Finite Group Databasebeta

← #13413084

Subgroups — #13413084

Order 1792.

702 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11733426C211yesmaximal, characteristic
2#11731782C211yesmaximal, characteristic
3C7×#2100C211yesmaximal, characteristic
4#11727377C211yesmaximal, characteristic
5#11727342C211yesmaximal, characteristic
6#11726660C211yesmaximal, characteristic
7#11726658C211yesmaximal, characteristic
8#11726658C211yesmaximal, characteristic
9#11726601C211yesmaximal, characteristic
10#11726597C211yesmaximal, characteristic
11#11726593C211yesmaximal, characteristic
12#11726549C211yesmaximal, characteristic
13#11726535C211yesmaximal, characteristic
14#11726437C211yesmaximal, characteristic
15#11726371C211yesmaximal, characteristic
16C2×#6452—21no—
17C2×#6450C2211yescharacteristic
18C2×#6450C2211yescharacteristic
19C2×C4×Dic14C2211yescharacteristic
20C7×#389C2211yescharacteristic
21C7×#384C2211yescharacteristic
22C2×#6392C2211yescharacteristic
23C2×#6390C2211yescharacteristic
24C2×#6390C2211yescharacteristic
25C2×Dic7⋊C8C2211yescharacteristic
26C2×Dic7⋊C8C2211yescharacteristic
27C2×C8×Dic7C2211yescharacteristic
28#89757C2211yescharacteristic
29#89757C2211yescharacteristic
30#89756—21no—
31#89752—21no—
32#89748—21no—
33#89748C2211yescharacteristic
34#89748C2211yescharacteristic
35#89748C2211yescharacteristic
36C4⋊C4×Dic7C2211yescharacteristic
37#89744—21no—
38#89744—21no—
39C2×#6384C2211yescharacteristic
40C2×#6384C2211yescharacteristic
41C2×#6381C2211yescharacteristic
42C4×Dic7⋊C4C2211yescharacteristic
43#89700C2211yescharacteristic
44C2×C4⋊(C7⋊C8)C2211yescharacteristic
45#89421—21no—
46#89419—21no—
47C7×#340C2211yescharacteristic
48C7×#340C2211yescharacteristic
49C7×#340C2211yescharacteristic
50C7×#340C2211yescharacteristic
51C7×#336C2211yescharacteristic
52#89346C2211yescharacteristic
53#89345C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#26112—71nomaximal, Sylow
60C22×Dic14C2311yescharacteristic
61C22×C7×C8C2311yescharacteristic
62C22×C7×C8C2311yescharacteristic
63C2×C7×C4⋊C4—21no—
64C2×C7×C4⋊C4—21no—
65C2×C7×C4⋊C4—21no—
66C2×C7×C4⋊C4C2311yescharacteristic
67C2×C7×C4⋊C4C2311yescharacteristic
68C2×C7×C4⋊C4C2311yescharacteristic
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C42×C7C2311yescharacteristic
71C2×C4⋊Dic7—21no—
72C2×C4⋊Dic7—21no—
73C2×C4⋊Dic7C2311yescharacteristic
74C2×C4⋊Dic7C2311yescharacteristic
75C2×C4⋊Dic7C2311yescharacteristic
76C2×Dic7⋊C4—21no—
77C2×Dic7⋊C4—21no—
78C2×Dic7⋊C4—21no—
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#6452—44no—
97#6450—22no—
98#6450—22no—
99#6450—41no—
100#6450Q814yes—
101C4×Dic14—22no—
102C4×Dic14—41no—
103C7×#95—21no—
104C7⋊#95—21no—
105C7⋊#95—21no—
106C7⋊#95—21no—
107C7⋊#95—21no—
108C7⋊#95D411yescharacteristic
109C7⋊#95D411yescharacteristic
110#6392—41no—
111#6390—22no—
112#6390—22no—
113Dic7⋊C8—22no—
114Dic7⋊C8—41no—
115C8×Dic7—22no—
116#6384—22no—
117#6384—22no—
118#6381—41no—
119C4⋊(C7⋊C8)—41no—
120#2552—71no—
121Q8×C4⋊C4—71no—
122#2100—71no—
123#2100D711yescharacteristic
124#2087—71no—
125#2087—71no—
126#1947—71no—
127#1939—71no—
128#1863—71no—
129#1863—71no—
130#1834—71no—
131#1803—71no—
132#1803—71no—
133#1803—71no—
134C4×#103—71no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7C2×D411yescharacteristic
140C22×C4×C7C2×D411yescharacteristic
141C22×C4×C7C2411yescharacteristic
142C22×Dic7—21no—
143C22×Dic7—21no—
144C22×Dic7—21no—
145C22×Dic7—21no—
146C22×Dic7C2×D411yescharacteristic
147C22×Dic7C2×D411yescharacteristic
148C22×Dic7C2×D411yescharacteristic
149C22×Dic7C2×D411yescharacteristic
150C2×Dic14—21no—
151C2×Dic14—21no—
152C2×Dic14—21no—
153C2×Dic14C2×Q812yes—
154C2×Dic14#4112yes—
155C2×Dic14#4112yes—
156C2×C7×C8—21no—
157C2×C7×C8—21no—
158C2×C7×C8—21no—
159C2×C7×C8—21no—
160C2×C7×C8—21no—
161C2×C7×C8—21no—
162C7×C4⋊C4—21no—
163C7×C4⋊C4—21no—
164C7×C4⋊C4—21no—
165C7×C4⋊C4—21no—
166C7×C4⋊C4—21no—
167C7×C4⋊C4—21no—
168C7×C4⋊C4—21no—
169C7×C4⋊C4—42no—
170C7×C4⋊C4—81no—
171C7×C4⋊C4—81no—
172C7×C4⋊C4C2×Q812yes—
173C42×C7—21no—
174C42×C7—21no—
175C4⋊Dic7—21no—
176C4⋊Dic7—21no—
177C4⋊Dic7—21no—
178C4⋊Dic7—21no—
179C4⋊Dic7—21no—
180C4⋊Dic7—21no—
181C4⋊Dic7—42no—
182C4⋊Dic7—81no—
183Dic7⋊C4—24no—
184Dic7⋊C4—22no—
185Dic7⋊C4—42no—
186Dic7⋊C4—42no—
187Dic7⋊C4—42no—
188Dic7⋊C4—42no—
189Dic7⋊C4—42no—
190Dic7⋊C4—42no—
191Dic7⋊C4—81no—
192Dic7⋊C4—81no—
193Dic7⋊C4—81no—
194Dic7⋊C4Q1614yes—
195C4×Dic7—21no—
196C4×Dic7—21no—
197C4×Dic7—24no—
198C4×Dic7—42no—
199C4×Dic7—42no—
200C4×Dic7—42no—
201C4×Dic7C2×Q812yes—
202C4×Dic7#4112yes—
203C2×C7⋊C8—21no—
204C2×C7⋊C8—21no—
205C2×C7⋊C8—21no—
206C2×C7⋊C8—21no—
207C2×C7⋊C8—21no—
208C2×C7⋊C8—21no—
209C2×#125—141no—
210C2×C4×Q8—71no—
211C2×C4×Q8—71no—
212C2×C4×Q8—71no—
213C2×#107—71no—
214C2×#107—71no—
215C2×C4⋊C8—71no—
216C2×C4⋊C8—71no—
217C2×C4⋊C8—71no—
218C2×#103—71no—
219C2×#103—71no—
220C2×#103—71no—
221C2×#103—71no—
222C2×C4×C8—71no—
223#398—141no—
224#398—141no—
225#389—71no—
226#389—71no—
227#389—71no—
228#389—141no—
229#389—141no—
230#389—141no—
231#389C2×D711yescharacteristic
232#384—71no—
233#384—71no—
234#384—71no—
235#384—141no—
236#384C2×D711yescharacteristic
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#340C2×D711yescharacteristic
247#340C2×D711yescharacteristic
248#340C2×D711yescharacteristic
249#340C2×D711yescharacteristic
250#336—71no—
251#336C2×D711yescharacteristic
252C23×C7C22×D411yescharacteristic
253C2×C4×C7—21no—
254C2×C4×C7—21no—
255C2×C4×C7—22no—
256C2×C4×C7—21no—
257C2×C4×C7—21no—
258C2×C4×C7—21no—
259C2×C4×C7—41no—
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×C7C2×Q1612yes—
271C2×C4×C7C22×Q811yescharacteristic
272C2×C4×C7C2×#4111yescharacteristic
273C2×C4×C7C2×#4111yescharacteristic
274C2×C4×C7C2×#4111yescharacteristic
275C2×C4×C7H(5,𝔽2)11yescharacteristic
276C2×C4×C72−1+411yescharacteristic
277C2×Dic7—22no—
278C2×Dic7—21no—
279C2×Dic7—22no—
280C2×Dic7—22no—
281C2×Dic7—21no—
282C2×Dic7—21no—
283C2×Dic7—21no—
284C2×Dic7—21no—
285C2×Dic7—21no—
286C2×Dic7—21no—
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×Dic7C2×Q1612yes—
299C2×Dic7C2×Q1612yes—
300C2×Dic7AGL(1,ℤ/8)12yes—
301Dic14—22no—
302Dic14—22no—
303Dic14—22no—
304Dic14#12514yescomplemented
305C7×C8—41no—
306C7×C8—41no—
307C7⋊C8—41no—
308C7⋊C8—41no—
309C22×Q8—71no—
310C22×C8—71no—
311C22×C8—71no—
312C22×C8C22×D711yescharacteristic
313C22×C8C22×D711yescharacteristic
314#125—284no—
315C4×Q8—74no—
316C4×Q8—142no—
317C4×Q8—142no—
318C4×Q8—142no—
319C4×Q8—281no—
320C4×Q8—281no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—71no—
325C2×C4⋊C4—71no—
326C2×C4⋊C4—71no—
327C2×C4⋊C4—71no—
328C2×C4⋊C4—71no—
329C2×C4⋊C4—141no—
330C2×C4⋊C4—141no—
331C2×C4⋊C4—141no—
332C2×C4⋊C4—141no—
333C2×C4⋊C4—141no—
334C2×C4⋊C4—141no—
335C2×C4⋊C4—141no—
336C2×C4⋊C4—141no—
337C2×C4⋊C4—141no—
338C2×C4⋊C4—141no—
339C2×C4⋊C4—141no—
340C2×C4⋊C4—141no—
341C2×C4⋊C4C22×D711yescharacteristic
342C2×C4⋊C4C22×D711yescharacteristic
343C2×C4⋊C4C22×D711yescharacteristic
344C2×C4⋊C4C22×D711yescharacteristic
345C2×C42—71no—
346C2×C42—71no—
347C2×C42—141no—
348C2×C42—141no—
349C2×C42—141no—
350C2×C42—141no—
351C2×C42C22×D711yescharacteristic
352#107—281no—
353#107—281no—
354C4⋊C8—142no—
355C4⋊C8—281no—
356C4⋊C8—281no—
357#103—142no—
358#103—142no—
359#103—142no—
360#103—142no—
361C4×C8—142no—
362#95—21no—
363#95—71no—
364#95—71no—
365#95—141no—
366#95—141no—
367#95—141no—
368#95—141no—
369C22×C7C2×C22⋊Q811yescharacteristic
370C22×C7#54611yescharacteristic
371C22×C7#54811yescharacteristic
372C22×C7C22×Q1611yescharacteristic
373C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C7#57711yescharacteristic
375C22×C7#57711yescharacteristic
376C4×C7—22no—
377C4×C7—41no—
378C4×C7—42no—
379C4×C7—81no—
380C4×C7—81no—
381C4×C7—81no—
382C4×C7C2×#12511yescharacteristic
383C4×C7#54411yescharacteristic
384C4×C7#55211yescharacteristic
385C4×C7#55311yescharacteristic
386Dic7—22no—
387Dic7—24no—
388Dic7—22no—
389Dic7—41no—
390Dic7—81no—
391Dic7—81no—
392Dic7—81no—
393Dic7#47714yes—
394C2×Q8—72no—
395C2×Q8—72no—
396C2×Q8—72no—
397C2×Q8—141no—
398C2×Q8—141no—
399C2×Q8—141no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—71no—
405C22×C4—71no—
406C22×C4—71no—
407C22×C4—71no—
408C22×C4—141no—
409C22×C4—141no—
410C22×C4—141no—
411C22×C4—141no—
412C22×C4D4×D711yescharacteristic
413C22×C4D4×D711yescharacteristic
414C22×C4C23×D711yescharacteristic
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—141no—
422C2×C8—141no—
423C2×C8—141no—
424C2×C8—141no—
425C2×C8—141no—
426C2×C8—141no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—42no—
435C4⋊C4—74no—
436C4⋊C4—81no—
437C4⋊C4—81no—
438C4⋊C4—142no—
439C4⋊C4—144no—
440C4⋊C4—141no—
441C4⋊C4—141no—
442C4⋊C4—141no—
443C4⋊C4—141no—
444C4⋊C4—141no—
445C4⋊C4—141no—
446C4⋊C4—282no—
447C4⋊C4—282no—
448C4⋊C4—282no—
449C4⋊C4—282no—
450C4⋊C4—282no—
451C4⋊C4—282no—
452C4⋊C4—282no—
453C4⋊C4—561no—
454C4⋊C4—561no—
455C4⋊C4—561no—
456C4⋊C4—561no—
457C4⋊C4Q8×D712yes—
458C42—21no—
459C42—21no—
460C42—72no—
461C42—72no—
462C42—144no—
463C42—141no—
464C42—141no—
465C42—282no—
466C42—282no—
467C42—282no—
468C2×C7#244211yescharacteristic
469C2×C7C2×#47711yescharacteristic
470C2×C7#308411yescharacteristic
471C2×C7#329911yescharacteristic
472C2×C7#333211yescharacteristic
473C2×C7#336311yescharacteristic
474C2×C7#336811yescharacteristic
475C23C2×D4×D711yescharacteristic
476Q8—74no—
477Q8—142no—
478Q8—142no—
479Q8—142no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—72no—
498C2×C4—72no—
499C2×C4—72no—
500C2×C4—72no—
501C2×C4—72no—
502C2×C4—142no—
503C2×C4—141no—
504C2×C4—141no—
505C2×C4—141no—
506C2×C4—142no—
507C2×C4—141no—
508C2×C4—142no—
509C2×C4—141no—
510C2×C4—141no—
511C2×C4—141no—
512C2×C4—281no—
513C2×C4—281no—
514C2×C4—281no—
515C2×C4—281no—
516C2×C4—281no—
517C2×C4—281no—
518C2×C4—281no—
519C2×C4—281no—
520C2×C4—281no—
521C2×C4D7×Q1612yes—
522C2×C4C2×Q8×D711yescharacteristic
523C2×C4D7×#4111yescharacteristic
524C2×C4D7×#4111yescharacteristic
525C2×C4D7×#4111yescharacteristic
526C2×C4#655311yescharacteristic
527C2×C4#655411yescharacteristic
528C8—41no—
529C8—41no—
530C8—281no—
531C8—281no—
532C7#2611211yescharacteristic, complemented, Sylow
533C22D7×C22⋊Q811yescharacteristic
534C22#9034511yescharacteristic
535C22#9036811yescharacteristic
536C22#9045311yescharacteristic
537C22C2×D7×Q1611yescharacteristic
538C22D7×AGL(1,ℤ/8)11yescharacteristic
539C22#9046611yescharacteristic
540C4—22no—
541C4—42no—
542C4—41no—
543C4—74no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4—144no—
548C4—142no—
549C4—142no—
550C4—281no—
551C4—561no—
552C4—561no—
553C4—561no—
554C4D7×#12511yescharacteristic
555C4#9038011yescharacteristic
556C4#9039911yescharacteristic
557C4#9040011yescharacteristic
558C2#1173558011yescharacteristic
559C2#1173850811yescharacteristic
560C2D7×#47711yescharacteristic
561C2#1173879211yescharacteristic
562C2#1173893511yescharacteristic
563C2#1173906911yescharacteristic
564C2#1173915411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2100C2
socle, prime radicalC23×C7C22×D4
hypercenter#2100D7
hypocenterC7#26112
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
304. Dic14#125semidirect
532. C7#26112semidirect

Maximal subgroups

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

subgroupindex
#117334262
#117317822
C7×#21002
#117273772
#117273422
#117266602
#117266582
#117266012
#117265972
#117265932
#117265492
#117265352
#117264372
#117263712
#261127