Finite Group Databasebeta

← #72246710

Subgroups — #72246710

Order 4032.

3828 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72246706C214yesmaximal, complemented
2#72246705C212yesmaximal, complemented
3#72246704C218yesmaximal, complemented
4C3×#10621657C212yesmaximal, complemented
5D4×(C3⋊D3)⋊D7C214yesmaximal, complemented
6#72246568C214yesmaximal, complemented
7C2×#11759644C214yesmaximal, complemented
8#72245744C212yesmaximal, complemented
9C2×C7×D4×C3⋊D3C211yesmaximal, characteristic, complemented
10D3×#6548—32nomaximal
11C23×C7×C3⋊D3C2212yescomplemented
12C22×(C3⋊D3)⋊D7C2214yescomplemented
13C2×C32×C7×D4C2211yescharacteristic, complemented
14C2×C7×#638C2212yescomplemented
15C7×D4×C3⋊D3C2214yescomplemented
16C7×D4×C3⋊D3C2214yescomplemented
17C2×C7×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
18C2×C4×C7×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×#4268C2218yescomplemented
20C3×#66730C2218yescomplemented
21C3×D4×D21C2218yescomplemented
22C3×#66728C2214yescomplemented
23#11759644C2218yescomplemented
24#11759644C2214yescomplemented
25#11759644C2218yescomplemented
26#11759644C2218yescomplemented
27#11759643C22116yescomplemented
28C2×#92694C2218yescomplemented
29C2×#92693C2214yescomplemented
30#11759638C22116yescomplemented
31#11759637C2214yescomplemented
32#11759635C2212yescomplemented
33#11759634C2218yescomplemented
34C4×(C3⋊D3)⋊D7C2214yescomplemented
35#11759632C2218yescomplemented
36#11759631C2214yescomplemented
37#11759630C2212yescomplemented
38#11759628C2214yescomplemented
39#10621657D312yescomplemented
40C2×D3×C7×D4—32no—
41C2×D3×C7×D4—61no—
42C3×#6548—32no—
43#10621596—38no—
44C2×D3×C22⋊D7—38no—
45#10621574—38no—
46#10621572—38no—
47D3×#1159—38no—
48D3×D4×D7—38no—
49#10621565—34no—
50D3×#1157—34no—
51#10596675—71nomaximal, Hall
52C23×C32×C7C2312yescomplemented
53C22×C7×C3⋊D3—44no—
54C22×C7×C3⋊D3C2314yes—
55C22×C7×C3⋊D3C2311yescharacteristic
56C22×C7×C3⋊D3C2314yescomplemented
57C22×C7×C3⋊D3C2312yescomplemented
58C22×C3×D21C2318yescomplemented
59C2×(C3⋊D3)⋊D7—48no—
60C2×(C3⋊D3)⋊D7C2314yes—
61C2×(C3⋊D3)⋊D7C2318yescomplemented
62C32×C7×D4C2314yescomplemented
63C2×C32×C4×C7C2311yescharacteristic, complemented
64C7×#638C2318yescomplemented
65C2×C7×C3⋊Dic3C2311yescharacteristic, complemented
66C7×C4⋊(C3⋊D3)C2314yescomplemented
67C4×C7×C3⋊D3C2312yes—
68C4×C7×C3⋊D3C2312yescomplemented
69C3×#4268C2318yescomplemented
70C3×#4268C23116yescomplemented
71C2×C3×Dic21C2318yescomplemented
72C3×D84C2314yescomplemented
73C3×C4×D21C2318yescomplemented
74C3×Dic42C2314yescomplemented
75#92696C2314yescomplemented
76#92695C2314yescomplemented
77#92694C2318yescomplemented
78#92694C23116yescomplemented
79#92693C2314yes—
80#92693C2318yescomplemented
81D21⋊Dic3C2318yescomplemented
82C2×#6548—91noHall
83C23×D3×C7—34no—
84C23×D3×C7—62no—
85C22×D3×D7—38no—
86C2×C3×C7×D4—21no—
87C2×C3×C7×D4C2×D312yescomplemented
88C2×#4268C2×D318yescomplemented
89#66730C2×D318yescomplemented
90D4×D21C2×D318yescomplemented
91#66728C2×D314yescomplemented
92C2×C7×#67—34no—
93C2×C7×#67—62no—
94D3×C7×D4—38no—
95D3×C7×D4—38no—
96D3×C7×D4—64no—
97D3×C7×D4—64no—
98C2×C7×D12—32no—
99C2×C7×D12—61no—
100C2×C4×D3×C7—32no—
101C2×C4×D3×C7—61no—
102C2×C3×C22⋊D7—38no—
103C3×#1159—38no—
104C3×D4×D7—38no—
105C3×#1157—34no—
106#66694—316no—
107D3×C22⋊D7—38no—
108D3×C22⋊D7—316no—
109D3×C22⋊D7—316no—
110D3×C22⋊D7—316no—
111D7×#67—316no—
112C2×#4247—38no—
113C2×#4245—38no—
114#66686—316no—
115C2×D3×Dic7—38no—
116#66684—316no—
117#66683—38no—
118#66681—38no—
119D3×D28—34no—
120D7×D12—38no—
121C4×D3×D7—38no—
122#66676—38no—
123#66675—38no—
124#66673—34no—
125#66672—38no—
126D3×Dic14—34no—
127#66669—34no—
128C2×D4×C3⋊D3D711yescharacteristic, complemented
129C3×#1004—72no—
130#64330—74no—
131C2×#3811—74no—
132#64314—78no—
133#64312—74no—
134D32×D4—74no—
135#64308—72no—
136#64306—72no—
137C22×C32×C7—42no—
138C22×C32×C7C2414yes—
139C22×C32×C7C2411yescharacteristic
140C2×C7×C3⋊D3—22no—
141C2×C7×C3⋊D3—28no—
142C2×C7×C3⋊D3—44no—
143C2×C7×C3⋊D3—42no—
144C2×C7×C3⋊D3C2414yes—
145C2×C7×C3⋊D3C2411yescharacteristic
146C2×C7×C3⋊D3C2411yescharacteristic
147C2×C3×D21—48no—
148C2×C3×D21C2418yes—
149(C3⋊D3)⋊D7—28no—
150(C3⋊D3)⋊D7—48no—
151C32×C4×C7C2412yes—
152C7×C3⋊Dic3C2412yes—
153C3×Dic21C2418yes—
154C22×C7×D4—91no—
155C22×C22⋊D7—94no—
156#6548—32no—
157#6548—92no—
158#6548—98no—
159#6548—94no—
160C2×#1159—94no—
161C2×D4×D7—94no—
162C2×#1157—92no—
163D3×H(5,𝔽2)—212no—
164C23×C3×C7—22no—
165C23×C3×C7C22×D314yescomplemented
166C22×D21C22×D318yescomplemented
167C22×D3×C7—38no—
168C22×D3×C7—32no—
169C22×D3×C7—38no—
170C22×D3×C7—34no—
171C22×D3×C7—61no—
172C22×D3×C7—64no—
173C22×D3×C7—62no—
174C22×D3×C7—64no—
175C22×D3×C7—128no—
176C22×D3×C7—124no—
177C22×D3×C7—124no—
178C22×C3×D7—38no—
179C2×D3×D7—38no—
180C2×D3×D7—316no—
181C2×D3×D7—1216no—
182C3×C7×D4—24no—
183C3×C7×D4C22×D318yescomplemented
184C2×C3×C4×C7—21no—
185C2×C3×C4×C7C22×D312yescomplemented
186#4268C22×D318yescomplemented
187#4268C22×D3116yescomplemented
188C2×Dic21C22×D318yescomplemented
189D84C22×D314yescomplemented
190C4×D21C22×D318yescomplemented
191Dic42C22×D314yescomplemented
192C7×#67—316no—
193C7×#67—68no—
194C2×C7×Dic3—32no—
195C2×C7×Dic3—61no—
196C7×D12—38no—
197C7×D12—64no—
198C4×D3×C7—34no—
199C4×D3×C7—34no—
200C4×D3×C7—62no—
201C4×D3×C7—62no—
202C3×C22⋊D7—38no—
203C3×C22⋊D7—316no—
204C2×C3×Dic7—38no—
205C3×D28—34no—
206C3×C4×D7—38no—
207C3×Dic14—34no—
208#4248—38no—
209#4247—316no—
210#4247—38no—
211#4246—38no—
212#4245—38no—
213#4245—316no—
214D21⋊C4—38no—
215D3×Dic7—38no—
216D3×Dic7—316no—
217Dic3×D7—38no—
218C23×C3⋊D3C2×D712yescomplemented
219C22×D32—74no—
220C2×C32×D4C2×D711yescharacteristic, complemented
221C2×#638C2×D712yescomplemented
222D4×C3⋊D3C2×D714yescomplemented
223D4×C3⋊D3C2×D714yescomplemented
224C2×C4⋊(C3⋊D3)C2×D711yescharacteristic, complemented
225C2×C4×C3⋊D3C2×D711yescharacteristic, complemented
226C2×C3×#67—78no—
227C3×#237—78no—
228C3×D3×D4—78no—
229C3×#235—74no—
230#3811—74no—
231#3811—78no—
232#3811—78no—
233#3811—78no—
234D3×#67—716no—
235C2×#626—78no—
236C2×#624—74no—
237#3805—74no—
238#3804—716no—
239#3802—72no—
240D3×D12—78no—
241C4×D32—74no—
242#3799—78no—
243#3798—74no—
244#3797—72no—
245#3796—74no—
246C2×C32×C7—21no—
247C2×C32×C7—24no—
248C2×C32×C7C2511yescharacteristic
249C7×C3⋊D3—21no—
250C7×C3⋊D3—24no—
251C7×C3⋊D3H(5,𝔽2)12yescomplemented
252C3×D21—28no—
253C24×C7—92no—
254C23×D7—94no—
255C2×C7×D4—92no—
256C2×C7×D4—94no—
257C2×C7×D4—94no—
258C2×C7×D4—91no—
259C2×C7×D4D3211yescharacteristic, complemented
260C22×C4×C7—91no—
261C2×C22⋊D7—38no—
262C2×C22⋊D7—98no—
263C2×C22⋊D7—94no—
264C2×C22⋊D7—98no—
265C2×C22⋊D7—98no—
266C2×C22⋊D7—98no—
267C22×Dic7—94no—
268#1159—38no—
269#1159—98no—
270#1159—916no—
271D4×D7—38no—
272D4×D7—98no—
273D4×D7—916no—
274#1157—34no—
275#1157—94no—
276#1157—94no—
277#1157—94no—
278C2×D28—92no—
279C2×C4×D7—94no—
280C2×Dic14—92no—
281C3×H(5,𝔽2)—212no—
282#1009—214no—
283#1009—218no—
284D3×#41—214no—
285D3×#41—218no—
286#1004—72no—
287#1004—218no—
288#1004—218no—
289C2×D3×D4—32no—
290C2×D3×D4—61no—
291C2×D3×D4—218no—
292C2×D3×D4—218no—
293C22×C3×C7—21no—
294C22×C3×C7—24no—
295C22×C3×C7—44no—
296C22×C3×C7—42no—
297C22×C3×C7—42no—
298C22×C3×C7C23×D318yes—
299C22×C3×C7C23×D312yes—
300C2×D21—48no—
301C2×D21C23×D318yes—
302C2×D3×C7—32no—
303C2×D3×C7—38no—
304C2×D3×C7—32no—
305C2×D3×C7—61no—
306C2×D3×C7—61no—
307C2×D3×C7—64no—
308C2×D3×C7—616no—
309C2×D3×C7—64no—
310C2×D3×C7—62no—
311C2×D3×C7—62no—
312C2×D3×C7—128no—
313C2×D3×C7—124no—
314C2×D3×C7—128no—
315C2×D3×C7—124no—
316C2×D3×C7—124no—
317C2×D3×C7—122no—
318C2×D3×C7—122no—
319C2×C3×D7—38no—
320C2×C3×D7—128no—
321D3×D7—616no—
322D3×D7—1216no—
323C3×C4×C7—22no—
324C3×C4×C7C23×D314yes—
325Dic21C23×D318yes—
326C3×Dic7—38no—
327C7×Dic3—34no—
328C7×Dic3—62no—
329C23×C32C22×D712yescomplemented
330C22×C3⋊D3—44no—
331C22×C3⋊D3C22×D714yes—
332C22×C3⋊D3C22×D711yescharacteristic
333C22×C3⋊D3C22×D714yescomplemented
334C22×C3⋊D3C22×D712yescomplemented
335C22×C3×D3—78no—
336C2×D32—74no—
337C2×D32—78no—
338C2×D32—288no—
339C32×D4C22×D714yescomplemented
340C2×C32×C4C22×D711yescharacteristic, complemented
341#638C22×D718yescomplemented
342C2×C3⋊Dic3C22×D711yescharacteristic, complemented
343C4⋊(C3⋊D3)C22×D714yescomplemented
344C4×C3⋊D3C22×D712yes—
345C4×C3⋊D3C22×D712yescomplemented
346C3×#67—716no—
347C3×#67—78no—
348C2×C3×Dic3—78no—
349C3×D12—74no—
350C3×C4×D3—78no—
351C3×Dic6—74no—
352#627—74no—
353#626—78no—
354#626—716no—
355#625—74no—
356#624—74no—
357#624—78no—
358D3×Dic3—78no—
359C2×H(5,𝔽2)—631noSylow
360C32×C7C2×H(5,𝔽2)11yescharacteristic, complemented, Hall
361C23×C7—94no—
362C23×C7—91no—
363C23×C7—92no—
364C23×C7—94no—
365C23×C7—364no—
366C23×C7C2×D3212yescomplemented
367C22×D7—38no—
368C22×D7—94no—
369C22×D7—98no—
370C22×D7—368no—
371C7×D4—98no—
372C7×D4—94no—
373C7×D4C2×D3214yescomplemented
374C2×C4×C7—91no—
375C2×C4×C7—92no—
376C2×C4×C7—92no—
377C2×C4×C7C2×D3211yescharacteristic, complemented
378C22⋊D7—38no—
379C22⋊D7—316no—
380C22⋊D7—98no—
381C22⋊D7—916no—
382C2×Dic7—38no—
383C2×Dic7—94no—
384C2×Dic7—98no—
385D28—34no—
386D28—94no—
387C4×D7—38no—
388C4×D7—98no—
389Dic14—34no—
390Dic14—94no—
391C23×D3—34no—
392C23×D3—62no—
393C23×D3—218no—
394C3×#41—218no—
395C3×#41—214no—
396C2×C3×D4—21no—
397C2×C3×D4—218no—
398C2×C3×D4—218no—
399C2×C3×D4D3×D712yescomplemented
400C2×#67—34no—
401C2×#67—62no—
402C2×#67—78no—
403C2×#67—218no—
404C2×#67—2116no—
405#239—214no—
406#239—218no—
407D3×Q8—214no—
408#237—78no—
409#237—214no—
410#237—218no—
411#237—2116no—
412D3×D4—38no—
413D3×D4—38no—
414D3×D4—64no—
415D3×D4—64no—
416D3×D4—78no—
417D3×D4—214no—
418D3×D4—218no—
419D3×D4—2116no—
420D3×D4—218no—
421D3×D4—2116no—
422D3×D4—2116no—
423D3×D4—2116no—
424#235—74no—
425#235—218no—
426#235—218no—
427#235—2116no—
428C2×D12—32no—
429C2×D12—61no—
430C2×D12—218no—
431C2×D12—218no—
432C2×C4×D3—32no—
433C2×C4×D3—61no—
434C2×C4×D3—218no—
435C2×C4×D3—218no—
436C2×C3×C7—21no—
437C2×C3×C7—21no—
438C2×C3×C7—28no—
439C2×C3×C7—22no—
440C2×C3×C7—21no—
441C2×C3×C7—44no—
442C2×C3×C7C24×D312yes—
443D21—28no—
444C3×D7—68no—
445D3×C7—34no—
446D3×C7—62no—
447D3×C7—61no—
448D3×C7—61no—
449D3×C7—68no—
450D3×C7—62no—
451D3×C7—124no—
452C22×C32—42no—
453C22×C32C23×D714yes—
454C22×C32C23×D711yescharacteristic
455C2×C3⋊D3—22no—
456C2×C3⋊D3—28no—
457C2×C3⋊D3—44no—
458C2×C3⋊D3—42no—
459C2×C3⋊D3C23×D714yes—
460C2×C3⋊D3C23×D711yescharacteristic
461C2×C3⋊D3C23×D711yescharacteristic
462C2×C3×D3—78no—
463C2×C3×D3—288no—
464D32—148no—
465D32—288no—
466C32×C4C23×D712yes—
467C3⋊Dic3C23×D712yes—
468C3×Dic3—78no—
469H(5,𝔽2)—212no—
470H(5,𝔽2)—634no—
471H(5,𝔽2)—638no—
472H(5,𝔽2)—632no—
473C2×#41—632no—
474C2×#41—634no—
475C22×D4—91no—
476C22×D4—634no—
477C22×D4—634no—
478C22×C7—42no—
479C22×C7—91no—
480C22×C7—94no—
481C22×C7—91no—
482C22×C7—188no—
483C22×C7—182no—
484C22×C7—364no—
485C22×C7—362no—
486C22×C7C22×D3214yes—
487C22×C7C22×D3211yescharacteristic
488C2×D7—38no—
489C2×D7—128no—
490C2×D7—188no—
491C2×D7—368no—
492C4×C7—92no—
493C4×C7C22×D3212yes—
494Dic7—38no—
495C23×C3—22no—
496C23×C3—218no—
497C23×C3C2×D3×D714yescomplemented
498C22×D3—32no—
499C22×D3—38no—
500C22×D3—34no—
501C22×D3—38no—
502C22×D3—61no—
503C22×D3—64no—
504C22×D3—62no—
505C22×D3—64no—
506C22×D3—78no—
507C22×D3—128no—
508C22×D3—124no—
509C22×D3—124no—
510C22×D3—218no—
511C22×D3—2116no—
512C22×D3—8416no—
513C3×Q8—214no—
514C3×D4—24no—
515C3×D4—218no—
516C3×D4—2116no—
517C3×D4—214no—
518C3×D4C2×D3×D718yescomplemented
519C2×C3×C4—21no—
520C2×C3×C4—218no—
521C2×C3×C4—218no—
522C2×C3×C4C2×D3×D712yescomplemented
523#67—316no—
524#67—68no—
525#67—78no—
526#67—716no—
527#67—218no—
528#67—218no—
529#67—2116no—
530C2×Dic3—32no—
531C2×Dic3—61no—
532C2×Dic3—78no—
533C2×Dic3—218no—
534D12—38no—
535D12—64no—
536D12—74no—
537D12—218no—
538D12—2116no—
539C4×D3—34no—
540C4×D3—34no—
541C4×D3—62no—
542C4×D3—62no—
543C4×D3—78no—
544C4×D3—218no—
545C4×D3—218no—
546C4×D3—2116no—
547Dic6—74no—
548Dic6—218no—
549C3×C7—21no—
550C3×C7D3×H(5,𝔽2)12yescomplemented
551C2×C32—21no—
552C2×C32—24no—
553C2×C32C24×D711yescharacteristic
554C3⋊D3—21no—
555C3⋊D3—24no—
556C3⋊D3#654812yescomplemented
557C3×D3—148no—
558C24—92no—
559C24—634no—
560#41—218no—
561#41—214no—
562#41—634no—
563#41—634no—
564#41—634no—
565#41—6316no—
566#41—638no—
567C2×Q8—632no—
568C2×D4—92no—
569C2×D4—94no—
570C2×D4—94no—
571C2×D4—91no—
572C2×D4—218no—
573C2×D4—218no—
574C2×D4—632no—
575C2×D4—638no—
576C2×D4—638no—
577C2×D4—6316no—
578C2×D4—634no—
579C2×D4—638no—
580C2×D4—638no—
581C2×D4—638no—
582C2×D4(C3⋊D3)⋊D711yescharacteristic, complemented
583C22×C4—91no—
584C22×C4—634no—
585C22×C4—634no—
586C2×C7—24no—
587C2×C7—21no—
588C2×C7—92no—
589C2×C7—184no—
590C2×C7—181no—
591C2×C7C23×D3211yescharacteristic
592D7—68no—
593C22×C3—21no—
594C22×C3—24no—
595C22×C3—44no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—218no—
599C22×C3—848no—
600C22×C3C22×D3×D712yes—
601C22×C3C22×D3×D718yes—
602C2×D3—32no—
603C2×D3—32no—
604C2×D3—38no—
605C2×D3—61no—
606C2×D3—61no—
607C2×D3—64no—
608C2×D3—64no—
609C2×D3—616no—
610C2×D3—62no—
611C2×D3—62no—
612C2×D3—78no—
613C2×D3—128no—
614C2×D3—128no—
615C2×D3—124no—
616C2×D3—124no—
617C2×D3—124no—
618C2×D3—122no—
619C2×D3—122no—
620C2×D3—288no—
621C2×D3—4216no—
622C2×D3—8416no—
623C3×C4—22no—
624C3×C4—218no—
625C3×C4C22×D3×D714yes—
626Dic3—34no—
627Dic3—62no—
628Dic3—78no—
629C32C2×#654811yescharacteristic, complemented, Sylow
630C23—91no—
631C23—94no—
632C23—94no—
633C23—92no—
634C23—218no—
635C23—364no—
636C23—634no—
637C23—638no—
638C23—2528no—
639C23C2×(C3⋊D3)⋊D712yescomplemented
640Q8—214no—
641Q8—634no—
642D4—98no—
643D4—94no—
644D4—218no—
645D4—2116no—
646D4—214no—
647D4—634no—
648D4—638no—
649D4—6316no—
650D4C2×(C3⋊D3)⋊D714yescomplemented
651C2×C4—91no—
652C2×C4—92no—
653C2×C4—92no—
654C2×C4—218no—
655C2×C4—218no—
656C2×C4—638no—
657C2×C4—634no—
658C2×C4—638no—
659C2×C4C2×(C3⋊D3)⋊D711yescharacteristic, complemented
660C7#1059667511yescharacteristic, complemented, Sylow
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—22no—
664C2×C3—28no—
665C2×C3—21no—
666C2×C3—44no—
667C2×C3—428no—
668C2×C3C23×D3×D712yes—
669D3—34no—
670D3—62no—
671D3—61no—
672D3—61no—
673D3—62no—
674D3—68no—
675D3—124no—
676D3—148no—
677C22—42no—
678C22—91no—
679C22—91no—
680C22—94no—
681C22—182no—
682C22—188no—
683C22—218no—
684C22—362no—
685C22—364no—
686C22—848no—
687C22—1268no—
688C22—2528no—
689C22C22×(C3⋊D3)⋊D711yescharacteristic
690C22C22×(C3⋊D3)⋊D714yes—
691C4—92no—
692C4—218no—
693C4C22×(C3⋊D3)⋊D712yes—
694C3—21no—
695C3D3×#654812yescomplemented
696C2—21no—
697C2—24no—
698C2—92no—
699C2—181no—
700C2—184no—
701C2—428no—
702C2C23×(C3⋊D3)⋊D711yescharacteristic
subgroupG/H
center, FrattiniC2C23×(C3⋊D3)⋊D7
commutator, socle, cosocleC2×C32×C7C25
FittingC2×C32×C7×D4C22
hypercenterC2×D4(C3⋊D3)⋊D7
hypocenterC32×C7C2×H(5,𝔽2)
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C2 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #72246706C2semidirect
2. #72246705C2semidirect
3. #72246704C2semidirect
4. C3×#10621657C2semidirect
5. D4×(C3⋊D3)⋊D7C2semidirect
6. #72246568C2semidirect
7. C2×#11759644C2semidirect
8. #72245744C2semidirect
9. C2×C7×D4×C3⋊D3C2semidirect
11. C23×C7×C3⋊D3C22semidirect
12. C22×(C3⋊D3)⋊D7C22semidirect
13. C2×C32×C7×D4C22semidirect
14. C2×C7×#638C22semidirect
15. C7×D4×C3⋊D3C22semidirect
16. C7×D4×C3⋊D3C22semidirect
17. C2×C7×C4⋊(C3⋊D3)C22semidirect
18. C2×C4×C7×C3⋊D3C22semidirect
19. C2×C3×#4268C22semidirect
20. C3×#66730C22semidirect
21. C3×D4×D21C22semidirect
22. C3×#66728C22semidirect
23. #11759644C22semidirect
24. #11759644C22semidirect
25. #11759644C22semidirect
26. #11759644C22semidirect
27. #11759643C22semidirect
28. C2×#92694C22semidirect
29. C2×#92693C22semidirect
30. #11759638C22semidirect
31. #11759637C22semidirect
32. #11759635C22semidirect
33. #11759634C22semidirect
34. C4×(C3⋊D3)⋊D7C22semidirect
35. #11759632C22semidirect
36. #11759631C22semidirect
37. #11759630C22semidirect
38. #11759628C22semidirect
39. #10621657D3semidirect
52. C23×C32×C7C23semidirect
56. C22×C7×C3⋊D3C23semidirect
57. C22×C7×C3⋊D3C23semidirect
58. C22×C3×D21C23semidirect
61. C2×(C3⋊D3)⋊D7C23semidirect
62. C32×C7×D4C23semidirect
63. C2×C32×C4×C7C23semidirect
64. C7×#638C23semidirect
65. C2×C7×C3⋊Dic3C23semidirect
66. C7×C4⋊(C3⋊D3)C23semidirect
68. C4×C7×C3⋊D3C23semidirect
69. C3×#4268C23semidirect
70. C3×#4268C23semidirect
71. C2×C3×Dic21C23semidirect
72. C3×D84C23semidirect
73. C3×C4×D21C23semidirect
74. C3×Dic42C23semidirect
75. #92696C23semidirect
76. #92695C23semidirect
77. #92694C23semidirect
78. #92694C23semidirect
80. #92693C23semidirect
81. D21⋊Dic3C23semidirect
87. C2×C3×C7×D4C2×D3semidirect
88. C2×#4268C2×D3semidirect
89. #66730C2×D3semidirect
90. D4×D21C2×D3semidirect
91. #66728C2×D3semidirect
128. C2×D4×C3⋊D3D7semidirect
165. C23×C3×C7C22×D3semidirect
166. C22×D21C22×D3semidirect
183. C3×C7×D4C22×D3semidirect
185. C2×C3×C4×C7C22×D3semidirect
186. #4268C22×D3semidirect
187. #4268C22×D3semidirect
188. C2×Dic21C22×D3semidirect
189. D84C22×D3semidirect
190. C4×D21C22×D3semidirect
191. Dic42C22×D3semidirect
218. C23×C3⋊D3C2×D7semidirect
220. C2×C32×D4C2×D7semidirect
221. C2×#638C2×D7semidirect
222. D4×C3⋊D3C2×D7semidirect
223. D4×C3⋊D3C2×D7semidirect
224. C2×C4⋊(C3⋊D3)C2×D7semidirect
225. C2×C4×C3⋊D3C2×D7semidirect
251. C7×C3⋊D3H(5,𝔽2)semidirect
259. C2×C7×D4D32semidirect
329. C23×C32C22×D7semidirect
333. C22×C3⋊D3C22×D7semidirect
334. C22×C3⋊D3C22×D7semidirect
339. C32×D4C22×D7semidirect
340. C2×C32×C4C22×D7semidirect
341. #638C22×D7semidirect
342. C2×C3⋊Dic3C22×D7semidirect
343. C4⋊(C3⋊D3)C22×D7semidirect
345. C4×C3⋊D3C22×D7semidirect
360. C32×C7C2×H(5,𝔽2)semidirect
366. C23×C7C2×D32semidirect
373. C7×D4C2×D32semidirect
377. C2×C4×C7C2×D32semidirect
399. C2×C3×D4D3×D7semidirect
497. C23×C3C2×D3×D7semidirect
518. C3×D4C2×D3×D7semidirect
522. C2×C3×C4C2×D3×D7semidirect
550. C3×C7D3×H(5,𝔽2)semidirect
556. C3⋊D3#6548semidirect
582. C2×D4(C3⋊D3)⋊D7semidirect
629. C32C2×#6548semidirect
639. C23C2×(C3⋊D3)⋊D7semidirect
650. D4C2×(C3⋊D3)⋊D7semidirect
659. C2×C4C2×(C3⋊D3)⋊D7semidirect
660. C7#10596675semidirect
695. C3D3×#6548semidirect

Maximal subgroups

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

subgroupindex
#722467062
#722467052
#722467042
C3×#106216572
D4×(C3⋊D3)⋊D72
#722465682
C2×#117596442
#722457442
C2×C7×D4×C3⋊D32
D3×#65483
#105966757