Finite Group Databasebeta

← #13422377

Subgroups — #13422377

Order 1792.

664 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740674C211yesmaximal, characteristic
2#11733485C211yesmaximal, characteristic
3C7×#2043C211yesmaximal, characteristic
4#11729535C211yesmaximal, characteristic
5#11728015C211yesmaximal, characteristic
6#11728007C211yesmaximal, characteristic
7#11727995C211yesmaximal, characteristic
8#11727990C211yesmaximal, characteristic
9#11727990C211yesmaximal, characteristic
10#11727988C211yesmaximal, characteristic
11#11727976C211yesmaximal, characteristic
12Dic7×#103C211yesmaximal, characteristic
13#11727356C211yesmaximal, characteristic
14#11726375C211yesmaximal, characteristic
15#11726363C211yesmaximal, characteristic
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×Q8×Dic7C2211yescharacteristic
18C2×Q8×Dic7C2211yescharacteristic
19C2×C7×#103C2211yescharacteristic
20C2×C7×#103C2211yescharacteristic
21C2×C7×#103C2211yescharacteristic
22C2×C7×#103C2211yescharacteristic
23C7×#389C2211yescharacteristic
24#90002C2211yescharacteristic
25#90002C2211yescharacteristic
26C2×#6409C2211yescharacteristic
27C2×#6409C2211yescharacteristic
28C2×#6409C2211yescharacteristic
29C2×#6409C2211yescharacteristic
30C2×#6392C2211yescharacteristic
31C2×Dic7⋊C8C2211yescharacteristic
32C2×C8×Dic7C2211yescharacteristic
33#89758—21no—
34#89757—21no—
35#89757C2211yescharacteristic
36#89757C2211yescharacteristic
37#89753—21no—
38#89753—21no—
39#89749—21no—
40#89749C2211yescharacteristic
41C4⋊C4×Dic7—21no—
42C4⋊C4×Dic7C2211yescharacteristic
43C2×#6382C2211yescharacteristic
44C4×C4⋊Dic7C2211yescharacteristic
45C4×C4⋊Dic7C2211yescharacteristic
46#89700C2211yescharacteristic
47#89433—21no—
48#89427—21no—
49C7×#336C2211yescharacteristic
50#89346C2211yescharacteristic
51#89346C2211yescharacteristic
52#89346C2211yescharacteristic
53#89345C2211yescharacteristic
54#89345C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89319C2211yescharacteristic
59#26757—71nomaximal, Sylow
60C22×C7×Q8C2311yescharacteristic
61C22×C7×Q8C2311yescharacteristic
62C22×C7×C8C2311yescharacteristic
63C22×C7×C8C2311yescharacteristic
64C7×C4⋊Q8—22no—
65C7×C4⋊Q8—22no—
66C2×C7×C4⋊C4—21no—
67C2×C7×C4⋊C4—21no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C42×C7C2311yescharacteristic
72Q8×Dic7—22no—
73Q8×Dic7—22no—
74Q8×Dic7—41no—
75Q8×Dic7—41no—
76C2×C4⋊Dic7—21no—
77C2×C4⋊Dic7—21no—
78C2×C4⋊Dic7—21no—
79C2×C4⋊Dic7—21no—
80C2×C4⋊Dic7D411yescharacteristic
81C2×C4⋊Dic7D411yescharacteristic
82C2×C4⋊Dic7C2311yescharacteristic
83C2×C4⋊Dic7C2311yescharacteristic
84C2×C4⋊Dic7C2311yescharacteristic
85C2×C4⋊Dic7C2311yescharacteristic
86C2×Dic7⋊C4—21no—
87C2×C4×Dic7—21no—
88C2×C4×Dic7—21no—
89C2×C4×Dic7—21no—
90C2×C4×Dic7—21no—
91C2×C4×Dic7C2311yescharacteristic
92C2×C4×Dic7C2311yescharacteristic
93C22×C7⋊C8C2311yescharacteristic
94C22×C7⋊C8C2311yescharacteristic
95C7×#103—22no—
96C7×#103—22no—
97C7×#103—22no—
98C7×#103—22no—
99C7×#95—21no—
100#6409—22no—
101#6409—22no—
102#6409—41no—
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⋊#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95D411yescharacteristic
116C7⋊#95D411yescharacteristic
117#6392—22no—
118Dic7⋊C8—41no—
119C8×Dic7—41no—
120#6382—22no—
121#2508—71no—
122#2365—71no—
123#2074—71no—
124#2066—71no—
125#2043—71no—
126#2043D711yescharacteristic
127#1933—71no—
128#1927—71no—
129#1920—71no—
130#1918—71no—
131#1916—71no—
132#1863—71no—
133#1863—71no—
134#1805—71no—
135C4×#103—71no—
136C2×C7×Q8—21no—
137C2×C7×Q8—21no—
138C2×C7×Q8—21no—
139C2×C7×Q8—21no—
140C2×C7×Q8—21no—
141C2×C7×Q8—21no—
142C2×C7×Q8—21no—
143C2×C7×Q8—21no—
144C2×C7×Q8—21no—
145C2×C7×Q8—21no—
146C2×C7×Q8#4112yes—
147C2×C7×Q8#4112yes—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2411yescharacteristic
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7C2×D411yescharacteristic
160C22×Dic7C2×D411yescharacteristic
161C22×Dic7C2×D411yescharacteristic
162C22×Dic7C2×D411yescharacteristic
163C2×C7×C8—21no—
164C2×C7×C8—21no—
165C2×C7×C8—21no—
166C2×C7×C8—21no—
167C2×C7×C8—21no—
168C2×C7×C8—21no—
169C7×C4⋊C4—24no—
170C7×C4⋊C4—24no—
171C7×C4⋊C4—21no—
172C7×C4⋊C4—21no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—81no—
175C7×C4⋊C4#4112yes—
176C42×C7—21no—
177C42×C7—21no—
178C4⋊Dic7—22no—
179C4⋊Dic7—21no—
180C4⋊Dic7—22no—
181C4⋊Dic7—21no—
182C4⋊Dic7—21no—
183C4⋊Dic7—21no—
184C4⋊Dic7—21no—
185C4⋊Dic7—21no—
186C4⋊Dic7—21no—
187C4⋊Dic7—42no—
188C4⋊Dic7—42no—
189C4⋊Dic7—81no—
190C4⋊Dic7—81no—
191C4⋊Dic7#4112yes—
192Dic7⋊C4—42no—
193C4×Dic7—21no—
194C4×Dic7—21no—
195C4×Dic7—21no—
196C4×Dic7—21no—
197C4×Dic7—42no—
198C4×Dic7—42no—
199C4×Dic7—42no—
200C4×Dic7—42no—
201C2×C7⋊C8—21no—
202C2×C7⋊C8—21no—
203C2×C7⋊C8—21no—
204C2×C7⋊C8—21no—
205C2×C7⋊C8—21no—
206C2×C7⋊C8—21no—
207C2×C4⋊Q8C2×D711yescharacteristic
208C2×C4×Q8—71no—
209C2×C4×Q8—71no—
210C2×#107—71no—
211C2×#106—71no—
212C2×C4⋊C8—71no—
213C2×#103—71no—
214C2×#103—71no—
215C2×#103—71no—
216C2×#103—71no—
217C2×#103C2×D711yescharacteristic
218C2×#103C2×D711yescharacteristic
219C2×#103C2×D711yescharacteristic
220C2×#103C2×D711yescharacteristic
221C2×C4×C8—71no—
222#400—141no—
223#398—141no—
224#391—71no—
225#391—71no—
226#389—71no—
227#389—71no—
228#389—71no—
229#389—141no—
230#389C2×D711yescharacteristic
231#387—141no—
232#387—141no—
233#387—141no—
234#382—71no—
235#382—141no—
236C4×C4⋊C4—71no—
237C4×C4⋊C4—71no—
238C4×C4⋊C4—71no—
239C4×C4⋊C4—141no—
240#340—71no—
241#340—71no—
242#340—71no—
243#340—71no—
244#340—71no—
245#340—71no—
246#336—71no—
247#336—71no—
248#336—71no—
249#336C2×D711yescharacteristic
250C23×C7C22×D411yescharacteristic
251C7×Q8—22no—
252C7×Q8—22no—
253C7×Q8—22no—
254C7×Q8—22no—
255C7×Q8—41no—
256C7×Q8—41no—
257C7×Q8—41no—
258C7×Q8—41no—
259C2×C4×C7—21no—
260C2×C4×C7—21no—
261C2×C4×C7—21no—
262C2×C4×C7—22no—
263C2×C4×C7—22no—
264C2×C4×C7—22no—
265C2×C4×C7—21no—
266C2×C4×C7—21no—
267C2×C4×C7—41no—
268C2×C4×C7—41no—
269C2×C4×C7—41no—
270C2×C4×C7—41no—
271C2×C4×C7—41no—
272C2×C4×C7—41no—
273C2×C4×C7—41no—
274C2×C4×C7—41no—
275C2×C4×C7—41no—
276C2×C4×C7#13512yes—
277C2×C4×C7C2×#4111yescharacteristic
278C2×C4×C7C2×#4111yescharacteristic
279C2×C4×C7C2×#4111yescharacteristic
280C2×C4×C7C2×#4111yescharacteristic
281C2×C4×C7H(5,𝔽2)11yescharacteristic
282C2×C4×C72−1+411yescharacteristic
283C2×Dic7—21no—
284C2×Dic7—21no—
285C2×Dic7—21no—
286C2×Dic7—21no—
287C2×Dic7—21no—
288C2×Dic7—22no—
289C2×Dic7—21no—
290C2×Dic7—21no—
291C2×Dic7—21no—
292C2×Dic7—21no—
293C2×Dic7—21no—
294C2×Dic7—21no—
295C2×Dic7—41no—
296C2×Dic7—41no—
297C2×Dic7—41no—
298C2×Dic7—41no—
299C2×Dic7—41no—
300C2×Dic7—41no—
301C2×Dic7—41no—
302C2×Dic7—41no—
303C2×Dic7—41no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7#13712yes—
307C7×C8—41no—
308C7×C8—41no—
309C7⋊C8—41no—
310C7⋊C8—41no—
311C22×Q8C22×D711yescharacteristic
312C22×Q8C22×D711yescharacteristic
313C22×C8—71no—
314C22×C8—71no—
315C22×C8C22×D711yescharacteristic
316C22×C8C22×D711yescharacteristic
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4×Q8—142no—
320C4×Q8—142no—
321C4×Q8—281no—
322C4×Q8—281no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—71no—
327C2×C4⋊C4—71no—
328C2×C4⋊C4—71no—
329C2×C4⋊C4—71no—
330C2×C4⋊C4—71no—
331C2×C4⋊C4—71no—
332C2×C4⋊C4—141no—
333C2×C4⋊C4—141no—
334C2×C4⋊C4—141no—
335C2×C4⋊C4—141no—
336C2×C4⋊C4—141no—
337C2×C4⋊C4C22×D711yescharacteristic
338C2×C4⋊C4C22×D711yescharacteristic
339C2×C42—71no—
340C2×C42—71no—
341C2×C42—141no—
342C2×C42—141no—
343C2×C42—141no—
344C2×C42—141no—
345C2×C42C22×D711yescharacteristic
346#107—142no—
347#106—142no—
348C4⋊C8—281no—
349#103—22no—
350#103—22no—
351#103—22no—
352#103—22no—
353#103—142no—
354#103—142no—
355#103—281no—
356#103—281no—
357C4×C8—281no—
358#95—21no—
359#95—71no—
360#95—71no—
361#95—141no—
362#95—141no—
363#95—141no—
364#95—141no—
365#95—141no—
366#95—141no—
367#95—141no—
368#95—141no—
369#95—141no—
370#95—141no—
371#95—141no—
372C22×C7#52511yescharacteristic
373C22×C7#54611yescharacteristic
374C22×C7#54811yescharacteristic
375C22×C7C2×#13511yescharacteristic
376C22×C7C2×#13711yescharacteristic
377C22×C7#57711yescharacteristic
378C22×C7#57811yescharacteristic
379C4×C7—22no—
380C4×C7—42no—
381C4×C7—41no—
382C4×C7—42no—
383C4×C7—42no—
384C4×C7—81no—
385C4×C7#52911yescharacteristic
386C4×C7#53911yescharacteristic
387C4×C7#55211yescharacteristic
388C4×C7#55311yescharacteristic
389Dic7—22no—
390Dic7—41no—
391Dic7—41no—
392Dic7—42no—
393Dic7—41no—
394Dic7—81no—
395Dic7—81no—
396Dic7—81no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8#115912yes—
408C2×Q8#115912yes—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—71no—
414C22×C4—71no—
415C22×C4—71no—
416C22×C4—71no—
417C22×C4—141no—
418C22×C4—141no—
419C22×C4—141no—
420C22×C4—141no—
421C22×C4D4×D711yescharacteristic
422C22×C4D4×D711yescharacteristic
423C22×C4C23×D711yescharacteristic
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—141no—
431C2×C8—141no—
432C2×C8—141no—
433C2×C8—141no—
434C2×C8—141no—
435C2×C8—141no—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—72no—
442C4⋊C4—81no—
443C4⋊C4—142no—
444C4⋊C4—142no—
445C4⋊C4—141no—
446C4⋊C4—141no—
447C4⋊C4—141no—
448C4⋊C4—141no—
449C4⋊C4—141no—
450C4⋊C4—141no—
451C4⋊C4—141no—
452C4⋊C4—282no—
453C4⋊C4—282no—
454C4⋊C4—282no—
455C4⋊C4—561no—
456C4⋊C4—561no—
457C4⋊C4#115912yes—
458C42—21no—
459C42—21no—
460C42—141no—
461C42—141no—
462C42—141no—
463C42—141no—
464C42—282no—
465C42—282no—
466C42—282no—
467C42—282no—
468C2×C7#246011yescharacteristic
469C2×C7#310811yescharacteristic
470C2×C7#312111yescharacteristic
471C2×C7#330311yescharacteristic
472C2×C7#331211yescharacteristic
473C2×C7#336411yescharacteristic
474C2×C7#337211yescharacteristic
475C23C2×D4×D711yescharacteristic
476Q8—22no—
477Q8—22no—
478Q8—22no—
479Q8—22no—
480Q8—41no—
481Q8—41no—
482Q8—41no—
483Q8—41no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—72no—
502C2×C4—141no—
503C2×C4—141no—
504C2×C4—141no—
505C2×C4—141no—
506C2×C4—141no—
507C2×C4—141no—
508C2×C4—141no—
509C2×C4—141no—
510C2×C4—141no—
511C2×C4—141no—
512C2×C4—141no—
513C2×C4—142no—
514C2×C4—281no—
515C2×C4—281no—
516C2×C4—281no—
517C2×C4—281no—
518C2×C4—281no—
519C2×C4—281no—
520C2×C4—281no—
521C2×C4—281no—
522C2×C4—281no—
523C2×C4—281no—
524C2×C4—281no—
525C2×C4#648212yes—
526C2×C4C2×#115911yescharacteristic
527C2×C4C2×#115911yescharacteristic
528C2×C4C2×#115911yescharacteristic
529C2×C4D7×#4111yescharacteristic
530C2×C4#655311yescharacteristic
531C2×C4#655411yescharacteristic
532C8—41no—
533C8—41no—
534C8—281no—
535C8—281no—
536C7#2675711yescharacteristic, complemented, Sylow
537C22#9027711yescharacteristic
538C22#9028911yescharacteristic
539C22#9036711yescharacteristic
540C22#9045311yescharacteristic
541C22C2×#648211yescharacteristic
542C22D7×#13711yescharacteristic
543C22#9047011yescharacteristic
544C4—22no—
545C4—42no—
546C4—42no—
547C4—42no—
548C4—41no—
549C4—81no—
550C4—142no—
551C4—281no—
552C4—281no—
553C4—281no—
554C4—282no—
555C4—561no—
556C4—561no—
557C4—561no—
558C4#9029111yescharacteristic
559C4#9030911yescharacteristic
560C4#9034111yescharacteristic
561C4#9035611yescharacteristic
562C2#1173435911yescharacteristic
563C2#1173747711yescharacteristic
564C2#1173761811yescharacteristic
565C2#1173786311yescharacteristic
566C2#1173790811yescharacteristic
567C2#1173906011yescharacteristic
568C2#1173919411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2043C2
socle, prime radicalC23×C7C22×D4
hypercenter#2043D7
hypocenterC7#26757
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
536. C7#26757semidirect

Maximal subgroups

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

subgroupindex
#117406742
#117334852
C7×#20432
#117295352
#117280152
#117280072
#117279952
#117279902
#117279882
#117279762
Dic7×#1032
#117273562
#117263752
#117263632
#267577