Finite Group Databasebeta

← #33994209

Subgroups — #33994209

Order 18688.

7094 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624018C214yesmaximal, complemented
2#22624007C214yesmaximal, complemented
3#22623925C214yesmaximal, complemented
4#22623913C214yesmaximal, complemented
5#22623795C216yesmaximal, complemented
6#22623737C211yesmaximal, characteristic, complemented
7#22623698C211yesmaximal, characteristic, complemented
8#22623637C216yesmaximal, complemented
9#22623582C211yesmaximal, characteristic, complemented
10#22623552C214yesmaximal, complemented
11#22623547C214yesmaximal, complemented
12#22623521C214yesmaximal, complemented
13Q8×#11924027C214yesmaximal, complemented
14#22623355C216yesmaximal, complemented
15#22623223C216yesmaximal, complemented
162−1+4×Dic73C211yesmaximal, characteristic, complemented
17#22623140C211yesmaximal, characteristic, complemented
18C22×Q8×Dic73C211yesmaximal, characteristic, complemented
19C73×#3486C211yesmaximal, characteristic, complemented
20C2×#14556639C2211yescharacteristic
21#17989319C22112yescomplemented
22Q8×Dic146C2214yescomplemented
23#17989316C2214yescomplemented
24#17989313C2214yescomplemented
25#17989313C2214yescomplemented
26#17989312C22112yescomplemented
27#17989311C22112yescomplemented
28#17989308C22112yescomplemented
29#17989306C22112yescomplemented
30#17989295C22112yes—
31#17989295C22112yescomplemented
32#17989294C22112yes—
33#17989289C22112yes—
34#17989283C22112yes—
35#17989279C22112yes—
36#17989279C22112yescomplemented
37#17989277C22112yes—
38#17989271C22112yescomplemented
39#17989256C2214yescomplemented
40Q8×C22⋊D73C2214yes—
41Q8×C22⋊D73C2214yes—
42Q8×C22⋊D73C2214yescomplemented
43#17989248C2214yes—
44#17989248C2214yes—
45#17989248C2214yescomplemented
46#17989244C2214yescomplemented
47#17989241C22112yes—
48#17989237C22112yes—
49#17989215C2216yes—
50#17989210C22112yescomplemented
51#17989206C22112yescomplemented
52#17989198C22112yescomplemented
53#17989197C22112yescomplemented
54#17989181C22124yes—
55#17989165C2216yes—
56#17989161C2216yes—
57#17989142C22112yescomplemented
58#17989140C2216yes—
59#17989139C2216yes—
60#17989139C2216yes—
61#17989139C22112yescomplemented
62#17989133C2216yes—
63#17989132C2216yes—
64#17989132C2216yes—
65#17989123C2216yes—
66#17989123C2216yes—
67#17989123C22112yescomplemented
68#17989118C2216yes—
69#17989118C2216yes—
70#17989117C22112yes—
71#17989117C22112yes—
72#17989116C22112yescomplemented
73#17989114C22112yes—
74#17989114C22112yes—
75#17989098C2216yes—
76#17989093C22112yes—
77#17989093C2214yes—
78#17989070C2216yes—
79#17989070C2214yescomplemented
80#17989069C2214yescomplemented
81#17989067C2216yes—
82#17989065C2211yescharacteristic
83#17989065C2214yescomplemented
84#17989063C2214yescomplemented
85#41×Dic73C2216yes—
86#41×Dic73C2214yescomplemented
87C4×#11924029C2214yescomplemented
88#17989055C2216yes—
89C4×#11924027C22112yes—
90C4×#11924027C22112yes—
91C2×Q8×Dic73C2214yes—
92C2×Q8×Dic73C2214yes—
93C2×Q8×Dic73C2213yes—
94C2×Q8×Dic73C2214yes—
95C2×Q8×Dic73C2213yes—
96C2×Q8×Dic73C2211yescharacteristic
97C2×Q8×Dic73C2214yes—
98C2×Q8×Dic73C2211yescharacteristic
99C2×Q8×Dic73C2214yescomplemented
100C4×Q8×D73C2214yescomplemented
101C22×C4⋊Dic73C2213yes—
102C22×C4×Dic73C2213yes—
103C2×2−1+4×C73C2211yescharacteristic
104C23×Q8×C73C2211yescharacteristic
105D4×Q8×C73C2214yes—
106D4×Q8×C73C2214yes—
107#548×C73C2214yes—
108#548×C73C2214yes—
109#536×C73C2216yes—
110#525×C73C2216yes—
111#519×C73C2211yescharacteristic
112#14556639—28no—
113C2×#11924029C2314yes—
114C2×#11924028C2316yes—
115C2×#11924027C2314yes—
116C2×#11924027C23112yes—
117C2×Q8×D73C2314yes—
118C23×Dic73C2311yescharacteristic
119C23×Dic73C2313yes—
120#14556591C23112yes—
121#14556590C2316yes—
122#14556590C2316yes—
123#14556590C23112yes—
124#14556589C2316yes—
125#14556589C23112yes—
126#14556587C2316yes—
127#14556586C23112yes—
128#14556586C23112yes—
129#14556586C23124yes—
130#14556584C23124yes—
131#14556584C23112yes—
132#14556584C23112yes—
133#14556583C23112yes—
134#14556582C2316yes—
135#14556582C2316yes—
136#14556582C23112yes—
137#14556582C23124yes—
138#14556581C23112yes—
139#14556581C23112yes—
140#14556581C23124yes—
141#14556580C2316yes—
142#14556580C23112yes—
143#14556578C2316yes—
144#14556577C23112yes—
145#14556577C23112yes—
146#14556575C2314yes—
147#14556575C23112yes—
148#14556575C23124yes—
149#14556574C23112yes—
150#14556573C23124yes—
151#14556572C23112yes—
152#14556572C2314yes—
153#14556571C23124yes—
154#14556570C2316yes—
155#14556570C2316yes—
156#14556570C23112yes—
157#14556568C2314yes—
158#14556568C23112yes—
159#14556568C23124yes—
160#14556568C2314yes—
161#14556568C23112yes—
162#14556567C23112yes—
163#14556567C23112yes—
164#14556567C23112yes—
165#14556565C2316yes—
166#14556565C2316yes—
167#14556565C23112yes—
168#14556563C2314yes—
169#14556563C23112yes—
170#14556563C2314yes—
171#14556563C23112yes—
172#14556562C23112yes—
173#14556560C2314yes—
174Q8×Dic73C2316yes—
175Q8×Dic73C2316yes—
176Q8×Dic73C23112yes—
177Q8×Dic73C23112yes—
178Q8×Dic73C2314yes—
179Q8×Dic73C2314yes—
180Q8×Dic73C2314yes—
181Q8×Dic73C2314yes—
182Q8×Dic73C23112yes—
183Q8×Dic73C23112yes—
184Q8×Dic73C23112yes—
185Q8×Dic73C2314yes—
186Q8×Dic73C2314yes—
187C4×Dic146C23112yes—
188C4×Dic146C23112yes—
189C4×Dic146C23112yes—
190#14556556C23112yes—
191#14556556C2316yes—
192#14556556C2316yes—
193#14556556C23112yes—
194C4×D292C23112yes—
195D4×Dic73C2316yes—
196D4×Dic73C2316yes—
197D4×Dic73C23112yes—
198D4×Dic73C23112yes—
199D4×Dic73C23112yes—
200D4×Dic73C2314yes—
201D4×Dic73C2314yes—
202#14556553C2316yes—
203#14556553C2316yes—
204C4×C22⋊D73C23112yes—
205C4×C22⋊D73C23112yes—
206C4×C22⋊D73C23112yes—
207C4×C22⋊D73C23112yes—
208#14556551C2314yes—
209#14556551C23112yes—
210#14556551C23112yes—
211#14556551C23112yes—
212#14556551C23112yes—
213#14556551C2314yes—
214#14556550C2316yes—
215#14556550C23112yes—
216#14556550C23112yes—
217#14556549C23112yes—
218#14556549C23112yes—
219#14556549C23112yes—
220#14556548C23112yes—
221#14556547C2314yes—
222#14556547C23112yes—
223#14556547C23112yes—
224#14556547C23112yes—
225C2×C4⋊Dic73C2313yes—
226C2×C4⋊Dic73C2316yes—
227C2×C4⋊Dic73C23112yes—
228C2×C4⋊Dic73C23112yes—
229C2×C4⋊Dic73C23112yes—
230C2×C4⋊Dic73C2313yes—
231C4⋊C4×D73C23112yes—
232C2×C4×Dic73C2316yes—
233C2×C4×Dic73C2316yes—
234C2×C4×Dic73C23112yes—
235C2×C4×Dic73C2316yes—
236C2×C4×Dic73C2316yes—
237C2×C4×Dic73C2313yes—
238C2×C4×Dic73C2313yes—
239C2×C4×Dic73C2313yes—
240C2×C4×Dic73C2313yes—
241C42×D73C23112yes—
2422−1+4×C73—28no—
243C2×#41×C73C2316yes—
244C2×#41×C73C2314yes—
245C22×Q8×C73—28no—
246C22×Q8×C73C2313yes—
247C22×Q8×C73C2314yes—
248C22×Q8×C73C2314yes—
249C22×Q8×C73C2314yes—
250C22×Q8×C73C2311yescharacteristic
251C23×C4×C73C2313yes—
252C4⋊Q8×C73C23112yes—
253#124×C73C23112yes—
254#123×C73C23112yes—
255C22⋊Q8×C73C2316yes—
256C22⋊Q8×C73C2316yes—
257C22⋊Q8×C73C23112yes—
258C22⋊Q8×C73C23112yes—
259#121×C73C2316yes—
260#121×C73C2316yes—
261#120×C73C2314yes—
262C4×Q8×C73C2314yes—
263C4×Q8×C73C2314yes—
264C4×D4×C73C23112yes—
265C4×D4×C73C23112yes—
266#117×C73C2316yes—
267#11924029—216no—
268#11924028—224no—
269#11924027—216no—
270#11924027—424no—
271C2×Dic146C2414yes—
272C2×Dic146C2416yes—
273C2×Dic146C24112yes—
274Q8×D73—216no—
275C2×D292C2416yes—
276C2×C22⋊D73C2414yes—
277C2×C22⋊D73C2414yes—
278C2×C22⋊D73C2414yes—
279C2×C22⋊D73C2414yes—
280C2×C22⋊D73C24112yes—
281C22×Dic73—24no—
282C22×Dic73—46no—
283C22×Dic73C2411yescharacteristic
284C22×Dic73C2411yescharacteristic
285C22×Dic73C2411yescharacteristic
286C22×Dic73C2411yescharacteristic
287C22×Dic73C2411yescharacteristic
288C22×Dic73C2414yes—
289C22×Dic73C2416yes—
290C22×Dic73C2413yes—
291C22×Dic73C2416yes—
292C22×Dic73C2413yes—
293C22×Dic73C24112yes—
294C22×Dic73C2411yescharacteristic
295C2×C4×D73C2414yes—
296C2×C4×D73C24112yes—
297C2×C4×D73C24112yes—
298C4⋊Dic73C24112yes—
299C4⋊Dic73C24112yes—
300C4⋊Dic73C24124yes—
301C4⋊Dic73C2416yes—
302C4⋊Dic73C24112yes—
303C4⋊Dic73C2414yes—
304C4⋊Dic73C24112yes—
305C4⋊Dic73C2416yes—
306C4⋊Dic73C2414yes—
307#11924007C24112yes—
308#11924007C2414yes—
309#11924007C2414yes—
310#11924007C24112yes—
311#11924007C24112yes—
312#11924007C2414yes—
313#11924007C24112yes—
314#11924007C24112yes—
315#11924007C24112yes—
316#11924007C2414yes—
317C22⋊Dic73C2414yes—
318C22⋊Dic73C2414yes—
319C22⋊Dic73C2414yes—
320C22⋊Dic73C24112yes—
321C22⋊Dic73C2414yes—
322C22⋊Dic73C24112yes—
323C22⋊Dic73C2414yes—
324#11924005C2414yes—
325#11924005C24112yes—
326#11924005C2414yes—
327#11924005C24112yes—
328#11924005C24112yes—
329#11924005C24112yes—
330C4×Dic73C2414yes—
331C4×Dic73C2416yes—
332C4×Dic73C24112yes—
333C4×Dic73C2416yes—
334C4×Dic73C2416yes—
335C4×Dic73C2414yes—
336C4×Dic73C2416yes—
337C4×Dic73C2416yes—
338C4×Dic73C2416yes—
339C4×Dic73C2416yes—
340C4×Dic73C2416yes—
341C4×Dic73C24112yes—
342C4×Dic73C24112yes—
343C24×C73C2411yescharacteristic
344#41×C73—216no—
345#41×C73—224no—
346C2×Q8×C73—216no—
347C2×Q8×C73—216no—
348C2×Q8×C73—216no—
349C2×Q8×C73—212no—
350C2×Q8×C73#4118yescomplemented
351C2×Q8×C73C24112yes—
352C2×Q8×C73C2416yes—
353C2×Q8×C73C2414yes—
354C2×D4×C73C2414yes—
355C2×D4×C73C2414yes—
356C2×D4×C73C2414yes—
357C2×D4×C73C2416yes—
358C22×C4×C73—212no—
359C22×C4×C73C2416yes—
360C22×C4×C73C2416yes—
361C22×C4×C73C24112yes—
362C22×C4×C73C2413yes—
363C22×C4×C73C2413yes—
364C4⋊C4×C73C2416yes—
365C4⋊C4×C73C2416yes—
366C4⋊C4×C73C24112yes—
367C4⋊C4×C73C24112yes—
368C22⋊C4×C73C2414yes—
369C22⋊C4×C73C2414yes—
370C22⋊C4×C73C2414yes—
371C22⋊C4×C73C24112yes—
372C22⋊C4×C73C24112yes—
373C42×C73C24112yes—
374C23×C73—22no—
375C23×C73—22no—
376C23×C73—22no—
377C23×C73C2514yes—
378C23×C73C2511yescharacteristic
379C23×C73C2511yescharacteristic
380C23×C73C2511yescharacteristic
381C22×D73C2514yes—
382Q8×C73—224no—
383Q8×C73—212no—
384Q8×C73C2×#41116yes—
385D4×C73—28no—
386D4×C73—28no—
387D4×C73—28no—
388D4×C73—212no—
389C2×C4×C73—26no—
390C2×C4×C73—212no—
391C2×C4×C73—212no—
392C2×C4×C73—224no—
393C2×C4×C73C2×#41112yes—
394C2×C4×C73C2514yes—
395C2×C4×C73C2514yes—
396C2×C4×C73C2516yes—
397C2×C4×C73C2514yes—
398C2×C4×C73C2516yes—
399C22⋊D73—28no—
400C22⋊D73—28no—
401C22⋊D73—28no—
402C22⋊D73—28no—
403C22⋊D73—412no—
404C2×Dic73—22no—
405C2×Dic73—212no—
406C2×Dic73—22no—
407C2×Dic73—22no—
408C2×Dic73—22no—
409C2×Dic73—22no—
410C2×Dic73—28no—
411C2×Dic73—43no—
412C2×Dic73—46no—
413C2×Dic73—43no—
414C2×Dic73—412no—
415C2×Dic732−1+414yescomplemented
416C2×Dic73C2511yescharacteristic
417C2×Dic73C2511yescharacteristic
418C2×Dic73C2516yes—
419C2×Dic73C2514yes—
420C2×Dic73C2514yes—
421C2×Dic73C2516yes—
422C2×Dic73C2514yes—
423C2×Dic73C2511yescharacteristic
424C2×Dic73C2511yescharacteristic
425D292—212no—
426C4×D73—224no—
427C4×D73—28no—
428C4×D73—412no—
429Dic146—212no—
430Dic146—28no—
431Dic146—412no—
432C22×C73—28no—
433C22×C73—21no—
434C22×C73—21no—
435C22×C73—21no—
436C22×C73—21no—
437C22×C73—21no—
438C22×C73—21no—
439C22×C73—24no—
440C22×C73—24no—
441C22×C73—24no—
442C22×C73C22×#4112yes—
443C22×C73C2×2−1+412yes—
444C22×C73#58512yes—
445C22×C73C2611yescharacteristic
446C2×D73—24no—
447C2×D73—24no—
448C2×D73—24no—
449C4×C73—24no—
450C4×C73—26no—
451C4×C73—24no—
452C4×C73—24no—
453C4×C73C22×#41112yes—
454Dic73—24no—
455Dic73—24no—
456Dic73—21no—
457Dic73—21no—
458Dic73—24no—
459Dic73—26no—
460Dic73—26no—
461Dic73C2×2−1+412yes—
462Dic73C2×2−1+412yes—
463#62788—731nomaximal, Sylow
464C2×C73—22no—
465C2×C73—22no—
466C2×C73—22no—
467C2×C73—44no—
468C2×C73C23×#4111yescharacteristic
469C2×C73C22×2−1+411yescharacteristic
470C2×C73C2×#58511yescharacteristic
471D73—44no—
472#3523—734no—
473#3522—734no—
474#3516—734no—
475#3516—734no—
476#3507—736no—
477#3502—731no—
478#3497—731no—
479#3492—736no—
480#3486—731no—
481#3486D7311yescharacteristic, complemented
482#3482—734no—
483#3482—734no—
484#3480—734no—
485Q8×#41—734no—
486#3461—736no—
487#3444—736no—
488C4×2−1+4—731no—
489C4×2−1+4—731no—
490C22×C4×Q8—731no—
491C73#6278811yescharacteristic, complemented, Sylow
492C2×2−1+4—731no—
493C2×2−1+4C2×D7311yescharacteristic
494C23×Q8C2×D7311yescharacteristic
495#559—7312no—
496Q82—734no—
497#557—7312no—
498#557—734no—
499#557—734no—
500#557—734no—
501#556—7312no—
502#556—7312no—
503#556—7312no—
504#554—7312no—
505#554—7312no—
506#554—7312no—
507#553—7312no—
508#553—7312no—
509#552—7312no—
510#552—7312no—
511#552—7312no—
512#552—7312no—
513#550—734no—
514D4×Q8—734no—
515D4×Q8—734no—
516D4×Q8—734no—
517D4×Q8C2×D7314yes—
518D4×Q8C2×D7314yes—
519#548—734no—
520#548—734no—
521#548—734no—
522#548—734no—
523#548C2×D7314yes—
524#548C2×D7314yes—
525#547—7312no—
526#547—7312no—
527#544—736no—
528#542—7312no—
529#542—7312no—
530#541—7312no—
531#541—7312no—
532#539—7324no—
533#537—736no—
534#536—736no—
535#536C2×D7316yes—
536#533—7312no—
537#533—736no—
538#533—736no—
539#533—7312no—
540#533—736no—
541#532—736no—
542#532—736no—
543#532—736no—
544#529—7312no—
545#529—7312no—
546#529—7312no—
547#529—736no—
548#529—736no—
549#529—7312no—
550#529—736no—
551#529—736no—
552#529—7312no—
553#529—7312no—
554#525—736no—
555#525—734no—
556#525—7312no—
557#525C2×D7316yes—
558#520—736no—
559#520—734no—
560#520—734no—
561#520—736no—
562#519—731no—
563#519—734no—
564#519—734no—
565#519C2×D7311yescharacteristic
566C4×#41—736no—
567C4×#41—734no—
568C4×#41—734no—
569C4×#41—7312no—
570C4×#41—7312no—
571C4×#41—736no—
572C2×C4×Q8—731no—
573C2×C4×Q8—733no—
574C2×C4×Q8—734no—
575C2×C4×Q8—734no—
576C2×C4×Q8—731no—
577C2×C4×Q8—733no—
578C2×C4×Q8—734no—
579C2×C4×Q8—734no—
580C2×C4×Q8—734no—
581C2×C4×Q8—734no—
582C22×C4⋊C4—733no—
583C22×C42—733no—
5842−1+4—28no—
5852−1+4—1468no—
586C2×#41—734no—
587C2×#41—7312no—
588C2×#41—734no—
589C2×#41—736no—
590C2×#41C22×D7316yes—
591C2×#41C22×D7314yes—
592C22×Q8—28no—
593C22×Q8—734no—
594C22×Q8C22×D7313yes—
595C22×Q8C22×D7314yes—
596C22×Q8C22×D7314yes—
597C22×Q8C22×D7314yes—
598C22×Q8C22×D7311yescharacteristic
599C23×C4—733no—
600C23×C4—731no—
601C23×C4C22×D7313yes—
602C4⋊Q8—736no—
603C4⋊Q8—7312no—
604C4⋊Q8—736no—
605C4⋊Q8—736no—
606C4⋊Q8—7312no—
607C4⋊Q8—7312no—
608C4⋊Q8C22×D73112yes—
609#127—736no—
610#126—7312no—
611#126—7312no—
612#126—7324no—
613#126—7312no—
614#126—7312no—
615#126—7324no—
616#125—7312no—
617#125—736no—
618#125—736no—
619#125—7312no—
620#125—7312no—
621#125—7324no—
622#125—7324no—
623#125—7312no—
624#124—736no—
625#124—7312no—
626#124—736no—
627#124—7312no—
628#124—7312no—
629#124C22×D73112yes—
630#123—734no—
631#123—7312no—
632#123—7312no—
633#123—734no—
634#123—7312no—
635#123—7324no—
636#123—7324no—
637#123C22×D73112yes—
638C22⋊Q8—7312no—
639C22⋊Q8—7312no—
640C22⋊Q8—7312no—
641C22⋊Q8—736no—
642C22⋊Q8—736no—
643C22⋊Q8—7312no—
644C22⋊Q8—7324no—
645C22⋊Q8—734no—
646C22⋊Q8—734no—
647C22⋊Q8—7312no—
648C22⋊Q8—7312no—
649C22⋊Q8—7324no—
650C22⋊Q8C22×D7316yes—
651C22⋊Q8C22×D7316yes—
652C22⋊Q8C22×D73112yes—
653C22⋊Q8C22×D73112yes—
654#121—734no—
655#121—734no—
656#121—7312no—
657#121—7312no—
658#121—7312no—
659#121—736no—
660#121—736no—
661#121—7312no—
662#121C22×D7316yes—
663#121C22×D7316yes—
664#120—734no—
665#120C22×D7314yes—
666C4×Q8—734no—
667C4×Q8—734no—
668C4×Q8—7312no—
669C4×Q8—7312no—
670C4×Q8—734no—
671C4×Q8—734no—
672C4×Q8—7312no—
673C4×Q8—7312no—
674C4×Q8—736no—
675C4×Q8—734no—
676C4×Q8—7312no—
677C4×Q8—736no—
678C4×Q8—734no—
679C4×Q8—736no—
680C4×Q8—736no—
681C4×Q8—7312no—
682C4×Q8—7312no—
683C4×Q8—7312no—
684C4×Q8—7312no—
685C4×Q8—7312no—
686C4×Q8C22×D7314yes—
687C4×Q8C22×D7314yes—
688C4×D4—734no—
689C4×D4—734no—
690C4×D4—736no—
691C4×D4—7312no—
692C4×D4—736no—
693C4×D4—7312no—
694C4×D4—7312no—
695C4×D4—7312no—
696C4×D4—7312no—
697C4×D4—7312no—
698C4×D4—7312no—
699C4×D4—736no—
700C4×D4—736no—
701C4×D4—734no—
702C4×D4—734no—
703C4×D4—7312no—
704C4×D4—7312no—
705C4×D4—7312no—
706C4×D4—7312no—
707C4×D4—7312no—
708C4×D4C22×D73112yes—
709C4×D4C22×D73112yes—
710#117—736no—
711#117—7312no—
712#117—7312no—
713#117—7312no—
714#117—7312no—
715#117—7312no—
716#117—734no—
717#117—7312no—
718#117—7312no—
719#117—7312no—
720#117—7312no—
721#117C22×D7316yes—
722C2×C4⋊C4—733no—
723C2×C4⋊C4—733no—
724C2×C4⋊C4—736no—
725C2×C4⋊C4—7312no—
726C2×C4⋊C4—7312no—
727C2×C4⋊C4—7312no—
728C2×C4⋊C4—7312no—
729C2×C42—733no—
730C2×C42—736no—
731C2×C42—736no—
732C2×C42—733no—
733C2×C42—736no—
734C2×C42—733no—
735C2×C42—736no—
736C2×C42—733no—
737C2×C42—7312no—
738C2×C42—7312no—
739C24C23×D7311yescharacteristic
740#41—216no—
741#41—224no—
742#41—29224no—
743#41—14616no—
744#41—14616no—
745#41—14624no—
746C2×Q8—216no—
747C2×Q8—216no—
748C2×Q8—216no—
749C2×Q8—212no—
750C2×Q8—7312no—
751C2×Q8—734no—
752C2×Q8—736no—
753C2×Q8—14616no—
754C2×Q8#1192402718yescomplemented
755C2×Q8C23×D73112yes—
756C2×Q8C23×D7316yes—
757C2×Q8C23×D7314yes—
758C2×D4—7312no—
759C2×D4—734no—
760C2×D4—734no—
761C2×D4—734no—
762C2×D4—734no—
763C2×D4—736no—
764C2×D4C23×D7314yes—
765C2×D4C23×D7316yes—
766C2×D4C23×D7314yes—
767C2×D4C23×D7314yes—
768C22×C4—212no—
769C22×C4—2926no—
770C22×C4—733no—
771C22×C4—736no—
772C22×C4—733no—
773C22×C4—7312no—
774C22×C4—7312no—
775C22×C4—731no—
776C22×C4—731no—
777C22×C4—731no—
778C22×C4—731no—
779C22×C4—731no—
780C22×C4—731no—
781C22×C4—734no—
782C22×C4—736no—
783C22×C4—734no—
784C22×C4—7312no—
785C22×C4—1464no—
786C22×C4C23×D7316yes—
787C22×C4C23×D7316yes—
788C22×C4C23×D7313yes—
789C22×C4C23×D73112yes—
790C22×C4C23×D7313yes—
791C4⋊C4—7312no—
792C4⋊C4—734no—
793C4⋊C4—734no—
794C4⋊C4—734no—
795C4⋊C4—734no—
796C4⋊C4—7312no—
797C4⋊C4—7312no—
798C4⋊C4—7312no—
799C4⋊C4—7312no—
800C4⋊C4—7312no—
801C4⋊C4—7312no—
802C4⋊C4—7312no—
803C4⋊C4—7324no—
804C4⋊C4—736no—
805C4⋊C4—7312no—
806C4⋊C4—736no—
807C4⋊C4—734no—
808C4⋊C4—734no—
809C4⋊C4—7312no—
810C4⋊C4C23×D7316yes—
811C4⋊C4C23×D7316yes—
812C4⋊C4C23×D73112yes—
813C4⋊C4C23×D73112yes—
814C22⋊C4—734no—
815C22⋊C4—734no—
816C22⋊C4—7312no—
817C22⋊C4—734no—
818C22⋊C4—734no—
819C22⋊C4—734no—
820C22⋊C4—7312no—
821C22⋊C4—7312no—
822C22⋊C4—734no—
823C22⋊C4—734no—
824C22⋊C4—7312no—
825C22⋊C4—7312no—
826C22⋊C4—7312no—
827C22⋊C4C23×D7314yes—
828C22⋊C4C23×D7314yes—
829C22⋊C4C23×D73112yes—
830C22⋊C4C23×D73112yes—
831C22⋊C4C23×D7314yes—
832C42—736no—
833C42—734no—
834C42—734no—
835C42—736no—
836C42—736no—
837C42—736no—
838C42—736no—
839C42—736no—
840C42—736no—
841C42—736no—
842C42—7312no—
843C42—7312no—
844C42—7312no—
845C42C23×D73112yes—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—734no—
850C23C24×D7314yes—
851C23C24×D7311yescharacteristic
852C23C24×D7311yescharacteristic
853C23C24×D7311yescharacteristic
854Q8—224no—
855Q8—212no—
856Q8—29212no—
857Q8—1468no—
858Q8—14612no—
859Q8C2×#11924027116yes—
860D4—28no—
861D4—28no—
862D4—28no—
863D4—212no—
864D4—29212no—
865D4—1468no—
866D4—1468no—
867D4—1468no—
868D4—1468no—
869D4—14612no—
870C2×C4—26no—
871C2×C4—212no—
872C2×C4—212no—
873C2×C4—224no—
874C2×C4—29212no—
875C2×C4—2923no—
876C2×C4—2926no—
877C2×C4—2923no—
878C2×C4—29212no—
879C2×C4—734no—
880C2×C4—731no—
881C2×C4—731no—
882C2×C4—731no—
883C2×C4—731no—
884C2×C4—736no—
885C2×C4—734no—
886C2×C4—734no—
887C2×C4—734no—
888C2×C4—736no—
889C2×C4—1468no—
890C2×C4—1462no—
891C2×C4—1462no—
892C2×C4—1462no—
893C2×C4—1462no—
894C2×C4—1468no—
895C2×C4—1462no—
896C2×C4—14612no—
897C2×C4—14624no—
898C2×C4C2×#11924027112yes—
899C2×C4C24×D7316yes—
900C2×C4C24×D7314yes—
901C2×C4C24×D7314yes—
902C2×C4C24×D7314yes—
903C2×C4C24×D7316yes—
904C22—28no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—1464no—
915C22—1464no—
916C22—1464no—
917C22C22×#1192402712yes—
918C222−1+4×D7312yes—
919C22#1798942412yes—
920C22C25×D7311yescharacteristic
921C4—24no—
922C4—26no—
923C4—24no—
924C4—24no—
925C4—732no—
926C4—732no—
927C4—1464no—
928C4—1461no—
929C4—1461no—
930C4—1464no—
931C4—1466no—
932C4—1464no—
933C4—1466no—
934C4C22×#11924027112yes—
935C2—22no—
936C2—22no—
937C2—22no—
938C2—44no—
939C2—2924no—
940C2C23×#1192402711yescharacteristic
941C2C2×2−1+4×D7311yescharacteristic
942C2C2×#1798942411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3486C2
hypercenter#3486D73
hypocenterC73#62788
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. #22624018C2semidirect
2. #22624007C2semidirect
3. #22623925C2semidirect
4. #22623913C2semidirect
5. #22623795C2semidirect
6. #22623737C2semidirect
7. #22623698C2semidirect
8. #22623637C2semidirect
9. #22623582C2semidirect
10. #22623552C2semidirect
11. #22623547C2semidirect
12. #22623521C2semidirect
13. Q8×#11924027C2semidirect
14. #22623355C2semidirect
15. #22623223C2semidirect
16. 2−1+4×Dic73C2semidirect
17. #22623140C2semidirect
18. C22×Q8×Dic73C2semidirect
19. C73×#3486C2semidirect
21. #17989319C22semidirect
22. Q8×Dic146C22semidirect
23. #17989316C22semidirect
24. #17989313C22semidirect
25. #17989313C22semidirect
26. #17989312C22semidirect
27. #17989311C22semidirect
28. #17989308C22semidirect
29. #17989306C22semidirect
31. #17989295C22semidirect
36. #17989279C22semidirect
38. #17989271C22semidirect
39. #17989256C22semidirect
42. Q8×C22⋊D73C22semidirect
45. #17989248C22semidirect
46. #17989244C22semidirect
50. #17989210C22semidirect
51. #17989206C22semidirect
52. #17989198C22semidirect
53. #17989197C22semidirect
57. #17989142C22semidirect
61. #17989139C22semidirect
67. #17989123C22semidirect
72. #17989116C22semidirect
79. #17989070C22semidirect
80. #17989069C22semidirect
83. #17989065C22semidirect
84. #17989063C22semidirect
86. #41×Dic73C22semidirect
87. C4×#11924029C22semidirect
99. C2×Q8×Dic73C22semidirect
100. C4×Q8×D73C22semidirect
350. C2×Q8×C73#41semidirect
415. C2×Dic732−1+4semidirect
481. #3486D73semidirect
491. C73#62788semidirect
754. C2×Q8#11924027semidirect

Maximal subgroups

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

subgroupindex
#226240182
#226240072
#226239252
#226239132
#226237952
#226237372
#226236982
#226236372
#226235822
#226235522
#226235472
#226235212
Q8×#119240272
#226233552
#226232232
2−1+4×Dic732
#226231402
C22×Q8×Dic732
C73×#34862
#6278873