Finite Group Databasebeta

← #13411949

Subgroups — #13411949

Order 1792.

658 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740482C211yesmaximal, characteristic
2#11733934C211yesmaximal, characteristic
3C7×#2026C211yesmaximal, characteristic
4#11729492C211yesmaximal, characteristic
5#11728001C211yesmaximal, characteristic
6#11727986C211yesmaximal, characteristic
7#11727975C211yesmaximal, characteristic
8Dic7×#103C211yesmaximal, characteristic
9#11727436C211yesmaximal, characteristic
10#11726601C211yesmaximal, characteristic
11#11726555C211yesmaximal, characteristic
12#11726550C211yesmaximal, characteristic
13#11726543C211yesmaximal, characteristic
14#11726377C211yesmaximal, characteristic
15#11726371C211yesmaximal, characteristic
16C2×C7×#125C2211yescharacteristic
17C2×Q8×Dic7C2211yescharacteristic
18C2×#6453C2211yescharacteristic
19C2×C7×#103C2211yescharacteristic
20C2×C7×#103C2211yescharacteristic
21C7×#391C2211yescharacteristic
22#90002C2211yescharacteristic
23C2×#6409C2211yescharacteristic
24C2×#6409C2211yescharacteristic
25C2×#6391C2211yescharacteristic
26C2×Dic7⋊C8C2211yescharacteristic
27C2×Dic7⋊C8C2211yescharacteristic
28C2×C8×Dic7C2211yescharacteristic
29#89755—21no—
30#89752—21no—
31#89748—21no—
32#89748C2211yescharacteristic
33#89748C2211yescharacteristic
34C4⋊C4×Dic7C2211yescharacteristic
35C4⋊C4×Dic7C2211yescharacteristic
36#89745C2211yescharacteristic
37#89744—21no—
38C2×#6382C2211yescharacteristic
39C4×C4⋊Dic7C2211yescharacteristic
40C4×Dic7⋊C4C2211yescharacteristic
41#89700C2211yescharacteristic
42C2×C4⋊(C7⋊C8)C2211yescharacteristic
43#89426—21no—
44#89425—21no—
45#89422—21no—
46#89421—21no—
47C7×#340C2211yescharacteristic
48C7×#340C2211yescharacteristic
49C7×#336C2211yescharacteristic
50#89346C2211yescharacteristic
51#89346C2211yescharacteristic
52#89346C2211yescharacteristic
53#89345C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#26027—71nomaximal, Sylow
60C22×C7×Q8C2311yescharacteristic
61C22×C7×C8C2311yescharacteristic
62C22×C7×C8C2311yescharacteristic
63C7×#125—22no—
64C7×#125—41no—
65C2×C7×C4⋊C4—21no—
66C2×C7×C4⋊C4—21no—
67C2×C7×C4⋊C4C2311yescharacteristic
68C2×C7×C4⋊C4C2311yescharacteristic
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C42×C7C2311yescharacteristic
71Q8×Dic7—22no—
72Q8×Dic7Q814yes—
73C2×C4⋊Dic7—21no—
74C2×C4⋊Dic7—21no—
75C2×C4⋊Dic7C2311yescharacteristic
76C2×C4⋊Dic7C2311yescharacteristic
77C2×C4⋊Dic7C2311yescharacteristic
78C2×C4⋊Dic7C2311yescharacteristic
79C2×Dic7⋊C4—21no—
80C2×Dic7⋊C4—21no—
81C2×Dic7⋊C4—21no—
82C2×Dic7⋊C4—21no—
83C2×Dic7⋊C4—21no—
84C2×Dic7⋊C4—21no—
85C2×Dic7⋊C4—21no—
86C2×Dic7⋊C4D411yescharacteristic
87C2×Dic7⋊C4D411yescharacteristic
88C2×C4×Dic7—21no—
89C2×C4×Dic7—21no—
90C2×C4×Dic7—21no—
91C2×C4×Dic7—21no—
92C2×C4×Dic7C2311yescharacteristic
93C2×C4×Dic7C2311yescharacteristic
94C22×C7⋊C8C2311yescharacteristic
95C22×C7⋊C8C2311yescharacteristic
96#6453—22no—
97#6453—41no—
98C7×#103—22no—
99C7×#103—41no—
100C7×#95—21no—
101C7×#95—21no—
102#6409—22no—
103#6409—41no—
104C7⋊#95—21no—
105C7⋊#95—21no—
106C7⋊#95—21no—
107C7⋊#95—21no—
108C7⋊#95—21no—
109C7⋊#95—21no—
110C7⋊#95—21no—
111C7⋊#95D411yescharacteristic
112C7⋊#95D411yescharacteristic
113#6391—22no—
114Dic7⋊C8—22no—
115Dic7⋊C8—41no—
116C8×Dic7—22no—
117#6382—22no—
118C4⋊(C7⋊C8)—41no—
119#2552—71no—
120#2355—71no—
121#2066—71no—
122#2066—71no—
123#2026—71no—
124#2026D711yescharacteristic
125#1989—71no—
126#1989—71no—
127#1948—71no—
128#1939—71no—
129#1920—71no—
130#1920—71no—
131#1834—71no—
132#1803—71no—
133C4×#103—71no—
134C2×C7×Q8—21no—
135C2×C7×Q8—21no—
136C2×C7×Q8—21no—
137C2×C7×Q8—21no—
138C2×C7×Q8—21no—
139C2×C7×Q8C2×Q812yes—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2411yescharacteristic
147C22×Dic7—21no—
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C22×Dic7C2×D411yescharacteristic
152C22×Dic7C2×D411yescharacteristic
153C22×Dic7C2×D411yescharacteristic
154C22×Dic7C2×D411yescharacteristic
155C2×C7×C8—21no—
156C2×C7×C8—21no—
157C2×C7×C8—21no—
158C2×C7×C8—21no—
159C2×C7×C8—21no—
160C2×C7×C8—21no—
161C7×C4⋊C4—21no—
162C7×C4⋊C4—21no—
163C7×C4⋊C4—21no—
164C7×C4⋊C4—21no—
165C7×C4⋊C4—21no—
166C7×C4⋊C4—42no—
167C7×C4⋊C4—42no—
168C7×C4⋊C4#4112yes—
169C42×C7—21no—
170C42×C7—21no—
171C4⋊Dic7—21no—
172C4⋊Dic7—21no—
173C4⋊Dic7—24no—
174C4⋊Dic7—21no—
175C4⋊Dic7—21no—
176C4⋊Dic7—21no—
177C4⋊Dic7—21no—
178C4⋊Dic7—42no—
179C4⋊Dic7C2×Q812yes—
180C4⋊Dic7#4112yes—
181Dic7⋊C4—22no—
182Dic7⋊C4—22no—
183Dic7⋊C4—42no—
184Dic7⋊C4—42no—
185Dic7⋊C4—42no—
186Dic7⋊C4—81no—
187Dic7⋊C4—81no—
188Dic7⋊C4—81no—
189Dic7⋊C4—81no—
190C4×Dic7—21no—
191C4×Dic7—21no—
192C4×Dic7—24no—
193C4×Dic7—42no—
194C4×Dic7—81no—
195C4×Dic7—81no—
196C4×Dic7C2×Q812yes—
197C4×Dic7#4112yes—
198C2×C7⋊C8—21no—
199C2×C7⋊C8—21no—
200C2×C7⋊C8—21no—
201C2×C7⋊C8—21no—
202C2×C7⋊C8—21no—
203C2×C7⋊C8—21no—
204C2×#125—71no—
205C2×#125C2×D711yescharacteristic
206C2×C4×Q8—71no—
207C2×#106—71no—
208C2×#106—71no—
209C2×C4⋊C8—71no—
210C2×C4⋊C8—71no—
211C2×C4⋊C8—71no—
212C2×#103—71no—
213C2×#103—71no—
214C2×#103C2×D711yescharacteristic
215C2×#103C2×D711yescharacteristic
216C2×C4×C8—71no—
217#398—141no—
218#398—141no—
219#391—71no—
220#391C2×D711yescharacteristic
221#389—71no—
222#389—71no—
223#389—141no—
224#387—141no—
225#387—141no—
226#384—71no—
227#384—71no—
228#384—141no—
229#382—141no—
230C4×C4⋊C4—71no—
231C4×C4⋊C4—71no—
232C4×C4⋊C4—71no—
233C4×C4⋊C4—71no—
234C4×C4⋊C4—141no—
235#340—71no—
236#340—71no—
237#340—71no—
238#340—71no—
239#340—71no—
240#340—71no—
241#340—71no—
242#340—71no—
243#340C2×D711yescharacteristic
244#340C2×D711yescharacteristic
245#336—71no—
246#336C2×D711yescharacteristic
247C23×C7C22×D411yescharacteristic
248C7×Q8—22no—
249C7×Q8—22no—
250C7×Q8—41no—
251C7×Q8—41no—
252C2×C4×C7—22no—
253C2×C4×C7—22no—
254C2×C4×C7—21no—
255C2×C4×C7—21no—
256C2×C4×C7—21no—
257C2×C4×C7—21no—
258C2×C4×C7—21no—
259C2×C4×C7—21no—
260C2×C4×C7—41no—
261C2×C4×C7—41no—
262C2×C4×C7—41no—
263C2×C4×C7—41no—
264C2×C4×C7—41no—
265C2×C4×C7—41no—
266C2×C4×C7—41no—
267C2×C4×C7—41no—
268C2×C4×C7—41no—
269C2×C4×C7—41no—
270C2×C4×C7C22×Q811yescharacteristic
271C2×C4×C7C2×#4111yescharacteristic
272C2×C4×C7C2×#4111yescharacteristic
273C2×C4×C7C2×#4111yescharacteristic
274C2×C4×C7H(5,𝔽2)11yescharacteristic
275C2×C4×C72−1+411yescharacteristic
276C2×Dic7—21no—
277C2×Dic7—21no—
278C2×Dic7—22no—
279C2×Dic7—21no—
280C2×Dic7—21no—
281C2×Dic7—22no—
282C2×Dic7—21no—
283C2×Dic7—21no—
284C2×Dic7—21no—
285C2×Dic7—21no—
286C2×Dic7—41no—
287C2×Dic7—41no—
288C2×Dic7—41no—
289C2×Dic7—41no—
290C2×Dic7—41no—
291C2×Dic7—41no—
292C2×Dic7—41no—
293C2×Dic7—41no—
294C2×Dic7—41no—
295C2×Dic7—41no—
296C2×Dic7C22⋊Q812yes—
297C2×Dic7C22⋊Q812yes—
298C2×Dic7#13512yes—
299C2×Dic7#13712yes—
300C7×C8—41no—
301C7×C8—41no—
302C7⋊C8—41no—
303C7⋊C8—41no—
304C22×Q8C22×D711yescharacteristic
305C22×C8—71no—
306C22×C8—71no—
307C22×C8C22×D711yescharacteristic
308C22×C8C22×D711yescharacteristic
309#125—22no—
310#125—41no—
311#125—142no—
312#125—281no—
313C4×Q8—74no—
314C4×Q8—142no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—71no—
318C2×C4⋊C4—71no—
319C2×C4⋊C4—71no—
320C2×C4⋊C4—71no—
321C2×C4⋊C4—71no—
322C2×C4⋊C4—71no—
323C2×C4⋊C4—141no—
324C2×C4⋊C4—141no—
325C2×C4⋊C4—141no—
326C2×C4⋊C4—141no—
327C2×C4⋊C4—141no—
328C2×C4⋊C4—141no—
329C2×C4⋊C4—141no—
330C2×C4⋊C4—141no—
331C2×C4⋊C4—141no—
332C2×C4⋊C4C22×D711yescharacteristic
333C2×C4⋊C4C22×D711yescharacteristic
334C2×C4⋊C4C22×D711yescharacteristic
335C2×C42—71no—
336C2×C42—71no—
337C2×C42—141no—
338C2×C42—141no—
339C2×C42—141no—
340C2×C42—141no—
341C2×C42C22×D711yescharacteristic
342#106—142no—
343#106—142no—
344C4⋊C8—142no—
345C4⋊C8—281no—
346C4⋊C8—281no—
347#103—22no—
348#103—41no—
349#103—142no—
350#103—281no—
351C4×C8—142no—
352#95—21no—
353#95—21no—
354#95—71no—
355#95—71no—
356#95—141no—
357#95—141no—
358#95—141no—
359#95—141no—
360#95—141no—
361#95—141no—
362#95—141no—
363C22×C7C2×C22⋊Q811yescharacteristic
364C22×C7#54611yescharacteristic
365C22×C7#54811yescharacteristic
366C22×C7C2×#13511yescharacteristic
367C22×C7C2×#13711yescharacteristic
368C22×C7#57711yescharacteristic
369C22×C7#57711yescharacteristic
370C4×C7—41no—
371C4×C7—42no—
372C4×C7—42no—
373C4×C7—41no—
374C4×C7—81no—
375C4×C7—81no—
376C4×C7#53311yescharacteristic
377C4×C7#54411yescharacteristic
378C4×C7#55511yescharacteristic
379C4×C7#55611yescharacteristic
380Dic7—22no—
381Dic7—41no—
382Dic7—42no—
383Dic7—42no—
384Dic7—41no—
385Dic7—81no—
386Dic7—81no—
387Dic7#47914yes—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8Q8×D712yes—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—71no—
399C22×C4—71no—
400C22×C4—71no—
401C22×C4—71no—
402C22×C4—141no—
403C22×C4—141no—
404C22×C4—141no—
405C22×C4—141no—
406C22×C4D4×D711yescharacteristic
407C22×C4D4×D711yescharacteristic
408C22×C4C23×D711yescharacteristic
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—141no—
416C2×C8—141no—
417C2×C8—141no—
418C2×C8—141no—
419C2×C8—141no—
420C2×C8—141no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—42no—
427C4⋊C4—42no—
428C4⋊C4—72no—
429C4⋊C4—72no—
430C4⋊C4—142no—
431C4⋊C4—142no—
432C4⋊C4—144no—
433C4⋊C4—141no—
434C4⋊C4—141no—
435C4⋊C4—141no—
436C4⋊C4—141no—
437C4⋊C4—141no—
438C4⋊C4—141no—
439C4⋊C4—282no—
440C4⋊C4—282no—
441C4⋊C4—282no—
442C4⋊C4—282no—
443C4⋊C4—561no—
444C4⋊C4—561no—
445C4⋊C4—561no—
446C4⋊C4—561no—
447C4⋊C4#115912yes—
448C42—21no—
449C42—21no—
450C42—72no—
451C42—72no—
452C42—144no—
453C42—141no—
454C42—141no—
455C42—282no—
456C42—561no—
457C42—561no—
458C2×C7#243911yescharacteristic
459C2×C7C2×#47911yescharacteristic
460C2×C7#308411yescharacteristic
461C2×C7#330411yescharacteristic
462C2×C7#333111yescharacteristic
463C2×C7#336511yescharacteristic
464C2×C7#337211yescharacteristic
465C23C2×D4×D711yescharacteristic
466Q8—22no—
467Q8—22no—
468Q8—41no—
469Q8—41no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—72no—
489C2×C4—72no—
490C2×C4—72no—
491C2×C4—72no—
492C2×C4—141no—
493C2×C4—141no—
494C2×C4—142no—
495C2×C4—141no—
496C2×C4—141no—
497C2×C4—141no—
498C2×C4—141no—
499C2×C4—141no—
500C2×C4—141no—
501C2×C4—142no—
502C2×C4—281no—
503C2×C4—281no—
504C2×C4—281no—
505C2×C4—281no—
506C2×C4—281no—
507C2×C4—281no—
508C2×C4—281no—
509C2×C4—281no—
510C2×C4—281no—
511C2×C4—281no—
512C2×C4C2×#115911yescharacteristic
513C2×C4#654811yescharacteristic
514C2×C4C2×Q8×D711yescharacteristic
515C2×C4D7×#4111yescharacteristic
516C2×C4D7×#4111yescharacteristic
517C2×C4#655411yescharacteristic
518C8—41no—
519C8—41no—
520C8—281no—
521C8—281no—
522C7#2602711yescharacteristic, complemented, Sylow
523C22#9028211yescharacteristic
524C22D7×C22⋊Q811yescharacteristic
525C22#9036811yescharacteristic
526C22D7×#13511yescharacteristic
527C22#9046111yescharacteristic
528C22D7×#13711yescharacteristic
529C22#9046911yescharacteristic
530C4—41no—
531C4—41no—
532C4—42no—
533C4—42no—
534C4—74no—
535C4—81no—
536C4—81no—
537C4—142no—
538C4—282no—
539C4—282no—
540C4—281no—
541C4—281no—
542C4—561no—
543C4—561no—
544C4#9031311yescharacteristic
545C4#9031411yescharacteristic
546C4#9036111yescharacteristic
547C4#9036211yescharacteristic
548C2#1173422711yescharacteristic
549C2#1173769411yescharacteristic
550C2#1173770511yescharacteristic
551C2D7×#47911yescharacteristic
552C2#1173868011yescharacteristic
553C2#1173908011yescharacteristic
554C2#1173917711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2026C2
socle, prime radicalC23×C7C22×D4
hypercenter#2026D7
hypocenterC7#26027
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2026

Complements

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

NH ≅ G/Ntype
522. C7#26027semidirect

Maximal subgroups

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

subgroupindex
#117404822
#117339342
C7×#20262
#117294922
#117280012
#117279862
#117279752
Dic7×#1032
#117274362
#117266012
#117265552
#117265502
#117265432
#117263772
#117263712
#260277