacteristic
1142C2×C4C24×D7312yes—
1143C2×C4C24×D7318yes—
1144C2×C4C24×D7314yes—
1145C2×C4C24×D7312yes—
1146C2×C4C24×D7311yescharacteristic
1147C22—21no—
1148C22—28no—
1149C22—28no—
1150C22—22no—
1151C22—28no—
1152C22—1462no—
1153C22—1464no—
1154C22—1464no—
1155C22—1464no—
1156C22—1464no—
1157C22C25×D7311yescharacteristic
1158C4—21no—
1159C4—22no—
1160C4—28no—
1161C4—24no—
1162C4—24no—
1163C4—22no—
1164C4—734no—
1165C4—1464no—
1166C4—1464no—
1167C4—1468no—
1168C4—1464no—
1169C4—1464no—
1170C42−1+4×D7312yes—
1171C2—41no—
1172C2—48no—
1173C2—2922no—
1174C2—2924no—
1175C2C2×2−1+4×D7311yescharacteristic
1176C2#2262474112yes—
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3548C2
hypercenter#3548D73
hypocenterC73#63070
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #22624469C2semidirect
2. #22624466C2semidirect
3. #22624461C2semidirect
4. #22624459C2semidirect
5. #22624458C2semidirect
6. #22624456C2semidirect
7. #22624327C2semidirect
8. #22624326C2semidirect
9. #22624324C2semidirect
10. #22624078C2semidirect
11. #22624075C2semidirect
12. #22623934C2semidirect
13. #22623933C2semidirect
14. #22623929C2semidirect
15. #22623752C2semidirect
16. #22623751C2semidirect
17. C73×#3548C2semidirect
598. #3548D73semidirect
606. C73#63070semidirect

Maximal subgroups

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

subgroupindex
#226244692
#226244662
#226244612
#226244592
#226244582
#226244562
#226243272
#226243262
#226243242
#226240782
#226240752
#226239342
#226239332
#226239292
#226237522
#226237512
C73×#35482
#6307073