Finite Group Databasebeta

← #13405889

Subgroups — #13405889

Order 1792.

714 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#479C211yesmaximal, characteristic
2#11740486C211yesmaximal, characteristic
3#11739927C211yesmaximal, characteristic
4C2×#89600C211yesmaximal, characteristic
5#11729495C211yesmaximal, characteristic
6#11729385C211yesmaximal, characteristic
7#11728376C211yesmaximal, characteristic
8#11728368C211yesmaximal, characteristic
9#11728322C211yesmaximal, characteristic
10#11728313C211yesmaximal, characteristic
11#11728208C211yesmaximal, characteristic
12#11728010C211yesmaximal, characteristic
13#11728008C211yesmaximal, characteristic
14#11728001C211yesmaximal, characteristic
15#11728001C211yesmaximal, characteristic
16C2×C7×#125C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C4×Dic14C2211yescharacteristic
19C7×#479—24no—
20C2×C7×#107C2211yescharacteristic
21C2×C7×#106C2211yescharacteristic
22C2×C7×C4⋊C8C2211yescharacteristic
23C2×C7×#103C2211yescharacteristic
24C2×C7×#103C2211yescharacteristic
25#90002C2211yescharacteristic
26#90002C2211yescharacteristic
27C2×#6409C2211yescharacteristic
28C2×#6409C2211yescharacteristic
29C2×#6391C2211yescharacteristic
30C2×#6391C2211yescharacteristic
31C2×#6389C2211yescharacteristic
32C2×Dic7⋊C8C2211yescharacteristic
33C2×Dic7⋊C8C2211yescharacteristic
34C2×C8×Dic7C2211yescharacteristic
35#89756—21no—
36#89756—21no—
37#89755—21no—
38#89751—21no—
39#89745C2211yescharacteristic
40#89745C2211yescharacteristic
41#89745C2211yescharacteristic
42#89745C2211yescharacteristic
43#89745C2211yescharacteristic
44#89745C2211yescharacteristic
45#89744—21no—
46#89744—21no—
47#89707C2211yescharacteristic
48C4×C4⋊Dic7C2211yescharacteristic
49#89701—21no—
50#89700—21no—
51C2×#6377C2211yescharacteristic
52#89600—24no—
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#25488—71nomaximal, Sylow
62C22×C7×Q8C2311yescharacteristic
63C22×Dic14D411yescharacteristic
64C22×C7×C8C2311yescharacteristic
65C22×C7×C8C2311yescharacteristic
66C7×#125—22no—
67C7×#125—22no—
68C4×C7×Q8—22no—
69C4×C7×Q8—22no—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C42×C7—21no—
77C2×C42×C7C2311yescharacteristic
78C2×C4⋊Dic7—21no—
79C2×C4⋊Dic7—21no—
80C2×C4⋊Dic7D411yescharacteristic
81C2×C4⋊Dic7C2311yescharacteristic
82C2×C4⋊Dic7C2311yescharacteristic
83C2×C4⋊Dic7C2311yescharacteristic
84C2×C4⋊Dic7C2311yescharacteristic
85C2×Dic7⋊C4—21no—
86C2×Dic7⋊C4—21no—
87C2×Dic7⋊C4—21no—
88C2×Dic7⋊C4—21no—
89C2×Dic7⋊C4—21no—
90C2×Dic7⋊C4—21no—
91C2×Dic7⋊C4D411yescharacteristic
92C2×Dic7⋊C4D411yescharacteristic
93C2×C4×Dic7—21no—
94C2×C4×Dic7C2311yescharacteristic
95C2×C4×Dic7C2311yescharacteristic
96C22×C7⋊C8C2311yescharacteristic
97C22×C7⋊C8C2311yescharacteristic
98C4×Dic14—22no—
99C4×Dic14—22no—
100C7×#107—22no—
101C7×#106—22no—
102C7×C4⋊C8D414yes—
103C7×#103—22no—
104C7×#103—22no—
105#6409—22no—
106#6409Q814yescomplemented
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⋊#95—21no—
116C7⋊#95—21no—
117C7⋊#95—21no—
118#6391—22no—
119#6391—22no—
120#6389—22no—
121Dic7⋊C8—22no—
122Dic7⋊C8—22no—
123C8×Dic7—22no—
124#6377—22no—
125C2×#479D711yescharacteristic
126C2×#446—71no—
127#2584—71no—
128#2582—71no—
129#2088—71no—
130#2087—71no—
131#2066—71no—
132#2066—71no—
133#1992—71no—
134#1948—71no—
135#1944—71no—
136#1941—71no—
137#1935—71no—
138#1933—71no—
139#1763—71no—
140C2×C7×Q8—21no—
141C2×C7×Q8—21no—
142C2×C7×Q8—21no—
143C2×C7×Q8—21no—
144C2×C7×Q8—21no—
145C2×C7×Q8C2×Q812yes—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7C2×D411yescharacteristic
151C22×C4×C7C2×D411yescharacteristic
152C22×C4×C7C2411yescharacteristic
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7C2×D411yescharacteristic
158C22×Dic7C2×D411yescharacteristic
159C22×Dic7C2×D411yescharacteristic
160C22×Dic7C2×D411yescharacteristic
161C2×Dic14—22no—
162C2×Dic14—22no—
163C2×Dic14—41no—
164C2×C7×C8—21no—
165C2×C7×C8—21no—
166C2×C7×C8—21no—
167C2×C7×C8—21no—
168C2×C7×C8C2×D412yes—
169C2×C7×C8C2×D412yes—
170C7×C4⋊C4—21no—
171C7×C4⋊C4—21no—
172C7×C4⋊C4—21no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—21no—
176C7×C4⋊C4—42no—
177C7×C4⋊C4—42no—
178C7×C4⋊C4—42no—
179C42×C7—42no—
180C42×C7C2×D412yes—
181C42×C7#4112yes—
182C4⋊Dic7—22no—
183C4⋊Dic7—21no—
184C4⋊Dic7—21no—
185C4⋊Dic7—21no—
186C4⋊Dic7—21no—
187C4⋊Dic7—21no—
188C4⋊Dic7—21no—
189C4⋊Dic7—42no—
190C4⋊Dic7—81no—
191C4⋊Dic7C2×Q812yes—
192C4⋊Dic7#4112yes—
193Dic7⋊C4—22no—
194Dic7⋊C4—22no—
195Dic7⋊C4—42no—
196Dic7⋊C4—42no—
197Dic7⋊C4—81no—
198Dic7⋊C4—81no—
199Dic7⋊C4—81no—
200Dic7⋊C4—81no—
201C4×Dic7—21no—
202C4×Dic7—21no—
203C4×Dic7—21no—
204C4×Dic7—21no—
205C4×Dic7—81no—
206C2×C7⋊C8—21no—
207C2×C7⋊C8—21no—
208C2×C7⋊C8—21no—
209C2×C7⋊C8—21no—
210C2×C7⋊C8—21no—
211C2×C7⋊C8C2×Q812yes—
212C2×#125C2×D711yescharacteristic
213C2×C4×Q8—71no—
214C2×C4×Q8C2×D711yescharacteristic
215#479—24no—
216#446—144no—
217C2×#107C2×D711yescharacteristic
218C2×#106—71no—
219C2×#106—71no—
220C2×#106C2×D711yescharacteristic
221C2×C4⋊C8—71no—
222C2×C4⋊C8—71no—
223C2×C4⋊C8C2×D711yescharacteristic
224C2×#103—71no—
225C2×#103—71no—
226C2×#103C2×D711yescharacteristic
227C2×#103C2×D711yescharacteristic
228C2×#97—71no—
229C2×#97—71no—
230C2×C4×C8—71no—
231#398—141no—
232#398—141no—
233#398—141no—
234#395—141no—
235#391—71no—
236#391—71no—
237#391—141no—
238#389—71no—
239#389—71no—
240#389—71no—
241#389—71no—
242#389—71no—
243#389—71no—
244#389—141no—
245#389—141no—
246#389—141no—
247#384—71no—
248C4×C4⋊C4—71no—
249#340—71no—
250#340—71no—
251#340—71no—
252#340—71no—
253#340—71no—
254#340—71no—
255#340—71no—
256#340—71no—
257C23×C7C22×D411yescharacteristic
258C7×Q8—22no—
259C7×Q8—22no—
260C7×Q8—41no—
261C7×Q8—41no—
262C2×C4×C7—21no—
263C2×C4×C7—21no—
264C2×C4×C7—21no—
265C2×C4×C7—21no—
266C2×C4×C7—22no—
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—41no—
277C2×C4×C7—41no—
278C2×C4×C7#12112yes—
279C2×C4×C7#12112yes—
280C2×C4×C7C22×D411yescharacteristic
281C2×C4×C7C22×Q811yescharacteristic
282C2×C4×C7C2×#4111yescharacteristic
283C2×C4×C7C2×#4111yescharacteristic
284C2×C4×C72−1+411yescharacteristic
285C2×C4×C72−1+411yescharacteristic
286C2×Dic7—21no—
287C2×Dic7—21no—
288C2×Dic7—21no—
289C2×Dic7—21no—
290C2×Dic7—21no—
291C2×Dic7—22no—
292C2×Dic7—22no—
293C2×Dic7—21no—
294C2×Dic7—21no—
295C2×Dic7—21no—
296C2×Dic7—21no—
297C2×Dic7—21no—
298C2×Dic7—21no—
299C2×Dic7—41no—
300C2×Dic7—41no—
301C2×Dic7—41no—
302C2×Dic7—41no—
303C2×Dic7—41no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—41no—
307C2×Dic7—41no—
308C2×Dic7—41no—
309C2×Dic7#13712yes—
310Dic14—44no—
311C7×C8—22no—
312C7×C8—22no—
313C7⋊C8—22no—
314C7⋊C8—41no—
315C22×Q8—71no—
316C22×Q8C22×D711yescharacteristic
317C22×C8—71no—
318C22×C8—71no—
319C22×C8C22×D711yescharacteristic
320C22×C8C22×D711yescharacteristic
321#125—22no—
322#125—22no—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8—142no—
326C4×Q8—142no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—71no—
331C2×C4⋊C4—71no—
332C2×C4⋊C4—71no—
333C2×C4⋊C4—71no—
334C2×C4⋊C4—71no—
335C2×C4⋊C4—71no—
336C2×C4⋊C4—71no—
337C2×C4⋊C4—141no—
338C2×C4⋊C4—141no—
339C2×C4⋊C4—141no—
340C2×C4⋊C4—141no—
341C2×C4⋊C4—141no—
342C2×C4⋊C4—141no—
343C2×C4⋊C4—141no—
344C2×C4⋊C4—141no—
345C2×C4⋊C4C22×D711yescharacteristic
346C2×C4⋊C4C22×D711yescharacteristic
347C2×C4⋊C4C22×D711yescharacteristic
348C2×C42—21no—
349C2×C42—71no—
350C2×C42—71no—
351C2×C42—141no—
352C2×C42C22×D711yescharacteristic
353#107—22no—
354#106—22no—
355#106—142no—
356#106—142no—
357C4⋊C8—142no—
358C4⋊C8—142no—
359C4⋊C8C22⋊D714yes—
360#103—22no—
361#103—22no—
362#103—74no—
363#103—142no—
364#97—142no—
365#97—142no—
366C4×C8—142no—
367#95—141no—
368#95—141no—
369#95—141no—
370#95—141no—
371#95—141no—
372#95—141no—
373#95—141no—
374#95—141no—
375#95—141no—
376#95—141no—
377#95—141no—
378C22×C7C2×#12111yescharacteristic
379C22×C7#54811yescharacteristic
380C22×C7D4×Q811yescharacteristic
381C22×C7C2×#13711yescharacteristic
382C22×C7#57511yescharacteristic
383C22×C7#57711yescharacteristic
384C22×C7#57711yescharacteristic
385C4×C7—22no—
386C4×C7—22no—
387C4×C7—42no—
388C4×C7—81no—
389C4×C7—81no—
390C4×C7—81no—
391C4×C7#53311yescharacteristic
392C4×C7#54111yescharacteristic
393C4×C7#54711yescharacteristic
394C4×C7D4×Q811yescharacteristic
395Dic7—22no—
396Dic7—42no—
397Dic7—42no—
398Dic7—41no—
399Dic7—41no—
400Dic7—41no—
401Dic7—81no—
402Dic7—81no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—142no—
409C2×Q8—142no—
410C2×Q8—281no—
411C2×Q8Q8×D712yes—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—71no—
417C22×C4—71no—
418C22×C4—71no—
419C22×C4—71no—
420C22×C4—141no—
421C22×C4—141no—
422C22×C4—141no—
423C22×C4—141no—
424C22×C4D4×D711yescharacteristic
425C22×C4D4×D711yescharacteristic
426C22×C4C23×D711yescharacteristic
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—72no—
432C2×C8—141no—
433C2×C8—141no—
434C2×C8—141no—
435C2×C8—141no—
436C2×C8—141no—
437C2×C8C2×C22⋊D712yes—
438C2×C8C2×C22⋊D712yes—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—42no—
446C4⋊C4—42no—
447C4⋊C4—42no—
448C4⋊C4—72no—
449C4⋊C4—72no—
450C4⋊C4—142no—
451C4⋊C4—142no—
452C4⋊C4—142no—
453C4⋊C4—141no—
454C4⋊C4—141no—
455C4⋊C4—141no—
456C4⋊C4—141no—
457C4⋊C4—141no—
458C4⋊C4—141no—
459C4⋊C4—282no—
460C4⋊C4—282no—
461C4⋊C4—282no—
462C4⋊C4—561no—
463C4⋊C4—561no—
464C4⋊C4—561no—
465C4⋊C4—561no—
466C4⋊C4—561no—
467C42—42no—
468C42—141no—
469C42—141no—
470C42—141no—
471C42—141no—
472C42—561no—
473C42#115912yes—
474C42C2×C22⋊D712yes—
475C2×C7#242911yescharacteristic
476C2×C7#305611yescharacteristic
477C2×C7#306011yescharacteristic
478C2×C7#337111yescharacteristic
479C2×C7#337211yescharacteristic
480C2×C7#338711yescharacteristic
481C2×C7#338811yescharacteristic
482C23C2×D4×D711yescharacteristic
483Q8—22no—
484Q8—22no—
485Q8—41no—
486Q8—41no—
487Q8—284no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
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—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—72no—
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—141no—
514C2×C4—141no—
515C2×C4—141no—
516C2×C4—142no—
517C2×C4—142no—
518C2×C4—281no—
519C2×C4—281no—
520C2×C4—281no—
521C2×C4—281no—
522C2×C4—281no—
523C2×C4—281no—
524C2×C4—281no—
525C2×C4—281no—
526C2×C4—281no—
527C2×C4—281no—
528C2×C4#650112yes—
529C2×C4#650112yes—
530C2×C4C2×#115911yescharacteristic
531C2×C4C2×Q8×D711yescharacteristic
532C2×C4#655111yescharacteristic
533C2×C4D7×#4111yescharacteristic
534C2×C4#655411yescharacteristic
535C2×C4C22×C22⋊D711yescharacteristic
536C8—22no—
537C8—22no—
538C8—142no—
539C8—281no—
540C7#2548811yescharacteristic, complemented, Sylow
541C22#9032311yescharacteristic
542C22#9032411yescharacteristic
543C22#9046111yescharacteristic
544C22#9046111yescharacteristic
545C22D7×#13711yescharacteristic
546C22#9046811yescharacteristic
547C22C2×#650111yescharacteristic
548C4—22no—
549C4—22no—
550C4—42no—
551C4—81no—
552C4—81no—
553C4—81no—
554C4—142no—
555C4—282no—
556C4—282no—
557C4—281no—
558C4—281no—
559C4—281no—
560C4—561no—
561C4—561no—
562C4#9031311yescharacteristic
563C4#9031611yescharacteristic
564C4Q8×C22⋊D711yescharacteristic
565C4#9051511yescharacteristic
566C2#1173866311yescharacteristic
567C2#1173866411yescharacteristic
568C2#1173866911yescharacteristic
569C2#1173867011yescharacteristic
570C2#1174020211yescharacteristic
571C2#1174136111yescharacteristic
572C2#1174143011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#479C2
socle, prime radicalC23×C7C22×D4
hypercenterC2×#479D7
hypocenterC7#25488
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
106. #6409Q8semidirect
540. C7#25488semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4792
#117404862
#117399272
C2×#896002
#117294952
#117293852
#117283762
#117283682
#117283222
#117283132
#117282082
#117280102
#117280082
#117280012
#254887