Finite Group Databasebeta

← #33994531

Subgroups — #33994531

Order 18688.

11346 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989424C212yesmaximal, complemented
2#22623722C218yesmaximal, complemented
3#22623715C214yesmaximal, complemented
4#22623708C214yesmaximal, complemented
5#22623702C211yesmaximal, characteristic, complemented
6#22623698C212yesmaximal, complemented
7#22623694C216yesmaximal, complemented
8#22623693C216yesmaximal, complemented
9D4×#11924029C214yesmaximal, complemented
10#22623421C214yesmaximal, complemented
11#22623420C218yesmaximal, complemented
12#22623259C216yesmaximal, complemented
13#532×D73C216yesmaximal, complemented
14C2×C4×#11924029C211yesmaximal, characteristic, complemented
15C73×#3497C211yesmaximal, characteristic, complemented
16#17989424—232no—
17C2×#14556639C2212yescomplemented
18C2×#14556639C2218yescomplemented
19C2×#14556637C22112yescomplemented
20C2×#14556637C2218yescomplemented
21C22×#11924029C2211yescharacteristic
22C22×#11924029C2218yescomplemented
23C2×#41×D73C22112yescomplemented
24C2×#41×D73C2218yescomplemented
25#17989259C2214yescomplemented
26#17989256C2218yescomplemented
27Q8×D292C2214yescomplemented
28Q8×C22⋊D73C2218yescomplemented
29#17989249C2218yescomplemented
30#17989248C2218yescomplemented
31#17989244C2218yescomplemented
32#17989242C22112yescomplemented
33#17989240C22112yescomplemented
34#17989239C22124yescomplemented
35#17989234C22124yescomplemented
36#17989233C22124yescomplemented
37#17989230C22124yescomplemented
38#17989228C22124yescomplemented
39D4×D292C22112yescomplemented
40#17989222C22112yescomplemented
41#17989221C22124yescomplemented
42#17989168C2216yescomplemented
43#17989165C22112yescomplemented
44#17989160C22124yescomplemented
45#17989153C22124yescomplemented
46#17989145C22124yescomplemented
47#17989138C2216yescomplemented
48#17989137C2216yescomplemented
49#17989136C22112yescomplemented
50#17989135C2216yescomplemented
51#17989134C22112yescomplemented
52#17989134C22112yescomplemented
53#17989133C22112yescomplemented
54#17989132C22112yescomplemented
55#17989132C2214yescomplemented
56C4⋊Q8×D73C2216yescomplemented
57#127×D73C2216yescomplemented
58#124×D73C22112yescomplemented
59#17989100C22124yescomplemented
60#17989097C22124yescomplemented
61#121×D73C22112yescomplemented
62#121×D73C22112yescomplemented
63C4×#11924029C2214yescomplemented
64C4×#11924029C2214yescomplemented
65C4×#11924029C2214yescomplemented
66C4×#11924029C2214yescomplemented
67C2×Q8×Dic73C2211yescharacteristic, complemented
68C2×C4×D292C2213yescomplemented
69C2×#14556553C2213yescomplemented
70C4×D4×D73C22112yescomplemented
71C4×D4×D73C22112yescomplemented
72C2×#14556549C2213yescomplemented
73C2×C42×D73C2213yescomplemented
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#14556637—264no—
84#14556637—296no—
85C2×#11924029—264no—
86C2×#11924029D4116yescomplemented
87C2×#11924029C23112yes—
88C2×#11924029C23124yes—
89C2×#11924029C2318yes—
90C2×#11924029C2314yes—
91C2×#11924029C2314yes—
92C2×#11924028C23112yes—
93C2×#11924028C23124yes—
94C2×#11924028C23124yes—
95C2×#11924027C2318yes—
96C2×#11924027C23112yes—
97#41×D73—264no—
98#41×D73—296no—
99C2×Q8×D73C23112yes—
100C2×Q8×D73C2318yes—
101C22×D292C23124yes—
102C22×D292C2313yes—
103C2×D4×D73C23112yes—
104C2×D4×D73C23124yes—
105C2×D4×D73C23124yes—
106C2×D4×D73C23112yes—
107C2×D4×D73C23112yes—
108C22×C4×D73C23124yes—
109C22×C4×D73C2313yes—
110C22×C4×D73C2313yes—
111C22×C4×D73C2313yes—
112#14556591C2316yes—
113#14556590C2314yes—
114#14556590C23112yes—
115#14556589C23112yes—
116#14556588C2316yes—
117#14556587C2314yes—
118#14556587C23112yes—
119#14556587C23112yes—
120#14556580C23112yes—
121#14556579C23112yes—
122#14556578C23112yes—
123#14556577C2318yes—
124#14556577C23124yes—
125#14556576C23148yes—
126#14556573C23148yes—
127#14556571C23124yes—
128#14556570C23124yes—
129#14556567C23124yes—
130#14556566C23112yes—
131#14556566C23112yes—
132#14556566C23124yes—
133#14556565C2314yes—
134#14556565C23112yes—
135#14556565C23124yes—
136#14556564C23124yes—
137#14556564C23124yes—
138#14556563C2318yes—
139#14556563C23124yes—
140#14556562C23112yes—
141#14556562C23112yes—
142#14556562C23124yes—
143#14556561C23148yes—
144#14556559C23148yes—
145Q8×Dic73C2314yes—
146Q8×Dic73C2314yes—
147C4×D292C23112yes—
148C4×D292C23112yes—
149C4×D292C23112yes—
150C4×D292C23112yes—
151D4×Dic73C2314yes—
152D4×Dic73C23112yes—
153#14556553C2314yes—
154#14556553C23112yes—
155#14556553C23112yes—
156#14556553C23112yes—
157C4×C22⋊D73C23124yes—
158C4×C22⋊D73C23124yes—
159#14556551C2318yes—
160#14556551C23124yes—
161#14556549C23112yes—
162#14556549C23112yes—
163C2×C4⋊Dic73C2313yes—
164C4⋊C4×D73C23112yes—
165C4⋊C4×D73C23112yes—
166C2×#11924005C2316yes—
167C22⋊C4×D73C23124yes—
168C22⋊C4×D73C23124yes—
169C2×C4×Dic73C2311yescharacteristic
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×C73C23112yes—
186#121×C73C2314yes—
187#121×C73C23124yes—
188C4×Q8×C73C2314yes—
189C4×Q8×C73C2314yes—
190C4×D4×C73C23112yes—
191C4×D4×C73C23112yes—
192C2×C4⋊C4×C73C2313yes—
193C2×C42×C73C2313yes—
194C23×D73C24124yes—
195C23×D73C2413yes—
196#11924029—232no—
197#11924029—296no—
198#11924029—248no—
199#11924029C2×D4132yescomplemented
200#11924029C2×D4132yescomplemented
201#11924028—248no—
202#11924028—296no—
203#11924028—296no—
204#11924027—232no—
205#11924027—248no—
206C2×Dic146C24112yes—
207C2×Dic146C2418yes—
208Q8×D73—232no—
209Q8×D73—248no—
210C2×D292—296no—
211C2×D292C2×D4124yescomplemented
212C2×D292C2414yes—
213C2×D292C24124yes—
214C2×D292C24112yes—
215C2×D292C24112yes—
216C2×D292C24112yes—
217C2×C22⋊D73C2418yes—
218C2×C22⋊D73C24124yes—
219C2×C22⋊D73C2418yes—
220C2×C22⋊D73C2418yes—
221C2×C22⋊D73C24124yes—
222D4×D73—296no—
223D4×D73—296no—
224D4×D73—248no—
225D4×D73—424no—
226D4×D73—424no—
227C22×Dic73C2411yescharacteristic
228C22×Dic73C2418yes—
229C22×Dic73C2413yes—
230C22×Dic73C2411yescharacteristic
231C2×C4×D73—296no—
232C2×C4×D73—46no—
233C2×C4×D73—46no—
234C2×C4×D73C2×D4124yescomplemented
235C2×C4×D73C2416yes—
236C2×C4×D73C2416yes—
237C2×C4×D73C24124yes—
238C2×C4×D73C2418yes—
239C2×C4×D73C24124yes—
240C2×C4×D73C2416yes—
241C2×C4×D73C2416yes—
242C2×C4×D73C2416yes—
243C2×C4×D73C2416yes—
244C4⋊Dic73C2414yes—
245C4⋊Dic73C24112yes—
246C4⋊Dic73C24112yes—
247#11924007C2418yes—
248#11924007C24124yes—
249C22⋊Dic73C2418yes—
250C22⋊Dic73C24124yes—
251#11924005C2418yes—
252#11924005C2418yes—
253#11924005C24124yes—
254#11924005C24124yes—
255#11924005C24124yes—
256C4×Dic73C2411yescharacteristic
257C4×Dic73C2411yescharacteristic
258C4×Dic73C2411yescharacteristic
259C4×Dic73C2411yescharacteristic
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—248no—
288C22×D73—43no—
289C22×D73—43no—
290C22×D73—424no—
291C22×D73—424no—
292C22×D73C22×D4112yes—
293C22×D73C2518yes—
294C22×D73C2516yes—
295Q8×C73—224no—
296Q8×C73C22×D4116yes—
297D4×C73—216no—
298D4×C73—224no—
299D4×C73—28no—
300D4×C73—412no—
301C2×C4×C73—248no—
302C2×C4×C73—22no—
303C2×C4×C73—43no—
304C2×C4×C73C22×D4112yes—
305C2×C4×C73C2511yescharacteristic
306C2×C4×C73C2516yes—
307C2×C4×C73C2518yes—
308C2×C4×C73C2516yes—
309C2×C4×C73C2511yescharacteristic
310C22⋊D73—216no—
311C22⋊D73—248no—
312C22⋊D73—216no—
313C22⋊D73—216no—
314C22⋊D73—424no—
315C2×Dic73—216no—
316C2×Dic73—22no—
317C2×Dic73—43no—
318C2×Dic73C22×D414yes—
319C2×Dic73C2511yescharacteristic
320C2×Dic73C2516yes—
321C2×Dic73C2518yes—
322C2×Dic73C2511yescharacteristic
323C2×Dic73C2511yescharacteristic
324C2×Dic73C2511yescharacteristic
325D292—248no—
326D292—224no—
327D292—28no—
328D292—412no—
329D292C22×D4148yes—
330C4×D73—248no—
331C4×D73—248no—
332C4×D73—212no—
333C4×D73—216no—
334C4×D73—212no—
335C4×D73—46no—
336C4×D73—46no—
337C4×D73C22×D4124yes—
338C4×D73C22×D4124yes—
339Dic146—224no—
340Dic146—216no—
341C22×C73—21no—
342C22×C73—21no—
343C22×C73—28no—
344C22×C73—28no—
345C22×C73—28no—
346C22×C73C23×D412yes—
347C22×C73C2611yescharacteristic
348C2×D73—26no—
349C2×D73—26no—
350C2×D73—28no—
351C2×D73—28no—
352C2×D73—28no—
353C2×D73—412no—
354C2×D73—848no—
355C2×D73C23×D4112yes—
356C4×C73—28no—
357C4×C73—26no—
358C4×C73—21no—
359C4×C73C23×D4112yes—
360C4×C73#58512yescomplemented
361Dic73—28no—
362Dic73—26no—
363Dic73—21no—
364Dic73C23×D412yes—
365Dic73C23×D412yes—
366Dic73#58512yescomplemented
367#62812—731nomaximal, Sylow
368C2×C73—22no—
369C2×C73—48no—
370C2×C73C24×D411yescharacteristic
371C2×C73C2×#58511yescharacteristic
372C2×C73C2×#58511yescharacteristic
373D73—212no—
374D73—48no—
375C2×#585—732no—
376#3500—738no—
377#3499—734no—
378#3498—734no—
379#3497—732no—
380#3497—731no—
381#3497D7311yescharacteristic, complemented
382#3496—736no—
383#3496—736no—
384D4×#41—734no—
385D4×#41—734no—
386D4×#41—738no—
387#3449—736no—
388C2×#532—736no—
389C2×C4×#41—731no—
390C73#6281211yescharacteristic, complemented, Sylow
391#585—14632no—
392C2×2−1+4—732no—
393C2×2−1+4—738no—
394C2×2−1+4C2×D7312yescomplemented
395C2×H(5,𝔽2)—7312no—
396C2×H(5,𝔽2)—738no—
397C22×#41—7312no—
398C22×#41—738no—
399C22×#41—731no—
400C22×#41—738no—
401#550—738no—
402#550—734no—
403#550C2×D7314yescomplemented
404D4×Q8—738no—
405D4×Q8—734no—
406D4×Q8C2×D7314yescomplemented
407#548—738no—
408#548—738no—
409#548—738no—
410#548C2×D7318yescomplemented
411#547—7312no—
412#547—7324no—
413#547—7312no—
414#546—7324no—
415#546—7324no—
416#546—7324no—
417#546—7324no—
418D42—7312no—
419D42—7324no—
420D42—7312no—
421#537—7312no—
422#537—736no—
423#537C2×D7316yescomplemented
424#536—7324no—
425#535—7324no—
426#534—7324no—
427#532—7312no—
428#532—736no—
429#532—736no—
430#532—7312no—
431#532—734no—
432#532—7312no—
433#532—7312no—
434#532—7312no—
435#532—736no—
436#532C2×D7316yescomplemented
437C2×C4⋊Q8—736no—
438C2×#127—736no—
439C2×#124—7312no—
440#525—7324no—
441#525—7324no—
442C2×#121—7312no—
443C2×#121—7312no—
444C4×#41—734no—
445C4×#41—734no—
446C4×#41—734no—
447C4×#41—734no—
448C2×C4×Q8—731no—
449C2×C4×Q8C2×D7311yescharacteristic, complemented
450C2×C4×D4—7312no—
451C2×C4×D4—7312no—
452C2×C4×D4—733no—
453C2×C4×D4—733no—
454C2×#117—733no—
455C22×C42—733no—
4562−1+4—216no—
4572−1+4—14664no—
4582−1+4—14616no—
459H(5,𝔽2)—14696no—
460H(5,𝔽2)—14664no—
461C2×#41—7316no—
462C2×#41—734no—
463C2×#41—734no—
464C2×#41—7312no—
465C2×#41—7324no—
466C2×#41—738no—
467C2×#41—7312no—
468C2×#41—738no—
469C2×#41—7324no—
470C2×#41—7312no—
471C2×#41—7324no—
472C2×#41—14696no—
473C2×#41—14664no—
474C2×#41—14664no—
475C2×#41C22×D73112yes—
476C2×#41C22×D7318yes—
477C22×Q8—7312no—
478C22×Q8—738no—
479C22×Q8C22×D7318yes—
480C22×Q8C22×D7311yescharacteristic
481C22×D4—7312no—
482C22×D4—7312no—
483C22×D4—7324no—
484C22×D4—7312no—
485C22×D4—7324no—
486C22×D4—733no—
487C22×D4—7324no—
488C23×C4—733no—
489C23×C4—733no—
490C23×C4—733no—
491C23×C4—7324no—
492C4⋊Q8—7312no—
493C4⋊Q8—734no—
494C4⋊Q8—7312no—
495C4⋊Q8—736no—
496C4⋊Q8C22×D7316yes—
497#127—734no—
498#127—7312no—
499#127—7312no—
500#127—736no—
501#127C22×D7316yes—
502#124—7312no—
503#124—7312no—
504#124—738no—
505#124—7324no—
506#124—7312no—
507#124C22×D73112yes—
508#123—7348no—
509#123—7348no—
510C22⋊Q8—7324no—
511C22⋊Q8—7324no—
512C22⋊Q8—7324no—
513C22⋊Q8C22×D73124yes—
514#121—738no—
515#121—7324no—
516#121—7312no—
517#121—7312no—
518#121—7324no—
519#121—734no—
520#121—7312no—
521#121—7324no—
522#121—7312no—
523#121—7312no—
524#121—7324no—
525#121—7324no—
526#121—7324no—
527#121C22×D7314yes—
528#121C22×D73112yes—
529#121C22×D73124yes—
530#120—7348no—
531#120—7348no—
532C4×Q8—734no—
533C4×Q8—734no—
534C4×Q8C22×D7314yes—
535C4×Q8C22×D7314yes—
536C4×D4—734no—
537C4×D4—7312no—
538C4×D4—7324no—
539C4×D4—7324no—
540C4×D4—734no—
541C4×D4—7312no—
542C4×D4—7312no—
543C4×D4—7312no—
544C4×D4—738no—
545C4×D4—7324no—
546C4×D4—7312no—
547C4×D4—7312no—
548C4×D4—7312no—
549C4×D4—7312no—
550C4×D4C22×D73112yes—
551C4×D4C22×D73112yes—
552#117—7312no—
553#117—7312no—
554C2×C4⋊C4—733no—
555C2×C4⋊C4—7312no—
556C2×C4⋊C4—7312no—
557C2×C4⋊C4C22×D7313yes—
558C2×C22⋊C4—736no—
559C2×C22⋊C4—7324no—
560C2×C22⋊C4—7324no—
561C2×C42—733no—
562C2×C42—733no—
563C2×C42—731no—
564C2×C42—736no—
565C2×C42—736no—
566C2×C42—736no—
567C2×C42—736no—
568C2×C42C22×D7313yes—
569C24—733no—
570C24—7324no—
571#41—232no—
572#41—248no—
573#41—7332no—
574#41—7332no—
575#41—14696no—
576#41—14696no—
577#41—14632no—
578#41—14648no—
579#41—14648no—
580#41—14696no—
581#41—14632no—
582#41—14648no—
583C2×Q8—232no—
584C2×Q8—7312no—
585C2×Q8—738no—
586C2×Q8—14648no—
587C2×Q8—14632no—
588C2×Q8D4×D7318yescomplemented
589C2×Q8C23×D73112yes—
590C2×Q8C23×D7314yes—
591C2×D4—29224no—
592C2×D4—29224no—
593C2×D4—7324no—
594C2×D4—738no—
595C2×D4—7324no—
596C2×D4—738no—
597C2×D4—738no—
598C2×D4—7324no—
599C2×D4—7312no—
600C2×D4—7312no—
601C2×D4—734no—
602C2×D4—7324no—
603C2×D4—7312no—
604C2×D4—14696no—
605C2×D4—14648no—
606C2×D4—14696no—
607C2×D4—14696no—
608C2×D4C23×D7314yes—
609C2×D4C23×D7318yes—
610C2×D4C23×D73112yes—
611C2×D4C23×D73112yes—
612C22×C4—2926no—
613C22×C4—2926no—
614C22×C4—733no—
615C22×C4—736no—
616C22×C4—736no—
617C22×C4—731no—
618C22×C4—7324no—
619C22×C4—736no—
620C22×C4—736no—
621C22×C4—731no—
622C22×C4—738no—
623C22×C4—736no—
624C22×C4—736no—
625C22×C4—7324no—
626C22×C4—738no—
627C22×C4—7324no—
628C22×C4—14696no—
629C22×C4C23×D7311yescharacteristic
630C22×C4C23×D73124yes—
631C22×C4C23×D7313yes—
632C22×C4C23×D7313yes—
633C4⋊C4—738no—
634C4⋊C4—7324no—
635C4⋊C4—734no—
636C4⋊C4—7312no—
637C4⋊C4—7312no—
638C4⋊C4C23×D7314yes—
639C4⋊C4C23×D73112yes—
640C4⋊C4C23×D73112yes—
641C22⋊C4—738no—
642C22⋊C4—7324no—
643C22⋊C4—738no—
644C22⋊C4—738no—
645C22⋊C4—7324no—
646C22⋊C4—7324no—
647C22⋊C4—7324no—
648C22⋊C4C23×D7318yes—
649C22⋊C4C23×D73124yes—
650C42—731no—
651C42—731no—
652C42—731no—
653C42—731no—
654C42—736no—
655C42—736no—
656C42—736no—
657C42—736no—
658C42C23×D7316yes—
659C42C23×D7316yes—
660C23—2923no—
661C23—2923no—
662C23—29224no—
663C23—29224no—
664C23—7312no—
665C23—736no—
666C23—738no—
667C23—14648no—
668C23C24×D7318yes—
669C23C24×D7311yescharacteristic
670Q8—224no—
671Q8—14616no—
672Q8—14624no—
673Q8C2×D4×D73116yes—
674D4—216no—
675D4—224no—
676D4—28no—
677D4—412no—
678D4—29212no—
679D4—29224no—
680D4—7348no—
681D4—14648no—
682D4—14616no—
683D4—14616no—
684D4—14648no—
685D4—14616no—
686D4—14624no—
687D4—1468no—
688C2×C4—248no—
689C2×C4—22no—
690C2×C4—43no—
691C2×C4—2926no—
692C2×C4—2926no—
693C2×C4—2923no—
694C2×C4—734no—
695C2×C4—731no—
696C2×C4—731no—
697C2×C4—731no—
698C2×C4—7324no—
699C2×C4—7324no—
700C2×C4—731no—
701C2×C4—736no—
702C2×C4—738no—
703C2×C4—14612no—
704C2×C4—14616no—
705C2×C4—14648no—
706C2×C4—1462no—
707C2×C4—14616no—
708C2×C4—14648no—
709C2×C4—14612no—
710C2×C4C2×D4×D73112yes—
711C2×C4C24×D7311yescharacteristic
712C2×C4C24×D7316yes—
713C2×C4C24×D7318yes—
714C2×C4C24×D7316yes—
715C2×C4C24×D7311yescharacteristic
716C22—21no—
717C22—21no—
718C22—28no—
719C22—28no—
720C22—28no—
721C22—29212no—
722C22—58448no—
723C22—7312no—
724C22—1468no—
725C22—1468no—
726C22—1468no—
727C22—1466no—
728C22—1466no—
729C22C22×D4×D7312yes—
730C22C25×D7311yescharacteristic
731C4—28no—
732C4—26no—
733C4—21no—
734C4—732no—
735C4—732no—
736C4—732no—
737C4—1468no—
738C4—1461no—
739C4—1466no—
740C4C22×D4×D73112yes—
741C4#1798942412yescomplemented
742C2—22no—
743C2—48no—
744C2—2928no—
745C2—14612no—
746C2C23×D4×D7311yescharacteristic
747C2#585×D7311yescharacteristic
748C2C2×#1798942411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3497C2
hypercenter#3497D73
hypocenterC73#62812
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×#17989424C2semidirect
2. #22623722C2semidirect
3. #22623715C2semidirect
4. #22623708C2semidirect
5. #22623702C2semidirect
6. #22623698C2semidirect
7. #22623694C2semidirect
8. #22623693C2semidirect
9. D4×#11924029C2semidirect
10. #22623421C2semidirect
11. #22623420C2semidirect
12. #22623259C2semidirect
13. #532×D73C2semidirect
14. C2×C4×#11924029C2semidirect
15. C73×#3497C2semidirect
17. C2×#14556639C22semidirect
18. C2×#14556639C22semidirect
19. C2×#14556637C22semidirect
20. C2×#14556637C22semidirect
22. C22×#11924029C22semidirect
23. C2×#41×D73C22semidirect
24. C2×#41×D73C22semidirect
25. #17989259C22semidirect
26. #17989256C22semidirect
27. Q8×D292C22semidirect
28. Q8×C22⋊D73C22semidirect
29. #17989249C22semidirect
30. #17989248C22semidirect
31. #17989244C22semidirect
32. #17989242C22semidirect
33. #17989240C22semidirect
34. #17989239C22semidirect
35. #17989234C22semidirect
36. #17989233C22semidirect
37. #17989230C22semidirect
38. #17989228C22semidirect
39. D4×D292C22semidirect
40. #17989222C22semidirect
41. #17989221C22semidirect
42. #17989168C22semidirect
43. #17989165C22semidirect
44. #17989160C22semidirect
45. #17989153C22semidirect
46. #17989145C22semidirect
47. #17989138C22semidirect
48. #17989137C22semidirect
49. #17989136C22semidirect
50. #17989135C22semidirect
51. #17989134C22semidirect
52. #17989134C22semidirect
53. #17989133C22semidirect
54. #17989132C22semidirect
55. #17989132C22semidirect
56. C4⋊Q8×D73C22semidirect
57. #127×D73C22semidirect
58. #124×D73C22semidirect
59. #17989100C22semidirect
60. #17989097C22semidirect
61. #121×D73C22semidirect
62. #121×D73C22semidirect
63. C4×#11924029C22semidirect
64. C4×#11924029C22semidirect
65. C4×#11924029C22semidirect
66. C4×#11924029C22semidirect
67. C2×Q8×Dic73C22semidirect
68. C2×C4×D292C22semidirect
69. C2×#14556553C22semidirect
70. C4×D4×D73C22semidirect
71. C4×D4×D73C22semidirect
72. C2×#14556549C22semidirect
73. C2×C42×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
86. C2×#11924029D4semidirect
199. #11924029C2×D4semidirect
200. #11924029C2×D4semidirect
211. C2×D292C2×D4semidirect
234. C2×C4×D73C2×D4semidirect
267. C2×Q8×C73C2×D4semidirect
360. C4×C73#585semidirect
366. Dic73#585semidirect
381. #3497D73semidirect
390. C73#62812semidirect
394. C2×2−1+4C2×D73semidirect
403. #550C2×D73semidirect
406. D4×Q8C2×D73semidirect
410. #548C2×D73semidirect
423. #537C2×D73semidirect
436. #532C2×D73semidirect
449. C2×C4×Q8C2×D73semidirect
588. C2×Q8D4×D73semidirect
741. C4#17989424semidirect

Maximal subgroups

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

subgroupindex
C2×#179894242
#226237222
#226237152
#226237082
#226237022
#226236982
#226236942
#226236932
D4×#119240292
#226234212
#226234202
#226232592
#532×D732
C2×C4×#119240292
C73×#34972
#6281273