Finite Group Databasebeta

← #13408210

Subgroups — #13408210

Order 1792.

1096 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
1C2×C7×#540C211yesmaximal, characteristic
2C2×#89842C211yesmaximal, characteristic, complemented
3C2×#89837C211yesmaximal, characteristic, complemented
4#11739709C211yesmaximal, characteristic, complemented
5#11729519C211yesmaximal, characteristic, complemented
6#11729494C211yesmaximal, characteristic, complemented
7#11729434C212yesmaximal, complemented
8#11729433C212yesmaximal, complemented
9#11729361C212yesmaximal, complemented
10#11729360C212yesmaximal, complemented
11#11729336C211yesmaximal, characteristic, complemented
12C7×#540—24no—
13C7×#540—24no—
14C2×C7×#127C2211yescharacteristic
15C2×C7×#125C2211yescharacteristic
16C2×C7×#123—21no—
17C2×C7×#123—21no—
18C2×C7×#121—21no—
19C2×C7×#121—21no—
20C2×C7×#121C2211yescharacteristic
21C2×C7×#121C2211yescharacteristic
22C2×C4×C7×D4C2211yescharacteristic
23C2×C4×C7×D4C2211yescharacteristic
24C2×C7×#117C2211yescharacteristic
25C2×#6432C2211yescharacteristic
26C2×#6406C2212yes—
27C2×#6406C2212yes—
28C2×#6406C2212yes—
29C2×#6406C2212yes—
30#89984C2212yes—
31C2×C22⋊(C7⋊C8)C2212yes—
32#89842—24no—
33#89837—24no—
34#89758—21no—
35#89751—21no—
36C2×#6382C2212yes—
37C2×#6381C2212yes—
38#89721—21no—
39#89719—21no—
40#89708C2211yescharacteristic
41#89700C2212yes—
42C2×#6377C2211yescharacteristic
43C2×C4×C7⋊C8C2211yescharacteristic
44#89324C2212yes—
45#89324C2212yes—
46#89319C2212yes—
47#25685—71nomaximal, Sylow
48C22×C7×D4—21no—
49C22×C7×D4—21no—
50C22×C7×D4—21no—
51C22×C7×D4—21no—
52C22×C7×D4C2311yescharacteristic
53C22×C7×D4C2311yescharacteristic
54C23×C4×C7—21no—
55C23×C4×C7—21no—
56C23×C4×C7C2311yescharacteristic
57C22×Dic14—21no—
58C7×#127—22no—
59C7×#127D414yes—
60C7×#125—22no—
61C7×#125D414yes—
62C7×#123—28no—
63C7×#123—28no—
64C7×#121—28no—
65C7×#121—28no—
66C7×#121—22no—
67C7×#121—22no—
68C7×#121—22no—
69C7×#121—22no—
70C4×C7×D4—22no—
71C4×C7×D4—22no—
72C4×C7×D4—22no—
73C4×C7×D4—22no—
74C7×#117—22no—
75C7×#117—22no—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4D411yescharacteristic
79C2×C7×C4⋊C4D411yescharacteristic
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4—21no—
84C2×C7×C22⋊C4—21no—
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4D411yescharacteristic
87C2×C7×C22⋊C4D411yescharacteristic
88C2×C42×C7C2311yescharacteristic
89C2×C42×C7C2311yescharacteristic
90C2×C22⋊Dic7—22no—
91C2×C4⋊Dic7—21no—
92C2×C4⋊Dic7C2312yes—
93C2×C4⋊Dic7C2312yes—
94C2×Dic7⋊C4—22no—
95C22×C7⋊C8C2312yes—
96C22×C7⋊C8C2312yes—
97#6432—22no—
98#6432—22no—
99#6406—24no—
100#6406—24no—
101#6406—24no—
102#6406—24no—
103C7⋊#95—22no—
104C7⋊#95—21no—
105C7⋊#95—21no—
106C7⋊#95—22no—
107C22⋊(C7⋊C8)—24no—
108#6382—24no—
109#6381—24no—
110#6377—22no—
111C4×C7⋊C8—22no—
112C2×#540D711yescharacteristic
113C2×#501—71no—
114C2×#486—71no—
115#2628—71no—
116#2034—72no—
117#2033—72no—
118#1991—71no—
119#1961—71no—
120#1864—72no—
121#1862—72no—
122#1750—71no—
123C24×C7—21no—
124C24×C7—21no—
125C24×C7C2×D411yescharacteristic
126C2×C7×D4—24no—
127C2×C7×D4—24no—
128C2×C7×D4—24no—
129C2×C7×D4—24no—
130C2×C7×D4—21no—
131C2×C7×D4—21no—
132C2×C7×D4—22no—
133C2×C7×D4—22no—
134C2×C7×D4—22no—
135C2×C7×D4—22no—
136C2×C7×D4—82no—
137C2×C7×D4—82no—
138C2×C7×D4—82no—
139C2×C7×D4—82no—
140C2×C7×D4C2×D412yes—
141C2×C7×D4C2×D412yes—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—24no—
145C22×C4×C7—24no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—82no—
151C22×C4×C7—82no—
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2411yescharacteristic
158C22×Dic7—22no—
159C22×Dic7—22no—
160C2×Dic14—42no—
161C2×Dic14—82no—
162C7×C4⋊C4—24no—
163C7×C4⋊C4—24no—
164C7×C4⋊C4—22no—
165C7×C4⋊C4—22no—
166C7×C4⋊C4—21no—
167C7×C4⋊C4—21no—
168C7×C4⋊C4C2×D412yes—
169C7×C4⋊C4C2×D412yes—
170C7×C22⋊C4—24no—
171C7×C22⋊C4—24no—
172C7×C22⋊C4—24no—
173C7×C22⋊C4—24no—
174C7×C22⋊C4—22no—
175C7×C22⋊C4—22no—
176C42×C7—21no—
177C42×C7—21no—
178C42×C7C2×D412yes—
179C42×C7C2×D412yes—
180C22⋊Dic7—82no—
181C4⋊Dic7—22no—
182C4⋊Dic7—22no—
183C4⋊Dic7—22no—
184C4⋊Dic7—22no—
185C4⋊Dic7—42no—
186Dic7⋊C4—82no—
187C2×C7⋊C8—22no—
188C2×C7⋊C8—22no—
189C2×C7⋊C8—22no—
190C2×C7⋊C8—22no—
191C2×C7⋊C8—22no—
192C2×C7⋊C8#4114yes—
193#540—24no—
194#540—24no—
195C2×C4⋊Q8—71no—
196C2×#127C2×D711yescharacteristic
197C2×#125C2×D711yescharacteristic
198C2×#123—21no—
199C2×#123—21no—
200C2×#121—21no—
201C2×#121—21no—
202C2×#121C2×D711yescharacteristic
203C2×#121C2×D711yescharacteristic
204C2×C4×D4C2×D711yescharacteristic
205C2×C4×D4C2×D711yescharacteristic
206C2×#117C2×D711yescharacteristic
207#501—144no—
208#486—144no—
209C2×#107—72no—
210C2×#106—72no—
211C2×#102—72no—
212C2×#102—72no—
213C2×#102—72no—
214C2×#102—72no—
215C2×C22⋊C8—72no—
216C2×#97—71no—
217C2×C4×C8—71no—
218#400—141no—
219#399—141no—
220#395—141no—
221#393—141no—
222#389—72no—
223#382—71no—
224#380—72no—
225#340—72no—
226#340—72no—
227#336—72no—
228C23×C7—21no—
229C23×C7—22no—
230C23×C7—22no—
231C23×C7—21no—
232C23×C7—21no—
233C23×C7—22no—
234C23×C7—22no—
235C23×C7—41no—
236C23×C7—41no—
237C23×C7—41no—
238C23×C7—41no—
239C23×C7—42no—
240C23×C7—42no—
241C23×C7—42no—
242C23×C7—42no—
243C23×C7C22×D411yescharacteristic
244C7×D4—24no—
245C7×D4—24no—
246C7×D4—42no—
247C7×D4—42no—
248C7×D4—84no—
249C7×D4—84no—
250C7×D4—84no—
251C7×D4—84no—
252C2×C4×C7—22no—
253C2×C4×C7—22no—
254C2×C4×C7—21no—
255C2×C4×C7—21no—
256C2×C4×C7—21no—
257C2×C4×C7—22no—
258C2×C4×C7—22no—
259C2×C4×C7—21no—
260C2×C4×C7—21no—
261C2×C4×C7—22no—
262C2×C4×C7—22no—
263C2×C4×C7—42no—
264C2×C4×C7—42no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7—84no—
268C2×C4×C7—84no—
269C2×C4×C7#12012yes—
270C2×C4×C7#12012yes—
271C2×C4×C7C22×D411yescharacteristic
272C2×C4×C7C22×D411yescharacteristic
273C2×C4×C7C2×#4112yes—
274C2×C4×C72−1+412yes—
275C2×Dic7—42no—
276C2×Dic7—42no—
277C2×Dic7—42no—
278C2×Dic7—42no—
279C2×Dic7—42no—
280C2×Dic7—42no—
281Dic14—84no—
282C7⋊C8—24no—
283C7⋊C8—42no—
284C22×Q8—141no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4C22×D711yescharacteristic
290C22×D4C22×D711yescharacteristic
291C23×C4—21no—
292C23×C4—21no—
293C23×C4C22×D711yescharacteristic
294C22×C8—72no—
295C22×C8—72no—
296C4⋊Q8—142no—
297C4⋊Q8—142no—
298#127—22no—
299#127C22⋊D714yes—
300#125—22no—
301#125C22⋊D714yes—
302#123—28no—
303#123—28no—
304#121—28no—
305#121—28no—
306#121—22no—
307#121—22no—
308#121—22no—
309#121—22no—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—22no—
314#117—22no—
315#117—22no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—72no—
319C2×C4⋊C4—72no—
320C2×C4⋊C4—141no—
321C2×C4⋊C4—142no—
322C2×C4⋊C4C22⋊D711yescharacteristic
323C2×C4⋊C4C22⋊D711yescharacteristic
324C2×C4⋊C4C22×D711yescharacteristic
325C2×C4⋊C4C22×D711yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—142no—
331C2×C22⋊C4C22⋊D711yescharacteristic
332C2×C22⋊C4C22⋊D711yescharacteristic
333C2×C42C22×D711yescharacteristic
334C2×C42C22×D711yescharacteristic
335#107—144no—
336#106—144no—
337#102—144no—
338#102—144no—
339#102—144no—
340#102—144no—
341C22⋊C8—144no—
342#97—142no—
343C4×C8—142no—
344#95—142no—
345#95—141no—
346#95—141no—
347#95—142no—
348C22×C7—42no—
349C22×C7—41no—
350C22×C7—42no—
351C22×C7—42no—
352C22×C7—42no—
353C22×C7—42no—
354C22×C7—41no—
355C22×C7—42no—
356C22×C7—42no—
357C22×C7—41no—
358C22×C7—42no—
359C22×C7—82no—
360C22×C7—82no—
361C22×C7—82no—
362C22×C7—82no—
363C22×C7C2×#12011yescharacteristic
364C22×C7#53211yescharacteristic
365C22×C7#53611yescharacteristic
366C22×C7#57612yes—
367C22×C7#57712yes—
368C4×C7—22no—
369C4×C7—22no—
370C4×C7—41no—
371C4×C7—41no—
372C4×C7—42no—
373C4×C7—41no—
374C4×C7—42no—
375C4×C7#54712yes—
376C4×C7#54812yes—
377Dic7—82no—
378Dic7—82no—
379C24—21no—
380C24—21no—
381C24C2×C22⋊D711yescharacteristic
382C2×Q8—282no—
383C2×Q8—562no—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—82no—
395C2×D4—82no—
396C2×D4—82no—
397C2×D4—82no—
398C2×D4C2×C22⋊D712yes—
399C2×D4C2×C22⋊D712yes—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—82no—
409C22×C4—82no—
410C22×C4—142no—
411C22×C4—142no—
412C22×C4C2×C22⋊D711yescharacteristic
413C22×C4C2×C22⋊D711yescharacteristic
414C22×C4C2×C22⋊D711yescharacteristic
415C22×C4C2×C22⋊D711yescharacteristic
416C22×C4C2×C22⋊D711yescharacteristic
417C22×C4C23×D711yescharacteristic
418C2×C8—74no—
419C2×C8—142no—
420C2×C8—142no—
421C2×C8—142no—
422C2×C8—142no—
423C2×C8—142no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—142no—
431C4⋊C4—142no—
432C4⋊C4—142no—
433C4⋊C4—142no—
434C4⋊C4—282no—
435C4⋊C4—562no—
436C4⋊C4C2×C22⋊D712yes—
437C4⋊C4C2×C22⋊D712yes—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—562no—
445C42—21no—
446C42—21no—
447C42C2×C22⋊D712yes—
448C42C2×C22⋊D712yes—
449C2×C7—81no—
450C2×C7—82no—
451C2×C7—82no—
452C2×C7#243211yescharacteristic
453C2×C7#300811yescharacteristic
454C2×C7#300911yescharacteristic
455C2×C7#317912yes—
456C2×C7#324112yes—
457C23—21no—
458C23—21no—
459C23—22no—
460C23—22no—
461C23—21no—
462C23—22no—
463C23—22no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23C22×C22⋊D711yescharacteristic
473Q8—564no—
474D4—24no—
475D4—24no—
476D4—42no—
477D4—42no—
478D4—84no—
479D4—84no—
480D4—84no—
481D4—84no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—84no—
498C2×C4—84no—
499C2×C4—282no—
500C2×C4—282no—
501C2×C4—282no—
502C2×C4—282no—
503C2×C4—282no—
504C2×C4—282no—
505C2×C4#651612yes—
506C2×C4#651612yes—
507C2×C4D7×#4112yes—
508C2×C4#655412yes—
509C2×C4C22×C22⋊D711yescharacteristic
510C2×C4C22×C22⋊D711yescharacteristic
511C8—144no—
512C8—282no—
513C7#2568511yescharacteristic, complemented, Sylow
514C22—41no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—41no—
519C22—42no—
520C22—42no—
521C22—41no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—82no—
526C22—82no—
527C22—82no—
528C22—82no—
529C22#9051611yescharacteristic
530C22#9052311yescharacteristic
531C22#9052612yes—
532C22#9052712yes—
533C22C2×#651611yescharacteristic
534C4—22no—
535C4—22no—
536C4—41no—
537C4—41no—
538C4—42no—
539C4—41no—
540C4—42no—
541C4—562no—
542C4—562no—
543C4#9051512yes—
544C4#9052212yes—
545C2—81no—
546C2—82no—
547C2—82no—
548C2#1174087512yes—
549C2#1174087812yes—
550C2#1174153811yescharacteristic
551C2#1174154611yescharacteristic
552C2#1174155011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#540C2
socleC23×C7C22×D4
hypercenterC2×#540D7
hypocenterC7#25685
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
2. C2×#89842C2semidirect
3. C2×#89837C2semidirect
4. #11739709C2semidirect
5. #11729519C2semidirect
6. #11729494C2semidirect
7. #11729434C2semidirect
8. #11729433C2semidirect
9. #11729361C2semidirect
10. #11729360C2semidirect
11. #11729336C2semidirect
513. C7#25685semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5402
C2×#898422
C2×#898372
#117397092
#117295192
#117294942
#117294342
#117294332
#117293612
#117293602
#117293362
#256857