Finite Group Databasebeta

← #13412999

Subgroups — #13412999

Order 1792.

660 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11731604C211yesmaximal, characteristic
2#11731161C211yesmaximal, characteristic
3C7×#1949C211yesmaximal, characteristic
4#11728398C211yesmaximal, characteristic
5#11728369C211yesmaximal, characteristic
6#11728344C211yesmaximal, characteristic
7#11728317C211yesmaximal, characteristic
8#11728239C211yesmaximal, characteristic
9#11728223C211yesmaximal, characteristic
10#11727304C211yesmaximal, characteristic
11#11727229C211yesmaximal, characteristic
12#11726667C211yesmaximal, characteristic
13#11726666C211yesmaximal, characteristic
14#11726543C211yesmaximal, characteristic
15#11726541C211yesmaximal, characteristic
16C2×#6433—21no—
17C2×C4×Dic14C2211yescharacteristic
18C2×C7×#107C2211yescharacteristic
19C2×C7×#106C2211yescharacteristic
20C2×C7×C4⋊C8C2211yescharacteristic
21C7×#382C2211yescharacteristic
22C4×C7×C4⋊C4C2211yescharacteristic
23C2×#6390C2211yescharacteristic
24C2×#6390C2211yescharacteristic
25C2×Dic7⋊C8C2211yescharacteristic
26C2×Dic7⋊C8C2211yescharacteristic
27#89748C2211yescharacteristic
28#89748C2211yescharacteristic
29C4⋊C4×Dic7C2211yescharacteristic
30C4⋊C4×Dic7C2211yescharacteristic
31#89746C2211yescharacteristic
32#89746C2211yescharacteristic
33#89745C2211yescharacteristic
34#89745C2211yescharacteristic
35C2×#6384C2211yescharacteristic
36C2×#6384C2211yescharacteristic
37C2×#6382C2211yescharacteristic
38C2×#6382C2211yescharacteristic
39C2×#6381C2211yescharacteristic
40C2×#6381C2211yescharacteristic
41#89707C2211yescharacteristic
42C4×C4⋊Dic7C2211yescharacteristic
43#89700—21no—
44C2×#6377C2211yescharacteristic
45#89429—21no—
46#89429—21no—
47#89427—21no—
48#89427—21no—
49#89423—21no—
50#89420—21no—
51C7×#340C2211yescharacteristic
52C7×#340C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89345C2211yescharacteristic
56#89345C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#26104—71nomaximal, Sylow
60C22×Dic14C2311yescharacteristic
61C22×C7×C8C2311yescharacteristic
62C22×C7×C8C2311yescharacteristic
63C2×C7×C4⋊C4C2311yescharacteristic
64C2×C7×C4⋊C4C2311yescharacteristic
65C2×C7×C4⋊C4C2311yescharacteristic
66C2×C7×C4⋊C4C2311yescharacteristic
67C2×C42×C7—21no—
68C2×C42×C7C2311yescharacteristic
69C2×C4⋊Dic7—21no—
70C2×C4⋊Dic7—21no—
71C2×C4⋊Dic7D411yescharacteristic
72C2×C4⋊Dic7D411yescharacteristic
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×C4×Dic7—21no—
84C2×C4×Dic7—21no—
85C2×C4×Dic7—21no—
86C2×C4×Dic7C2311yescharacteristic
87C2×C4×Dic7C2311yescharacteristic
88C22×C7⋊C8C2311yescharacteristic
89C22×C7⋊C8C2311yescharacteristic
90#6433—44no—
91C4×Dic14—22no—
92C4×Dic14Q814yes—
93C7×#107—41no—
94C7×#106—41no—
95C7×C4⋊C8—22no—
96C7×#95—21no—
97C7×#95—21no—
98C7×#95—21no—
99C7⋊#95—21no—
100C7⋊#95—21no—
101C7⋊#95—21no—
102C7⋊#95—21no—
103C7⋊#95—21no—
104C7⋊#95—21no—
105C7⋊#95—21no—
106C7⋊#95—21no—
107C7⋊#95D411yescharacteristic
108C7⋊#95D411yescharacteristic
109#6390—41no—
110#6390—41no—
111Dic7⋊C8—22no—
112Dic7⋊C8—22no—
113#6384—22no—
114#6384—22no—
115#6382—22no—
116#6382—41no—
117#6381—22no—
118#6381—41no—
119#6377—22no—
120#2552—71no—
121#2356—71no—
122#2096—71no—
123#2095—71no—
124#2068—71no—
125#2066—71no—
126#1949D711yescharacteristic
127#1948—71no—
128#1947—71no—
129#1940—71no—
130#1920—71no—
131#1918—71no—
132#1847—71no—
133#1803—71no—
134#1763—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×Dic14—21no—
154C2×Dic14—21no—
155C2×Dic14C2×Q812yes—
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—21no—
170C42×C7—42no—
171C42×C7C2×Q812yes—
172C42×C7#4112yes—
173C4⋊Dic7—21no—
174C4⋊Dic7—22no—
175C4⋊Dic7—22no—
176C4⋊Dic7—21no—
177C4⋊Dic7—21no—
178C4⋊Dic7—21no—
179C4⋊Dic7—21no—
180C4⋊Dic7—42no—
181C4⋊Dic7—81no—
182C4⋊Dic7C2×Q812yes—
183Dic7⋊C4—24no—
184Dic7⋊C4—42no—
185Dic7⋊C4—42no—
186Dic7⋊C4—42no—
187Dic7⋊C4—42no—
188Dic7⋊C4—81no—
189Dic7⋊C4—81no—
190C4×Dic7—24no—
191C4×Dic7—21no—
192C4×Dic7—21no—
193C4×Dic7—21no—
194C4×Dic7—21no—
195C4×Dic7—42no—
196C4×Dic7—42no—
197C2×C7⋊C8—21no—
198C2×C7⋊C8—21no—
199C2×C7⋊C8—21no—
200C2×C7⋊C8—21no—
201C2×C7⋊C8#4112yes—
202C2×C7⋊C8#4112yes—
203C2×#125—141no—
204C2×C4×Q8—71no—
205C2×#107—71no—
206C2×#107—71no—
207C2×#107C2×D711yescharacteristic
208C2×#106—71no—
209C2×#106—71no—
210C2×#106C2×D711yescharacteristic
211C2×C4⋊C8—71no—
212C2×C4⋊C8—71no—
213C2×C4⋊C8C2×D711yescharacteristic
214C2×#103—71no—
215C2×#103—71no—
216C2×#103—71no—
217C2×#103—71no—
218C2×#97—71no—
219#398—141no—
220#398—141no—
221#391—71no—
222#391—71no—
223#389—71no—
224#389—71no—
225#389—141no—
226#387—141no—
227#387—141no—
228#384—71no—
229#384—71no—
230#384—71no—
231#383—141no—
232#382C2×D711yescharacteristic
233C4×C4⋊C4—71no—
234C4×C4⋊C4—71no—
235C4×C4⋊C4—71no—
236C4×C4⋊C4C2×D711yescharacteristic
237#376—141no—
238#340—71no—
239#340—71no—
240#340—71no—
241#340—71no—
242#340C2×D711yescharacteristic
243#340C2×D711yescharacteristic
244#336—71no—
245#336—71no—
246C23×C7C22×D411yescharacteristic
247C2×C4×C7—21no—
248C2×C4×C7—21no—
249C2×C4×C7—21no—
250C2×C4×C7—21no—
251C2×C4×C7—41no—
252C2×C4×C7—41no—
253C2×C4×C7—41no—
254C2×C4×C7—41no—
255C2×C4×C7—41no—
256C2×C4×C7—41no—
257C2×C4×C7—41no—
258C2×C4×C7—41no—
259C2×C4×C7—41no—
260C2×C4×C7—41no—
261C2×C4×C7—41no—
262C2×C4×C7—41no—
263C2×C4×C7C22⋊Q812yes—
264C2×C4×C7C22⋊Q812yes—
265C2×C4×C7C22×Q811yescharacteristic
266C2×C4×C7C2×#4111yescharacteristic
267C2×C4×C7C2×#4111yescharacteristic
268C2×C4×C7C2×#4111yescharacteristic
269C2×C4×C7H(5,𝔽2)11yescharacteristic
270C2×C4×C72−1+411yescharacteristic
271C2×Dic7—21no—
272C2×Dic7—21no—
273C2×Dic7—21no—
274C2×Dic7—21no—
275C2×Dic7—22no—
276C2×Dic7—22no—
277C2×Dic7—21no—
278C2×Dic7—21no—
279C2×Dic7—21no—
280C2×Dic7—21no—
281C2×Dic7—21no—
282C2×Dic7—21no—
283C2×Dic7—41no—
284C2×Dic7—41no—
285C2×Dic7—41no—
286C2×Dic7—41no—
287C2×Dic7—41no—
288C2×Dic7—41no—
289C2×Dic7—41no—
290C2×Dic7—41no—
291C2×Dic7—41no—
292C2×Dic7—41no—
293C2×Dic7AGL(1,ℤ/8)12yes—
294C2×Dic7#13712yes—
295Dic14—22no—
296Dic14—22no—
297Dic14—41no—
298Dic14—41no—
299C7×C8—41no—
300C7×C8—41no—
301C7⋊C8—22no—
302C7⋊C8—22no—
303C22×Q8—71no—
304C22×C8—71no—
305C22×C8—71no—
306C22×C8C22×D711yescharacteristic
307C22×C8C22×D711yescharacteristic
308#125—284no—
309C4×Q8—74no—
310C4×Q8—142no—
311C2×C4⋊C4—71no—
312C2×C4⋊C4—71no—
313C2×C4⋊C4—71no—
314C2×C4⋊C4—71no—
315C2×C4⋊C4—71no—
316C2×C4⋊C4—141no—
317C2×C4⋊C4—141no—
318C2×C4⋊C4—141no—
319C2×C4⋊C4—141no—
320C2×C4⋊C4—141no—
321C2×C4⋊C4—141no—
322C2×C4⋊C4—141no—
323C2×C4⋊C4—141no—
324C2×C4⋊C4—141no—
325C2×C4⋊C4C22×D711yescharacteristic
326C2×C4⋊C4C22×D711yescharacteristic
327C2×C4⋊C4C22×D711yescharacteristic
328C2×C4⋊C4C22×D711yescharacteristic
329C2×C42—21no—
330C2×C42—71no—
331C2×C42—71no—
332C2×C42—141no—
333C2×C42—141no—
334C2×C42—141no—
335C2×C42C22×D711yescharacteristic
336#107—41no—
337#107—142no—
338#107—281no—
339#106—41no—
340#106—142no—
341#106—281no—
342C4⋊C8—22no—
343C4⋊C8—142no—
344C4⋊C8—142no—
345#103—142no—
346#103—142no—
347#103—281no—
348#103—281no—
349#97—142no—
350#95—21no—
351#95—21no—
352#95—21no—
353#95—71no—
354#95—71no—
355#95—141no—
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#54711yescharacteristic
365C22×C7#55011yescharacteristic
366C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C7C2×#13711yescharacteristic
368C22×C7#57711yescharacteristic
369C22×C7#57811yescharacteristic
370C4×C7—22no—
371C4×C7—22no—
372C4×C7—81no—
373C4×C7—81no—
374C4×C7—81no—
375C4×C7—81no—
376C4×C7#53311yescharacteristic
377C4×C7#54411yescharacteristic
378C4×C7#55211yescharacteristic
379C4×C7#55311yescharacteristic
380Dic7—22no—
381Dic7—22no—
382Dic7—42no—
383Dic7—41no—
384Dic7—41no—
385Dic7—42no—
386Dic7—81no—
387Dic7—81no—
388C2×Q8—72no—
389C2×Q8—141no—
390C2×Q8—141no—
391C2×Q8—141no—
392C2×Q8—141no—
393C2×Q8—141no—
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—72no—
416C2×C8—72no—
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—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
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—282no—
439C4⋊C4—282no—
440C4⋊C4—282no—
441C4⋊C4—282no—
442C4⋊C4—282no—
443C4⋊C4—561no—
444C4⋊C4—561no—
445C4⋊C4—561no—
446C42—42no—
447C42—144no—
448C42—141no—
449C42—141no—
450C42—141no—
451C42—141no—
452C42—282no—
453C42—282no—
454C42#115712yes—
455C42Q8×D712yes—
456C2×C7#244111yescharacteristic
457C2×C7#307911yescharacteristic
458C2×C7#308211yescharacteristic
459C2×C7#334311yescharacteristic
460C2×C7#334411yescharacteristic
461C2×C7#339711yescharacteristic
462C2×C7#339811yescharacteristic
463C23C2×D4×D711yescharacteristic
464Q8—142no—
465Q8—142no—
466Q8—281no—
467Q8—281no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—72no—
485C2×C4—72no—
486C2×C4—141no—
487C2×C4—141no—
488C2×C4—141no—
489C2×C4—141no—
490C2×C4—142no—
491C2×C4—142no—
492C2×C4—141no—
493C2×C4—141no—
494C2×C4—141no—
495C2×C4—141no—
496C2×C4—141no—
497C2×C4—141no—
498C2×C4—281no—
499C2×C4—281no—
500C2×C4—281no—
501C2×C4—281no—
502C2×C4—281no—
503C2×C4—281no—
504C2×C4—281no—
505C2×C4—281no—
506C2×C4—281no—
507C2×C4—281no—
508C2×C4#645912yes—
509C2×C4#645912yes—
510C2×C4C2×#115711yescharacteristic
511C2×C4#654811yescharacteristic
512C2×C4C2×Q8×D711yescharacteristic
513C2×C4#655111yescharacteristic
514C2×C4D7×#4111yescharacteristic
515C2×C4D7×#4111yescharacteristic
516C8—41no—
517C8—41no—
518C8—142no—
519C8—142no—
520C7#2610411yescharacteristic, complemented, Sylow
521C22C2×#645911yescharacteristic
522C22#9029011yescharacteristic
523C22#9032211yescharacteristic
524C22#9046111yescharacteristic
525C22#9046211yescharacteristic
526C22D7×AGL(1,ℤ/8)11yescharacteristic
527C22D7×#13711yescharacteristic
528C4—22no—
529C4—22no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4—81no—
534C4—142no—
535C4—142no—
536C4—281no—
537C4—281no—
538C4—282no—
539C4—282no—
540C4—561no—
541C4—561no—
542C4#9024911yescharacteristic
543C4#9027211yescharacteristic
544C4#9037911yescharacteristic
545C4#9042011yescharacteristic
546C2#1173366911yescharacteristic
547C2#1173664311yescharacteristic
548C2#1173668511yescharacteristic
549C2#1173797111yescharacteristic
550C2#1173803511yescharacteristic
551C2#1173864111yescharacteristic
552C2#1173870011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#1949C2
socle, prime radicalC23×C7C22×D4
hypercenter#1949D7
hypocenterC7#26104
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
520. C7#26104semidirect

Maximal subgroups

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

subgroupindex
#117316042
#117311612
C7×#19492
#117283982
#117283692
#117283442
#117283172
#117282392
#117282232
#117273042
#117272292
#117266672
#117266662
#117265432
#117265412
#261047