Finite Group Databasebeta

← #13371041

Subgroups — #13371041

Order 1792.

982 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2345C211yesmaximal, characteristic, complemented
2C2×#89738C211yesmaximal, characteristic
3#11730899C211yesmaximal, characteristic
4#11729307C211yesmaximal, characteristic, complemented
5#11727386C211yesmaximal, characteristic, complemented
6#11727385C211yesmaximal, characteristic, complemented
7#11727371C211yesmaximal, characteristic, complemented
8#11727369C211yesmaximal, characteristic, complemented
9#11727276C211yesmaximal, characteristic
10#11727267C211yesmaximal, characteristic, complemented
11#11727229C211yesmaximal, characteristic, complemented
12C4×#6384C211yesmaximal, characteristic, complemented
13#11727217C211yesmaximal, characteristic, complemented
14#11727216C211yesmaximal, characteristic, complemented
15#11727202C211yesmaximal, characteristic, complemented
16C22×#1157C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×#1136C2211yescharacteristic
19C2×C4×Dic14C2211yescharacteristic
20C2×C4×Dic14C2211yescharacteristic
21C7×#389C2211yescharacteristic
22C7×#389C2211yescharacteristic
23C7×#387—21no—
24C7×#387—21no—
25C7×#380—21no—
26C7×#380C2211yescharacteristic
27C4×C7×C4⋊C4C2211yescharacteristic
28C4×C7×C4⋊C4C2211yescharacteristic
29C4×C7×C22⋊C4—21no—
30C4×C7×C22⋊C4C2211yescharacteristic
31#89984C2211yescharacteristic
32C2×C22⋊(C7⋊C8)C2211yescharacteristic
33C2×#6384C2211yescharacteristic
34C2×#6384C2211yescharacteristic
35C2×#6384C2211yescharacteristic
36C2×#6384C2211yescharacteristic
37#89738C418yescomplemented
38C2×#6383C2211yescharacteristic
39C2×#6383C2211yescharacteristic
40C2×#6383C2211yescharacteristic
41C2×#6383C2211yescharacteristic
42C2×#6382C2211yescharacteristic
43C2×#6381C2211yescharacteristic
44#89729—21no—
45#89729—21no—
46#89711C2211yescharacteristic
47#89711C2211yescharacteristic
48C2×#6377C2211yescharacteristic
49C2×C4×C7⋊C8C2211yescharacteristic
50#89439—21no—
51#89438—21no—
52#89324C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89319C2211yescharacteristic
59#89319C2211yescharacteristic
60#22579—71nomaximal, Sylow
61C23×C4×C7—21no—
62C23×C4×C7C2311yescharacteristic
63C22×C22⋊D7—21no—
64C2×#1157—22no—
65C2×#1157—22no—
66C2×#1157—22no—
67C2×#1157—41no—
68C2×#1157—41no—
69C2×#1157C2×C414yes—
70C22×D28C2311yescharacteristic
71C22×C4×D7—21no—
72C22×Dic14C2311yescharacteristic
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4C2×C414yes—
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4D411yescharacteristic
84C2×C7×C22⋊C4D411yescharacteristic
85C2×C42×C7—21no—
86C2×C42×C7—21no—
87C2×C42×C7C2311yescharacteristic
88C2×C42×C7C2311yescharacteristic
89C2×C22⋊Dic7—21no—
90C2×(C2×D7)⋊C4—21no—
91C2×(C2×D7)⋊C4—21no—
92C2×(C2×D7)⋊C4—21no—
93C2×(C2×D7)⋊C4—21no—
94C2×C4⋊Dic7C2311yescharacteristic
95C2×C4⋊Dic7C2311yescharacteristic
96C2×Dic7⋊C4—21no—
97C2×Dic7⋊C4—21no—
98C2×C4×Dic7—21no—
99C2×C4×Dic7—21no—
100C2×#1136—41no—
101C2×#1136—41no—
102C2×#1136C2×C414yes—
103C22×C7⋊C8C2311yescharacteristic
104C22×C7⋊C8C2311yescharacteristic
105C22×C7⋊C8C2311yescharacteristic
106C22×C7⋊C8C2311yescharacteristic
107C4×Dic14—22no—
108C4×Dic14—22no—
109C4×Dic14—41no—
110C4×Dic14—41no—
111C7×#95—21no—
112C7×#95—21no—
113C7×#95—21no—
114C7×#95—21no—
115C7×#95—21no—
116C7×#95D411yescharacteristic
117C7×#95D411yescharacteristic
118C7⋊#95—21no—
119C22⋊(C7⋊C8)—22no—
120#6384—22no—
121#6384—22no—
122#6384C2×C414yes—
123#6384C2×C414yes—
124#6383—41no—
125#6383—41no—
126#6383C2×C414yes—
127#6383C2×C414yes—
128#6382—41no—
129#6381—41no—
130#6377—41no—
131C4×C7⋊C8—41no—
132C2×#417—71no—
133#2345D711yescharacteristic, complemented
134#2341—71no—
135#1936—71no—
136#1934—71no—
137#1926—71no—
138#1925—71no—
139#1865—71no—
140#1863—71no—
141#1823—71no—
142#1809—71no—
143#1788—71no—
144#1763—71no—
145C4×#103—71no—
146#1753—71no—
147C24×C7C2×D411yescharacteristic
148C23×D7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—24no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—81no—
159C22×C4×C7—81no—
160C22×C4×C7C22×C412yes—
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2×D411yescharacteristic
165C22×C4×C7C2×D411yescharacteristic
166C22×C4×C7#4112yes—
167C22×C4×C7C2411yescharacteristic
168C2×C22⋊D7—24no—
169C2×C22⋊D7—42no—
170C2×C22⋊D7—42no—
171C22×Dic7—21no—
172C22×Dic7—21no—
173C22×Dic7—21no—
174#1157—28no—
175#1157—44no—
176#1157—44no—
177#1157—44no—
178C2×D28—21no—
179C2×D28—21no—
180C2×D28—21no—
181C2×D28—21no—
182C2×D28—21no—
183C2×D28C22×C412yes—
184C2×C4×D7—24no—
185C2×C4×D7—42no—
186C2×C4×D7—42no—
187C2×Dic14—21no—
188C2×Dic14—21no—
189C2×Dic14—21no—
190C2×Dic14C22×C412yes—
191C2×Dic14#4112yes—
192C2×Dic14#4112yes—
193C7×C4⋊C4—24no—
194C7×C4⋊C4—21no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—21no—
197C7×C4⋊C4—21no—
198C7×C4⋊C4—21no—
199C7×C4⋊C4—21no—
200C7×C4⋊C4—81no—
201C7×C4⋊C4—81no—
202C7×C4⋊C4C22×C412yes—
203C7×C4⋊C4C22×C412yes—
204C7×C22⋊C4—22no—
205C7×C22⋊C4—41no—
206C7×C22⋊C4—42no—
207C42×C7—21no—
208C42×C7—21no—
209C42×C7—21no—
210C42×C7—21no—
211C42×C7—81no—
212C42×C7—81no—
213C22⋊Dic7—81no—
214(C2×D7)⋊C4—42no—
215(C2×D7)⋊C4—42no—
216(C2×D7)⋊C4—81no—
217(C2×D7)⋊C4—81no—
218C4⋊Dic7—21no—
219C4⋊Dic7—21no—
220C4⋊Dic7—21no—
221C4⋊Dic7—21no—
222Dic7⋊C4—42no—
223Dic7⋊C4—42no—
224C4×Dic7—42no—
225C4×Dic7—42no—
226#1136—44no—
227C2×C7⋊C8—21no—
228C2×C7⋊C8—21no—
229C2×C7⋊C8—21no—
230C2×C7⋊C8—21no—
231C2×C7⋊C8—21no—
232C2×C7⋊C8—21no—
233C2×C7⋊C8—21no—
234C2×C7⋊C8—21no—
235C2×C7⋊C8—21no—
236C2×C7⋊C8—21no—
237C2×C7⋊C8C22×C412yes—
238C2×C7⋊C8C22×C412yes—
239C22×#41—71no—
240C22×M16—71no—
241C2×C4×Q8—71no—
242C2×C4×Q8—71no—
243C22×C4⋊C4C2×D711yescharacteristic
244C2×#107—71no—
245C2×#106—71no—
246#417—78no—
247C2×#103—71no—
248C2×#103—71no—
249C2×#103—71no—
250C2×#103—71no—
251C2×#102—71no—
252C2×#102—71no—
253C2×#102—71no—
254C2×#102—71no—
255C2×C22⋊C8—71no—
256C2×#97—71no—
257C2×C4×C8—71no—
258#390—71no—
259#390—71no—
260#390—141no—
261#390—141no—
262#389C2×D711yescharacteristic
263#389C2×D711yescharacteristic
264#387—21no—
265#387—21no—
266#380—21no—
267#380—71no—
268#380—141no—
269#380C2×D711yescharacteristic
270C4×C4⋊C4C2×D711yescharacteristic
271C4×C4⋊C4C2×D711yescharacteristic
272C4×C22⋊C4—21no—
273C4×C22⋊C4—141no—
274C4×C22⋊C4C2×D711yescharacteristic
275#340—71no—
276#340—71no—
277#340—71no—
278#340—71no—
279#340—71no—
280#340—71no—
281#336—71no—
282#336—71no—
283C23×C7—21no—
284C23×C7—21no—
285C23×C7—21no—
286C23×C7—21no—
287C23×C7—21no—
288C23×C7—21no—
289C23×C7C4×D412yes—
290C23×C7C22×D411yescharacteristic
291C22×D7—22no—
292C22×D7—41no—
293C22×D7—41no—
294C22×D7—41no—
295C22×D7—41no—
296C22×D7—41no—
297C22×D7—41no—
298C2×C4×C7—21no—
299C2×C4×C7—21no—
300C2×C4×C7—21no—
301C2×C4×C7—21no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—22no—
306C2×C4×C7—22no—
307C2×C4×C7—22no—
308C2×C4×C7—21no—
309C2×C4×C7—21no—
310C2×C4×C7—21no—
311C2×C4×C7—21no—
312C2×C4×C7—21no—
313C2×C4×C7—21no—
314C2×C4×C7—21no—
315C2×C4×C7—21no—
316C2×C4×C7—21no—
317C2×C4×C7—41no—
318C2×C4×C7—41no—
319C2×C4×C7—41no—
320C2×C4×C7—41no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—84no—
328C2×C4×C7C4×D412yes—
329C2×C4×C7#13712yes—
330C2×C4×C7C23×C411yescharacteristic
331C2×C4×C7C2×#4111yescharacteristic
332C2×C4×C7C2×#4111yescharacteristic
333C2×C4×C7C2×#4111yescharacteristic
334C2×C4×C7H(5,𝔽2)11yescharacteristic
335C2×C4×C7H(5,𝔽2)11yescharacteristic
336C22⋊D7—48no—
337C2×Dic7—22no—
338C2×Dic7—22no—
339C2×Dic7—22no—
340C2×Dic7—41no—
341C2×Dic7—41no—
342C2×Dic7—41no—
343C2×Dic7—41no—
344C2×Dic7—41no—
345C2×Dic7—41no—
346D28—22no—
347D28—22no—
348D28—41no—
349D28—41no—
350C4×D7—48no—
351Dic14—22no—
352Dic14—22no—
353Dic14—22no—
354Dic14#11714yes—
355C7⋊C8—22no—
356C7⋊C8—22no—
357C7⋊C8—41no—
358C7⋊C8—41no—
359C2×#41—74no—
360C2×#41—142no—
361C2×#41—142no—
362C2×#41—142no—
363C2×#41—281no—
364C2×#41—281no—
365C22×Q8—71no—
366C22×D4—71no—
367C22×D4—141no—
368C23×C4—21no—
369C23×C4—141no—
370C23×C4C22×D711yescharacteristic
371C2×M16—74no—
372C2×M16—281no—
373C2×M16—281no—
374C22×C8—71no—
375C22×C8—71no—
376C22×C8—71no—
377C22×C8—71no—
378C4×Q8—142no—
379C4×Q8—142no—
380C4×Q8—281no—
381C4×Q8—281no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—71no—
387C2×C4⋊C4—71no—
388C2×C4⋊C4—141no—
389C2×C4⋊C4—141no—
390C2×C4⋊C4C4×D714yes—
391C2×C4⋊C4C22×D711yescharacteristic
392C2×C4⋊C4C22×D711yescharacteristic
393C2×C4⋊C4C22×D711yescharacteristic
394C2×C4⋊C4C22×D711yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—141no—
397C2×C22⋊C4—141no—
398C2×C22⋊C4—141no—
399C2×C22⋊C4—141no—
400C2×C22⋊C4—141no—
401C2×C22⋊C4C22⋊D711yescharacteristic
402C2×C22⋊C4C22⋊D711yescharacteristic
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—141no—
406C2×C42—141no—
407C2×C42C22×D711yescharacteristic
408C2×C42C22×D711yescharacteristic
409#107—281no—
410#106—281no—
411#103—74no—
412#103—74no—
413#103—142no—
414#103—142no—
415#102—74no—
416#102—74no—
417#102—281no—
418#102—281no—
419C22⋊C8—142no—
420#97—281no—
421C4×C8—281no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—141no—
428#95C22⋊D711yescharacteristic
429#95C22⋊D711yescharacteristic
430C22×C7—22no—
431C22×C7—22no—
432C22×C7—22no—
433C22×C7—41no—
434C22×C7—41no—
435C22×C7—41no—
436C22×C7—41no—
437C22×C7C2×C4×D411yescharacteristic
438C22×C7#54611yescharacteristic
439C22×C7#54611yescharacteristic
440C22×C7C2×#13711yescharacteristic
441C22×C7#57511yescharacteristic
442C22×C7#57611yescharacteristic
443C22×C7#57711yescharacteristic
444C2×D7—42no—
445C2×D7—42no—
446C2×D7—42no—
447C2×D7—81no—
448C2×D7—81no—
449C2×D7—81no—
450C2×D7—81no—
451C4×C7—22no—
452C4×C7—22no—
453C4×C7—41no—
454C4×C7—42no—
455C4×C7—42no—
456C4×C7—41no—
457C4×C7—41no—
458C4×C7—81no—
459C4×C7—81no—
460C4×C7C2×#11711yescharacteristic
461C4×C7#51811yescharacteristic
462C4×C7#55111yescharacteristic
463C4×C7#55111yescharacteristic
464Dic7—24no—
465Dic7—81no—
466Dic7—81no—
467C24—141no—
468C24C2×C22⋊D711yescharacteristic
469#41—148no—
470#41—284no—
471#41—284no—
472#41—284no—
473C2×Q8—72no—
474C2×Q8—72no—
475C2×Q8—72no—
476C2×Q8—141no—
477C2×Q8—141no—
478C2×Q8—141no—
479C2×D4—72no—
480C2×D4—144no—
481C2×D4—141no—
482C2×D4—141no—
483C2×D4—141no—
484C2×D4—141no—
485C2×D4—141no—
486C2×D4—282no—
487C2×D4—282no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—24no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—81no—
498C22×C4—81no—
499C22×C4—141no—
500C22×C4—144no—
501C22×C4—141no—
502C22×C4—141no—
503C22×C4—282no—
504C22×C4—282no—
505C22×C4C2×C4×D712yes—
506C22×C4#115712yes—
507C22×C4C2×C22⋊D711yescharacteristic
508C22×C4C2×C22⋊D711yescharacteristic
509C22×C4C2×C22⋊D711yescharacteristic
510C22×C4C2×C22⋊D711yescharacteristic
511C22×C4C2×C22⋊D711yescharacteristic
512C22×C4C23×D711yescharacteristic
513M16—284no—
514C2×C8—72no—
515C2×C8—72no—
516C2×C8—141no—
517C2×C8—141no—
518C2×C8—141no—
519C2×C8—141no—
520C2×C8—141no—
521C2×C8—141no—
522C2×C8—141no—
523C2×C8—141no—
524C2×C8—141no—
525C2×C8—141no—
526C4⋊C4—24no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—81no—
534C4⋊C4—81no—
535C4⋊C4—141no—
536C4⋊C4—141no—
537C4⋊C4—141no—
538C4⋊C4—141no—
539C4⋊C4—282no—
540C4⋊C4—282no—
541C4⋊C4C2×C4×D712yes—
542C4⋊C4C2×C4×D712yes—
543C22⋊C4—22no—
544C22⋊C4—41no—
545C22⋊C4—42no—
546C22⋊C4—282no—
547C22⋊C4—282no—
548C22⋊C4—561no—
549C22⋊C4—561no—
550C22⋊C4—561no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—81no—
556C42—81no—
557C42—282no—
558C42—282no—
559C2×C7—42no—
560C2×C7#234211yescharacteristic
561C2×C7C4×#13711yescharacteristic
562C2×C7#294611yescharacteristic
563C2×C7#330911yescharacteristic
564C2×C7#331611yescharacteristic
565C2×C7#332611yescharacteristic
566C2×C7#333311yescharacteristic
567D7—82no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—142no—
575C23—281no—
576C23—281no—
577C23—281no—
578C23—281no—
579C23—281no—
580C23—281no—
581C23C4×C22⋊D712yes—
582C23C22×C22⋊D711yescharacteristic
583Q8—74no—
584Q8—142no—
585Q8—142no—
586Q8—142no—
587D4—142no—
588D4—142no—
589D4—288no—
590D4—281no—
591D4—281no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4—142no—
623C2×C4—142no—
624C2×C4—142no—
625C2×C4—288no—
626C2×C4—281no—
627C2×C4—281no—
628C2×C4—281no—
629C2×C4—281no—
630C2×C4—281no—
631C2×C4—281no—
632C2×C4C4×C22⋊D712yes—
633C2×C4#650512yes—
634C2×C4C22×C4×D711yescharacteristic
635C2×C4C2×#115711yescharacteristic
636C2×C4D7×#4111yescharacteristic
637C2×C4D7×#4111yescharacteristic
638C2×C4#655311yescharacteristic
639C2×C4#655311yescharacteristic
640C8—142no—
641C8—142no—
642C8—281no—
643C8—281no—
644C7#2257911yescharacteristic, complemented, Sylow
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—282no—
653C22—282no—
654C22—282no—
655C22—561no—
656C22—561no—
657C22—561no—
658C22—561no—
659C22C2×C4×C22⋊D711yescharacteristic
660C22C2×#650511yescharacteristic
661C22#9051311yescharacteristic
662C22#9052011yescharacteristic
663C22#9052011yescharacteristic
664C22#9052611yescharacteristic
665C22#9052711yescharacteristic
666C4—22no—
667C4—22no—
668C4—42no—
669C4—42no—
670C4—41no—
671C4—41no—
672C4—41no—
673C4—81no—
674C4—81no—
675C4—144no—
676C4—561no—
677C4—561no—
678C4D7×#11711yescharacteristic
679C4#9021211yescharacteristic
680C4#9021811yescharacteristic
681C4#9021811yescharacteristic
682C2—42no—
683C2—562no—
684C2#1173971611yescharacteristic
685C2C4×#650511yescharacteristic
686C2#1173998211yescharacteristic
687C2#1174106411yescharacteristic
688C2#1174106611yescharacteristic
689C2#1174108611yescharacteristic
690C2#1174108711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2345C2
socleC23×C7C22×D4
prime radicalC22×#1157C22
cosocleC22×C4×C7C24
hypercenter#2345D7
hypocenterC7#22579
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2345

Complements

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

NH ≅ G/Ntype
1. C7×#2345C2semidirect
4. #11729307C2semidirect
5. #11727386C2semidirect
6. #11727385C2semidirect
7. #11727371C2semidirect
8. #11727369C2semidirect
10. #11727267C2semidirect
11. #11727229C2semidirect
12. C4×#6384C2semidirect
13. #11727217C2semidirect
14. #11727216C2semidirect
15. #11727202C2semidirect
37. #89738C4semidirect
133. #2345D7semidirect
644. C7#22579semidirect

Maximal subgroups

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

subgroupindex
C7×#23452
C2×#897382
#117308992
#117293072
#117273862
#117273852
#117273712
#117273692
#117272762
#117272672
#117272292
C4×#63842
#117272172
#117272162
#117272022
#225797