Finite Group Databasebeta

← #3497×D73 #33994153

Subgroups — #3497×D73 #33994153

Order 18688.

11210 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D73C212yesmaximal, complemented
2#22623702C211yesmaximal, characteristic, complemented
3#22623701C214yesmaximal, complemented
4#22623700C216yesmaximal, complemented
5#22623699C218yesmaximal, complemented
6#22623698C212yesmaximal, complemented
7#22623697C216yesmaximal, complemented
8#22623696C214yesmaximal, complemented
9#550×D73C214yesmaximal, complemented
10D4×Q8×D73C214yesmaximal, complemented
11#548×D73C218yesmaximal, complemented
12#537×D73C216yesmaximal, complemented
13#532×D73C216yesmaximal, complemented
14C2×C4×Q8×D73C211yesmaximal, characteristic, complemented
15C73×#3497C211yesmaximal, characteristic, complemented
16C2×#14556639C2212yescomplemented
17C2×#14556639C2218yescomplemented
18C2×#14556638C2218yescomplemented
19C2×#14556638C22112yescomplemented
202−1+4×D73—232no—
21C2×#41×D73C22112yes—
22C2×#41×D73C2218yes—
23C22×Q8×D73C2218yes—
24C22×Q8×D73C2211yescharacteristic
25#17989259C2214yescomplemented
26#17989258C22112yescomplemented
27#17989257C22112yescomplemented
28#17989256C2218yescomplemented
29#17989255C22124yescomplemented
30Q8×D292C2214yescomplemented
31D4×Dic146C22112yescomplemented
32#17989252C22112yescomplemented
33Q8×C22⋊D73C2218yescomplemented
34#17989250C22124yescomplemented
35#17989249C2218yescomplemented
36#17989248C2218yescomplemented
37#17989247C22124yescomplemented
38#17989246C22124yescomplemented
39#17989245C22124yescomplemented
40#17989244C2218yescomplemented
41#17989243C22124yescomplemented
42#17989168C2216yescomplemented
43#17989167C22124yescomplemented
44#17989166C22124yescomplemented
45#17989165C22112yescomplemented
46#17989164C22124yescomplemented
47#17989138C2216yescomplemented
48#17989137C2216yescomplemented
49#17989136C22112yescomplemented
50#17989135C2216yescomplemented
51#17989134C22112yescomplemented
52#17989134C22112yescomplemented
53#17989133C22112yescomplemented
54#17989132C22112yescomplemented
55#17989132C22112yescomplemented
56C4⋊Q8×D73C2216yes—
57#127×D73C2216yes—
58#124×D73C22112yes—
59C22⋊Q8×D73C22124yes—
60#121×D73C22112yes—
61#121×D73C22124yes—
62#121×D73C2214yes—
63C2×Q8×Dic73C2211yescharacteristic, complemented
64C2×C4×Dic146C2213yescomplemented
65C2×#14556556C2213yescomplemented
66C4×Q8×D73C2214yes—
67C4×Q8×D73C2214yes—
68C4×Q8×D73C2214yescomplemented
69C4×Q8×D73C2214yescomplemented
70C4×D4×D73C22112yes—
71C4×D4×D73C22112yes—
72C2×C4⋊C4×D73C2213yes—
73C2×C42×D73C2213yes—
74C2×2−1+4×C73C2212yescomplemented
75#550×C73C2214yescomplemented
76D4×Q8×C73C2214yescomplemented
77#548×C73C2218yescomplemented
78#537×C73C2216yescomplemented
79#532×C73C2216yescomplemented
80C2×C4×Q8×C73C2211yescharacteristic, complemented
81#14556639—264no—
82#14556639—216no—
83#14556638—296no—
84#14556638—264no—
85C2×#11924029C23112yes—
86C2×#11924029C2318yes—
87C2×#11924028C23112yes—
88C2×#11924028C23124yes—
89C2×#11924028C23124yes—
90C2×#11924027C23124yes—
91C2×#11924027C23112yes—
92C2×#11924027C23124yes—
93#41×D73—264no—
94#41×D73—296no—
95C22×Dic146C23124yes—
96C22×Dic146C2313yes—
97C2×Q8×D73—264no—
98C2×Q8×D73D4116yescomplemented
99C2×Q8×D73C23112yes—
100C2×Q8×D73C2318yes—
101C2×Q8×D73C23124yes—
102C2×Q8×D73C2314yes—
103C2×Q8×D73C2314yes—
104C2×D4×D73C2314yes—
105C2×D4×D73C23112yes—
106C2×D4×D73C2318yes—
107C2×D4×D73C23112yes—
108C22×C4×D73C23124yes—
109C22×C4×D73C2311yescharacteristic
110C22×C4×D73C2313yes—
111C22×C4×D73C2313yes—
112#14556591C2316yes—
113#14556590C23112yes—
114#14556590C23112yes—
115#14556589C23112yes—
116#14556588C2316yes—
117#14556587C23112yes—
118#14556587C23112yes—
119#14556587C23112yes—
120#14556580C23112yes—
121#14556579C23112yes—
122#14556578C23112yes—
123#14556577C23124yes—
124#14556577C23124yes—
125#14556571C23124yes—
126#14556570C23124yes—
127#14556569C23148yes—
128#14556568C23148yes—
129#14556567C23124yes—
130#14556566C2314yes—
131#14556566C23112yes—
132#14556566C23124yes—
133#14556565C2314yes—
134#14556565C23112yes—
135#14556565C23124yes—
136#14556564C2318yes—
137#14556564C23124yes—
138#14556564C23148yes—
139#14556563C2318yes—
140#14556563C23124yes—
141#14556563C23148yes—
142#14556562C2314yes—
143#14556562C23112yes—
144#14556562C23124yes—
145Q8×Dic73C2314yes—
146Q8×Dic73C2314yes—
147C4×Dic146C23112yes—
148C4×Dic146C23112yes—
149#14556556C23112yes—
150#14556556C23112yes—
151C4×D292C23112yes—
152C4×D292C23112yes—
153D4×Dic73C23112yes—
154D4×Dic73C23112yes—
155#14556553C23112yes—
156#14556553C23112yes—
157C4×C22⋊D73C23124yes—
158C4×C22⋊D73C23124yes—
159#14556551C23124yes—
160#14556551C23124yes—
161C2×C4⋊Dic73C2313yes—
162C2×#11924007C2316yes—
163C4⋊C4×D73C2314yes—
164C4⋊C4×D73C23112yes—
165C4⋊C4×D73C23112yes—
166C4⋊C4×D73C23112yes—
167C22⋊C4×D73C2318yes—
168C22⋊C4×D73C23124yes—
169C2×C4×Dic73C2313yes—
170C2×C4×Dic73C2313yes—
171C2×C4×Dic73C2313yes—
172C42×D73C2316yes—
173C42×D73C2316yes—
174C42×D73C2316yes—
175C42×D73C2316yes—
1762−1+4×C73—216no—
177C2×#41×C73C23112yes—
178C2×#41×C73C2318yes—
179C22×Q8×C73C2318yes—
180C22×Q8×C73C2311yescharacteristic
181C4⋊Q8×C73C2316yes—
182#127×C73C2316yes—
183#124×C73C23112yes—
184C22⋊Q8×C73C23124yes—
185#121×C73C2314yes—
186#121×C73C23112yes—
187#121×C73C23124yes—
188C4×Q8×C73C2314yes—
189C4×Q8×C73C2314yes—
190C4×D4×C73C23112yes—
191C4×D4×C73C23112yes—
192C2×C4⋊C4×C73C2313yes—
193C2×C42×C73C2313yes—
194C23×D73C2418yes—
195C23×D73C2411yescharacteristic
196#11924029—232no—
197#11924029—248no—
198#11924028—248no—
199#11924028—296no—
200#11924028—296no—
201#11924027—296no—
202#11924027—248no—
203#11924027—296no—
204C2×Dic146—296no—
205C2×Dic146C2×D4124yescomplemented
206C2×Dic146C24124yes—
207C2×Dic146C24112yes—
208C2×Dic146C24112yes—
209Q8×D73—232no—
210Q8×D73—248no—
211Q8×D73—296no—
212Q8×D73C2×D4132yes—
213Q8×D73C2×D4132yescomplemented
214C2×D292C2414yes—
215C2×D292C2418yes—
216C2×D292C24112yes—
217C2×D292C24112yes—
218C2×C22⋊D73C2418yes—
219C2×C22⋊D73C2418yes—
220C2×C22⋊D73C2418yes—
221C2×C22⋊D73C24124yes—
222C2×C22⋊D73C24124yes—
223D4×D73—232no—
224D4×D73—248no—
225D4×D73—216no—
226D4×D73—424no—
227C22×Dic73C2411yescharacteristic
228C22×Dic73C24124yes—
229C22×Dic73C2413yes—
230C22×Dic73C2413yes—
231C2×C4×D73—296no—
232C2×C4×D73—24no—
233C2×C4×D73—46no—
234C2×C4×D73C2×D4124yes—
235C2×C4×D73C2411yescharacteristic
236C2×C4×D73C2411yescharacteristic
237C2×C4×D73C2411yescharacteristic
238C2×C4×D73C2416yes—
239C2×C4×D73C2418yes—
240C2×C4×D73C24124yes—
241C2×C4×D73C24124yes—
242C2×C4×D73C2416yes—
243C2×C4×D73C2416yes—
244C2×C4×D73C2416yes—
245C2×C4×D73C2411yescharacteristic
246C4⋊Dic73C24112yes—
247C4⋊Dic73C2414yes—
248C4⋊Dic73C24112yes—
249#11924007C24124yes—
250#11924007C2418yes—
251#11924007C24124yes—
252C22⋊Dic73C2418yes—
253C22⋊Dic73C24124yes—
254#11924005C2418yes—
255#11924005C24124yes—
256#11924005C2418yes—
257#11924005C24124yes—
258C4×Dic73C2416yes—
259C4×Dic73C2416yes—
260C4×Dic73C2416yes—
261C4×Dic73C2416yes—
262C4×Dic73C2416yes—
263C4×Dic73C2416yes—
264#41×C73—232no—
265#41×C73—248no—
266C2×Q8×C73—232no—
267C2×Q8×C73C2×D418yescomplemented
268C2×Q8×C73C24112yes—
269C2×Q8×C73C2414yes—
270C2×D4×C73C2414yes—
271C2×D4×C73C2418yes—
272C2×D4×C73C24112yes—
273C2×D4×C73C24112yes—
274C22×C4×C73C2411yescharacteristic
275C22×C4×C73C24124yes—
276C22×C4×C73C2413yes—
277C22×C4×C73C2413yes—
278C4⋊C4×C73C24112yes—
279C4⋊C4×C73C2414yes—
280C4⋊C4×C73C24112yes—
281C22⋊C4×C73C2418yes—
282C22⋊C4×C73C24124yes—
283C42×C73C2416yes—
284C42×C73C2416yes—
285C23×C73C2518yes—
286C23×C73C2511yescharacteristic
287C22×D73—22no—
288C22×D73—22no—
289C22×D73—216no—
290C22×D73—216no—
291C22×D73—216no—
292C22×D73C22×D414yes—
293C22×D73C2518yes—
294C22×D73C2511yescharacteristic
295C22×D73C2511yescharacteristic
296Q8×C73—224no—
297Q8×C73C22×D4116yes—
298D4×C73—216no—
299D4×C73—224no—
300D4×C73—28no—
301D4×C73—412no—
302C2×C4×C73—248no—
303C2×C4×C73—22no—
304C2×C4×C73—43no—
305C2×C4×C73C22×D4112yes—
306C2×C4×C73C2511yescharacteristic
307C2×C4×C73C2516yes—
308C2×C4×C73C2518yes—
309C2×C4×C73C2516yes—
310C2×C4×C73C2511yescharacteristic
311C22⋊D73—216no—
312C22⋊D73—216no—
313C22⋊D73—248no—
314C22⋊D73—216no—
315C22⋊D73—424no—
316C2×Dic73—248no—
317C2×Dic73—22no—
318C2×Dic73—43no—
319C2×Dic73C22×D4112yes—
320C2×Dic73C2511yescharacteristic
321C2×Dic73C2516yes—
322C2×Dic73C2518yes—
323C2×Dic73C2516yes—
324C2×Dic73C2511yescharacteristic
325D292—216no—
326D292—224no—
327D292—28no—
328D292—412no—
329C4×D73—216no—
330C4×D73—22no—
331C4×D73—212no—
332C4×D73—248no—
333C4×D73—22no—
334C4×D73—248no—
335C4×D73—22no—
336C4×D73—46no—
337C4×D73C22×D4124yes—
338C4×D73C22×D4124yes—
339C4×D732−1+414yescomplemented
340Dic146—224no—
341Dic146—248no—
342Dic146C22×D4148yes—
343C22×C73—21no—
344C22×C73—21no—
345C22×C73—28no—
346C22×C73—28no—
347C22×C73—28no—
348C22×C73C23×D412yes—
349C22×C73C2611yescharacteristic
350C2×D73—21no—
351C2×D73—21no—
352C2×D73—28no—
353C2×D73—28no—
354C2×D73—28no—
355C2×D73—28no—
356C2×D73—432no—
357C2×D73C23×D412yes—
358C2×D73C23×D412yes—
359C2×D73C2×2−1+412yes—
360C2×D73#58512yes—
361C4×C73—28no—
362C4×C73—21no—
363C4×C73—26no—
364C4×C73C23×D4112yes—
365C4×C73C2×2−1+412yescomplemented
366Dic73—28no—
367Dic73—21no—
368Dic73—26no—
369Dic73C23×D4112yes—
370Dic73C2×2−1+412yescomplemented
371C2×#3497—731nomaximal, Sylow
372C2×C73—22no—
373C2×C73—48no—
374C2×C73C24×D411yescharacteristic
375C2×C73C22×2−1+411yescharacteristic
376C2×C73C2×#58511yescharacteristic
377D73—22no—
378D73—48no—
379D73#349714yesdirect product factor
380C22×2−1+4—732no—
381#3497—732no—
382#3497—734no—
383#3497—734no—
384#3497—738no—
385#3497—736no—
386#3497—736no—
387#3497—731no—
388#3497D7311yescharacteristic, direct product factor
389C2×#550—734no—
390C2×D4×Q8—734no—
391C2×#548—738no—
392C2×#537—736no—
393C2×#532—736no—
394C22×C4×Q8—731no—
395C73C2×#349711yescharacteristic, complemented, Sylow
396C2×2−1+4—738no—
397C2×2−1+4—7312no—
398C2×2−1+4—738no—
399C2×2−1+4—732no—
400C2×2−1+4—14632no—
401C2×2−1+4C2×D7312yescomplemented
402C22×#41—7312no—
403C22×#41—738no—
404C23×Q8—731no—
405C23×Q8—738no—
406#550—738no—
407#550—7312no—
408#550—7324no—
409#550—734no—
410#550—7312no—
411#550C2×D7314yescomplemented
412D4×Q8—738no—
413D4×Q8—7312no—
414D4×Q8—7324no—
415D4×Q8—734no—
416D4×Q8—7312no—
417D4×Q8C2×D7314yescomplemented
418#548—738no—
419#548—738no—
420#548—7324no—
421#548—7324no—
422#548—7324no—
423#548—738no—
424#548—7324no—
425#548C2×D7318yescomplemented
426#537—7312no—
427#537—7324no—
428#537—7324no—
429#537—7324no—
430#537—736no—
431#537C2×D7316yescomplemented
432#532—7312no—
433#532—736no—
434#532—736no—
435#532—7312no—
436#532—7312no—
437#532—7312no—
438#532—7312no—
439#532—7312no—
440#532—736no—
441#532C2×D7316yescomplemented
442C2×C4⋊Q8—736no—
443C2×#127—736no—
444C2×#124—7312no—
445C2×C22⋊Q8—7324no—
446C2×#121—734no—
447C2×#121—7312no—
448C2×#121—7324no—
449C2×C4×Q8—731no—
450C2×C4×Q8—734no—
451C2×C4×Q8—734no—
452C2×C4×Q8—734no—
453C2×C4×Q8—734no—
454C2×C4×Q8—733no—
455C2×C4×Q8—733no—
456C2×C4×Q8C2×D7311yescharacteristic, complemented
457C2×C4×D4—7312no—
458C2×C4×D4—7312no—
459C22×C4⋊C4—733no—
460C22×C42—733no—
4612−1+4—216no—
4622−1+4—14664no—
4632−1+4—14664no—
4642−1+4—14696no—
4652−1+4—14616no—
466C2×#41—7312no—
467C2×#41—738no—
468C2×#41—7324no—
469C2×#41—7312no—
470C2×#41—7324no—
471C2×#41—7324no—
472C2×#41—7312no—
473C2×#41—7324no—
474C2×#41—14696no—
475C2×#41—14664no—
476C2×#41C22×D73112yes—
477C2×#41C22×D7318yes—
478C22×Q8—7316no—
479C22×Q8—734no—
480C22×Q8—734no—
481C22×Q8—7312no—
482C22×Q8—7324no—
483C22×Q8—738no—
484C22×Q8—733no—
485C22×Q8—7324no—
486C22×Q8—14664no—
487C22×Q8C22×D7318yes—
488C22×Q8C22×D7311yescharacteristic
489C22×D4—7312no—
490C22×D4—734no—
491C22×D4—738no—
492C22×D4—7312no—
493C23×C4—733no—
494C23×C4—733no—
495C23×C4—7324no—
496C23×C4—731no—
497C4⋊Q8—7312no—
498C4⋊Q8—7312no—
499C4⋊Q8—7312no—
500C4⋊Q8—736no—
501C4⋊Q8C22×D7316yes—
502#127—7312no—
503#127—7312no—
504#127—7312no—
505#127—736no—
506#127C22×D7316yes—
507#124—7312no—
508#124—7312no—
509#124—7324no—
510#124—7324no—
511#124—7312no—
512#124C22×D73112yes—
513C22⋊Q8—7324no—
514C22⋊Q8—7324no—
515C22⋊Q8—7348no—
516C22⋊Q8—7324no—
517C22⋊Q8—7348no—
518C22⋊Q8C22×D73124yes—
519#121—734no—
520#121—738no—
521#121—7312no—
522#121—7324no—
523#121—7324no—
524#121—7348no—
525#121—734no—
526#121—7312no—
527#121—7324no—
528#121—734no—
529#121—7312no—
530#121—7324no—
531#121—738no—
532#121—7324no—
533#121—7348no—
534#121C22×D7314yes—
535#121C22×D73112yes—
536#121C22×D73124yes—
537C4×Q8—734no—
538C4×Q8—734no—
539C4×Q8—7312no—
540C4×Q8—7312no—
541C4×Q8—7312no—
542C4×Q8—7312no—
543C4×Q8C22×D7314yes—
544C4×Q8C22×D7314yes—
545C4×D4—7312no—
546C4×D4—7312no—
547C4×D4—7324no—
548C4×D4—7324no—
549C4×D4—7312no—
550C4×D4—7312no—
551C4×D4—7324no—
552C4×D4—7324no—
553C4×D4—7312no—
554C4×D4—7312no—
555C4×D4C22×D73112yes—
556C4×D4C22×D73112yes—
557C2×C4⋊C4—736no—
558C2×C4⋊C4—733no—
559C2×C4⋊C4—7312no—
560C2×C4⋊C4—7312no—
561C2×C4⋊C4—734no—
562C2×C4⋊C4—7312no—
563C2×C4⋊C4C22×D7313yes—
564C2×C22⋊C4—738no—
565C2×C22⋊C4—7324no—
566C2×C42—733no—
567C2×C42—733no—
568C2×C42—733no—
569C2×C42—736no—
570C2×C42—736no—
571C2×C42—736no—
572C2×C42—736no—
573C2×C42C22×D7313yes—
574C24—731no—
575C24—738no—
576#41—232no—
577#41—248no—
578#41—14696no—
579#41—14696no—
580#41—14696no—
581#41—14648no—
582#41—14648no—
583#41—14696no—
584#41—14632no—
585#41—14648no—
586C2×Q8—232no—
587C2×Q8—7332no—
588C2×Q8—7332no—
589C2×Q8—7324no—
590C2×Q8—7312no—
591C2×Q8—7324no—
592C2×Q8—7312no—
593C2×Q8—14696no—
594C2×Q8—14648no—
595C2×Q8—14696no—
596C2×Q8—14632no—
597C2×Q8D4×D7318yescomplemented
598C2×Q8C23×D73112yes—
599C2×Q8C23×D7314yes—
600C2×D4—29224no—
601C2×D4—7324no—
602C2×D4—738no—
603C2×D4—738no—
604C2×D4—738no—
605C2×D4—7324no—
606C2×D4—7312no—
607C2×D4—734no—
608C2×D4—738no—
609C2×D4—7312no—
610C2×D4—14616no—
611C2×D4—14648no—
612C2×D4—14632no—
613C2×D4C23×D7314yes—
614C2×D4C23×D7318yes—
615C2×D4C23×D73112yes—
616C2×D4C23×D73112yes—
617C22×C4—2926no—
618C22×C4—733no—
619C22×C4—736no—
620C22×C4—733no—
621C22×C4—7324no—
622C22×C4—731no—
623C22×C4—736no—
624C22×C4—736no—
625C22×C4—731no—
626C22×C4—7324no—
627C22×C4—731no—
628C22×C4—731no—
629C22×C4—731no—
630C22×C4—736no—
631C22×C4—738no—
632C22×C4—7324no—
633C22×C4—7324no—
634C22×C4—1464no—
635C22×C4—14696no—
636C22×C4C23×D7311yescharacteristic
637C22×C4C23×D73124yes—
638C22×C4C23×D7313yes—
639C22×C4C23×D7313yes—
640C4⋊C4—7324no—
641C4⋊C4—738no—
642C4⋊C4—7324no—
643C4⋊C4—7312no—
644C4⋊C4—734no—
645C4⋊C4—7312no—
646C4⋊C4C23×D73112yes—
647C4⋊C4C23×D7314yes—
648C4⋊C4C23×D73112yes—
649C22⋊C4—738no—
650C22⋊C4—7324no—
651C22⋊C4—738no—
652C22⋊C4—738no—
653C22⋊C4—7324no—
654C22⋊C4—7324no—
655C22⋊C4C23×D7318yes—
656C22⋊C4C23×D73124yes—
657C42—736no—
658C42—736no—
659C42—736no—
660C42—736no—
661C42—736no—
662C42—736no—
663C42C23×D7316yes—
664C42C23×D7316yes—
665C23—731no—
666C23—734no—
667C23—731no—
668C23—738no—
669C23—14616no—
670C23—14616no—
671C23—14616no—
672C23—1462no—
673C23—1462no—
674C23C24×D7318yes—
675C23C24×D7311yescharacteristic
676Q8—224no—
677Q8—7348no—
678Q8—14648no—
679Q8—14624no—
680Q8C2×D4×D73116yes—
681D4—216no—
682D4—224no—
683D4—28no—
684D4—412no—
685D4—29212no—
686D4—29224no—
687D4—14616no—
688D4—14648no—
689D4—14616no—
690D4—14616no—
691D4—14616no—
692D4—14624no—
693D4—1468no—
694C2×C4—248no—
695C2×C4—22no—
696C2×C4—43no—
697C2×C4—2926no—
698C2×C4—2923no—
699C2×C4—7312no—
700C2×C4—731no—
701C2×C4—736no—
702C2×C4—7324no—
703C2×C4—7324no—
704C2×C4—734no—
705C2×C4—731no—
706C2×C4—736no—
707C2×C4—738no—
708C2×C4—14648no—
709C2×C4—1462no—
710C2×C4—14612no—
711C2×C4—14616no—
712C2×C4—1462no—
713C2×C4—14648no—
714C2×C4—1462no—
715C2×C4—14648no—
716C2×C4—1462no—
717C2×C4C2×D4×D73112yes—
718C2×C4C24×D7311yescharacteristic
719C2×C4C24×D7316yes—
720C2×C4C24×D7318yes—
721C2×C4C24×D7316yes—
722C2×C4C24×D7311yescharacteristic
723C22—21no—
724C22—21no—
725C22—28no—
726C22—28no—
727C22—28no—
728C22—29232no—
729C22—732no—
730C22—732no—
731C22—732no—
732C22—732no—
733C22—1468no—
734C22—1468no—
735C22—1468no—
736C22—1468no—
737C22—1461no—
738C22—1461no—
739C22C22×D4×D7312yes—
740C22C25×D7311yescharacteristic
741C4—28no—
742C4—21no—
743C4—26no—
744C4—7312no—
745C4—732no—
746C4—1468no—
747C4—1461no—
748C4—1466no—
749C4C22×D4×D73112yes—
750C42−1+4×D7312yescomplemented
751C2—22no—
752C2—48no—
753C2—2928no—
754C2—734no—
755C2—1462no—
756C2C23×D4×D7311yescharacteristic
757C2C2×2−1+4×D7311yescharacteristic
758C2#585×D7311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3497C2
hypercenter#3497D73
hypocenterC73C2×#3497
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D73C2semidirect
2. #22623702C2semidirect
3. #22623701C2semidirect
4. #22623700C2semidirect
5. #22623699C2semidirect
6. #22623698C2semidirect
7. #22623697C2semidirect
8. #22623696C2semidirect
9. #550×D73C2semidirect
10. D4×Q8×D73C2semidirect
11. #548×D73C2semidirect
12. #537×D73C2semidirect
13. #532×D73C2semidirect
14. C2×C4×Q8×D73C2semidirect
15. C73×#3497C2semidirect
16. C2×#14556639C22semidirect
17. C2×#14556639C22semidirect
18. C2×#14556638C22semidirect
19. C2×#14556638C22semidirect
25. #17989259C22semidirect
26. #17989258C22semidirect
27. #17989257C22semidirect
28. #17989256C22semidirect
29. #17989255C22semidirect
30. Q8×D292C22semidirect
31. D4×Dic146C22semidirect
32. #17989252C22semidirect
33. Q8×C22⋊D73C22semidirect
34. #17989250C22semidirect
35. #17989249C22semidirect
36. #17989248C22semidirect
37. #17989247C22semidirect
38. #17989246C22semidirect
39. #17989245C22semidirect
40. #17989244C22semidirect
41. #17989243C22semidirect
42. #17989168C22semidirect
43. #17989167C22semidirect
44. #17989166C22semidirect
45. #17989165C22semidirect
46. #17989164C22semidirect
47. #17989138C22semidirect
48. #17989137C22semidirect
49. #17989136C22semidirect
50. #17989135C22semidirect
51. #17989134C22semidirect
52. #17989134C22semidirect
53. #17989133C22semidirect
54. #17989132C22semidirect
55. #17989132C22semidirect
63. C2×Q8×Dic73C22semidirect
64. C2×C4×Dic146C22semidirect
65. C2×#14556556C22semidirect
68. C4×Q8×D73C22semidirect
69. C4×Q8×D73C22semidirect
74. C2×2−1+4×C73C22semidirect
75. #550×C73C22semidirect
76. D4×Q8×C73C22semidirect
77. #548×C73C22semidirect
78. #537×C73C22semidirect
79. #532×C73C22semidirect
80. C2×C4×Q8×C73C22semidirect
98. C2×Q8×D73D4semidirect
205. C2×Dic146C2×D4semidirect
213. Q8×D73C2×D4semidirect
267. C2×Q8×C73C2×D4semidirect
339. C4×D732−1+4semidirect
365. C4×C73C2×2−1+4semidirect
370. Dic73C2×2−1+4semidirect
379. D73#3497direct (N × H)
388. #3497D73direct (N × H)
395. C73C2×#3497semidirect
401. C2×2−1+4C2×D73semidirect
411. #550C2×D73semidirect
417. D4×Q8C2×D73semidirect
425. #548C2×D73semidirect
431. #537C2×D73semidirect
441. #532C2×D73semidirect
456. C2×C4×Q8C2×D73semidirect
597. C2×Q8D4×D73semidirect
750. C42−1+4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D732
#226237022
#226237012
#226237002
#226236992
#226236982
#226236972
#226236962
#550×D732
D4×Q8×D732
#548×D732
#537×D732
#532×D732
C2×C4×Q8×D732
C73×#34972
C2×#349773