Finite Group Databasebeta

← #13281999

Subgroups — #13281999

Order 1792.

1302 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89750C212yesmaximal
2C2×#89748C211yesmaximal, characteristic
3C2×#89427C212yesmaximal
4C7×#1441C211yesmaximal, characteristic
5#11729319C211yesmaximal, characteristic
6#11727175C212yesmaximal
7#11727175C212yesmaximal
8#11727161C212yesmaximal
9#11727156C212yesmaximal
10C22×C7×C4⋊C4C2211yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C4⋊Dic7C2211yescharacteristic
13C22×C4⋊Dic7C2211yescharacteristic
14C22×Dic7⋊C4C2212yes—
15C22×Dic7⋊C4C2212yes—
16C22×C4×Dic7C2212yes—
17C22×C4×Dic7C2211yescharacteristic
18C2×C7×#95C2212yes—
19C2×C7×#95C2212yes—
20C2×C7×#95C2211yescharacteristic
21C2×C7⋊#95C2212yes—
22C2×C7⋊#95C2212yes—
23C2×C7⋊#95C2212yes—
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31#89750—28no—
32#89748C418yescomplemented
33#89427—28no—
34#14424—71nomaximal, Sylow
35C23×C4×C7C2312yes—
36C23×C4×C7C2311yescharacteristic
37C23×C4×C7C2311yescharacteristic
38C23×C4×C7C2312yes—
39C23×C4×C7C2311yescharacteristic
40C23×Dic7C2312yes—
41C23×Dic7C2312yes—
42C23×Dic7C2312yes—
43C23×Dic7C2312yes—
44C2×C7×C4⋊C4—24no—
45C2×C7×C4⋊C4—41no—
46C2×C7×C4⋊C4—41no—
47C2×C7×C4⋊C4—41no—
48C2×C7×C4⋊C4C2×C414yes—
49C2×C4⋊Dic7—24no—
50C2×C4⋊Dic7—41no—
51C2×C4⋊Dic7—41no—
52C2×C4⋊Dic7—41no—
53C2×C4⋊Dic7C2×C414yes—
54C2×Dic7⋊C4—24no—
55C2×Dic7⋊C4—24no—
56C2×Dic7⋊C4—24no—
57C2×Dic7⋊C4—24no—
58C2×Dic7⋊C4C2×C418yes—
59C2×Dic7⋊C4C2×C418yes—
60C2×C4×Dic7—22no—
61C2×C4×Dic7—22no—
62C2×C4×Dic7—24no—
63C2×C4×Dic7—24no—
64C2×C4×Dic7—42no—
65C2×C4×Dic7C2×C414yes—
66C7×#95—24no—
67C7×#95—24no—
68C7×#95—41no—
69C7⋊#95—24no—
70C7⋊#95—24no—
71C7⋊#95—24no—
72C7⋊#95—24no—
73C7⋊#95—24no—
74C7⋊#95—24no—
75C7⋊#95—24no—
76C7⋊#95—42no—
77C7⋊#95—41no—
78C7⋊#95D418yes—
79C2×#387—72no—
80C2×#387—72no—
81C2×#384—71no—
82#1445—72no—
83#1445—72no—
84#1441—71no—
85#1441D711yescharacteristic
86#1436—72no—
87#1434—72no—
88C24×C7C2411yescharacteristic
89C22×C4×C7—21no—
90C22×C4×C7—21no—
91C22×C4×C7—21no—
92C22×C4×C7—21no—
93C22×C4×C7—22no—
94C22×C4×C7—22no—
95C22×C4×C7—22no—
96C22×C4×C7—22no—
97C22×C4×C7—22no—
98C22×C4×C7—22no—
99C22×C4×C7—21no—
100C22×C4×C7—21no—
101C22×C4×C7—22no—
102C22×C4×C7—21no—
103C22×C4×C7—21no—
104C22×C4×C7—22no—
105C22×C4×C7—22no—
106C22×C4×C7—22no—
107C22×C4×C7—22no—
108C22×C4×C7—22no—
109C22×C4×C7—22no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7C22×C412yes—
115C22×C4×C7C22×C412yes—
116C22×C4×C7C22×C412yes—
117C22×C4×C7C2×D414yes—
118C22×C4×C7#4112yes—
119C22×C4×C7#4112yes—
120C22×Dic7—22no—
121C22×Dic7—22no—
122C22×Dic7—22no—
123C22×Dic7—22no—
124C22×Dic7—22no—
125C22×Dic7—22no—
126C22×Dic7—22no—
127C22×Dic7—22no—
128C22×Dic7—22no—
129C22×Dic7—22no—
130C22×Dic7—22no—
131C22×Dic7—22no—
132C22×Dic7—22no—
133C22×Dic7—22no—
134C22×Dic7—22no—
135C22×Dic7—22no—
136C22×Dic7—22no—
137C22×Dic7—22no—
138C22×Dic7—22no—
139C22×Dic7—22no—
140C22×Dic7—22no—
141C22×Dic7—22no—
142C22×Dic7—22no—
143C22×Dic7C22×C414yes—
144C22×Dic7C22×C414yes—
145C22×Dic7C2×D414yes—
146C22×Dic7C2×D414yes—
147C22×Dic7#4114yes—
148C7×C4⋊C4—44no—
149C7×C4⋊C4—44no—
150C4⋊Dic7—44no—
151C4⋊Dic7—44no—
152Dic7⋊C4—216no—
153Dic7⋊C4—216no—
154C4×Dic7—28no—
155C4×Dic7—48no—
156C22×C4⋊C4—72no—
157C22×C4⋊C4—72no—
158C22×C4⋊C4—71no—
159C22×C4⋊C4—71no—
160C22×C4⋊C4C2×D711yescharacteristic
161C22×C4⋊C4C2×D711yescharacteristic
162C22×C42—71no—
163C22×C42—72no—
164#387—148no—
165#387—148no—
166#384—78no—
167C2×#95—72no—
168C2×#95—72no—
169C2×#95—72no—
170C2×#95—72no—
171C2×#95—72no—
172C2×#95—72no—
173C2×#95—72no—
174C2×#95—72no—
175C2×#95—72no—
176C2×#95—71no—
177C2×#95C2×D712yes—
178C2×#95C2×D712yes—
179C2×#95C2×D711yescharacteristic
180C23×C7C23×C411yescharacteristic
181C23×C7C22×D412yes—
182C23×C7C2×#4111yescharacteristic
183C23×C7C2×#4111yescharacteristic
184C23×C7C2×#4112yes—
185C23×C7H(5,𝔽2)11yescharacteristic
186C23×C7H(5,𝔽2)11yescharacteristic
187C23×C72−1+412yes—
188C23×C72−1+411yescharacteristic
189C23×C72−1+411yescharacteristic
190C23×C72−1+412yes—
191C2×C4×C7—22no—
192C2×C4×C7—22no—
193C2×C4×C7—22no—
194C2×C4×C7—22no—
195C2×C4×C7—22no—
196C2×C4×C7—22no—
197C2×C4×C7—24no—
198C2×C4×C7—24no—
199C2×C4×C7—22no—
200C2×C4×C7—22no—
201C2×C4×C7—24no—
202C2×C4×C7—24no—
203C2×C4×C7—24no—
204C2×C4×C7—42no—
205C2×C4×C7—42no—
206C2×C4×C7—41no—
207C2×C4×C7—41no—
208C2×C4×C7—42no—
209C2×C4×C7—42no—
210C2×C4×C7—42no—
211C2×C4×C7—41no—
212C2×C4×C7—41no—
213C2×C4×C7—42no—
214C2×C4×C7—42no—
215C2×C4×C7—42no—
216C2×C4×C7—42no—
217C2×C4×C7—42no—
218C2×C4×C7—42no—
219C2×C4×C7—42no—
220C2×C4×C7—42no—
221C2×C4×C7#11714yes—
222C2×Dic7—24no—
223C2×Dic7—24no—
224C2×Dic7—24no—
225C2×Dic7—24no—
226C2×Dic7—24no—
227C2×Dic7—24no—
228C2×Dic7—24no—
229C2×Dic7—24no—
230C2×Dic7—24no—
231C2×Dic7—24no—
232C2×Dic7—24no—
233C2×Dic7—24no—
234C2×Dic7—42no—
235C2×Dic7—42no—
236C2×Dic7—42no—
237C2×Dic7—42no—
238C2×Dic7—42no—
239C2×Dic7—42no—
240C2×Dic7—42no—
241C2×Dic7—42no—
242C2×Dic7—42no—
243C2×Dic7—42no—
244C2×Dic7—42no—
245C2×Dic7—42no—
246C2×Dic7—42no—
247C2×Dic7—42no—
248C2×Dic7—42no—
249C2×Dic7C4×D418yes—
250C23×C4—72no—
251C23×C4—72no—
252C23×C4—72no—
253C23×C4—72no—
254C23×C4C22×D712yes—
255C23×C4C22×D711yescharacteristic
256C23×C4C22×D711yescharacteristic
257C23×C4C22×D712yes—
258C23×C4C22×D711yescharacteristic
259C2×C4⋊C4—24no—
260C2×C4⋊C4—41no—
261C2×C4⋊C4—41no—
262C2×C4⋊C4—41no—
263C2×C4⋊C4—78no—
264C2×C4⋊C4—78no—
265C2×C4⋊C4—74no—
266C2×C4⋊C4—144no—
267C2×C4⋊C4—144no—
268C2×C4⋊C4—144no—
269C2×C4⋊C4—144no—
270C2×C4⋊C4—144no—
271C2×C4⋊C4—281no—
272C2×C4⋊C4—281no—
273C2×C4⋊C4—281no—
274C2×C4⋊C4C4×D714yes—
275C2×C42—74no—
276C2×C42—142no—
277C2×C42—142no—
278C2×C42—144no—
279C2×C42—144no—
280C2×C42—282no—
281#95—24no—
282#95—24no—
283#95—41no—
284#95—78no—
285#95—144no—
286#95—144no—
287#95—144no—
288#95—144no—
289#95—144no—
290#95—144no—
291#95—144no—
292#95—281no—
293#95—282no—
294C22×C7C2×#11711yescharacteristic
295C22×C7C2×C4×D412yes—
296C22×C7#51811yescharacteristic
297C22×C7#51911yescharacteristic
298C22×C7#51912yes—
299C22×C7#53612yes—
300C22×C7#53612yes—
301C22×C7#53911yescharacteristic
302C22×C7#53911yescharacteristic
303C22×C7#53911yescharacteristic
304C22×C7#53911yescharacteristic
305C22×C7#54112yes—
306C22×C7#54112yes—
307C22×C7D4211yescharacteristic
308C22×C7#54712yes—
309C22×C7#54712yes—
310C22×C7#55012yes—
311C22×C7#55212yes—
312C22×C7#55212yes—
313C22×C7#55911yescharacteristic
314C22×C7#56311yescharacteristic
315C22×C7#56312yes—
316C22×C7#56311yescharacteristic
317C4×C7—24no—
318C4×C7—42no—
319C4×C7—42no—
320C4×C7—44no—
321C4×C7—82no—
322Dic7—28no—
323Dic7—44no—
324Dic7—44no—
325Dic7—82no—
326C24C23×D711yescharacteristic
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—74no—
353C22×C4—74no—
354C22×C4—74no—
355C22×C4—74no—
356C22×C4—74no—
357C22×C4—142no—
358C22×C4—142no—
359C22×C4—142no—
360C22×C4—142no—
361C22×C4—142no—
362C22×C4—142no—
363C22×C4—142no—
364C22×C4—142no—
365C22×C4—142no—
366C22×C4—142no—
367C22×C4—142no—
368C22×C4—142no—
369C22×C4—142no—
370C22×C4—142no—
371C22×C4—142no—
372C22×C4—142no—
373C22×C4—142no—
374C22×C4—142no—
375C22×C4—142no—
376C22×C4—142no—
377C22×C4—142no—
378C22×C4—142no—
379C22×C4—142no—
380C22×C4C2×C4×D712yes—
381C22×C4C2×C4×D712yes—
382C22×C4C2×C4×D712yes—
383C22×C4D4×D714yes—
384C22×C4#115912yes—
385C22×C4#116112yes—
386C4⋊C4—44no—
387C4⋊C4—44no—
388C4⋊C4—1416no—
389C4⋊C4—1416no—
390C4⋊C4—284no—
391C4⋊C4—284no—
392C42—148no—
393C42—288no—
394C2×C7#231311yescharacteristic
395C2×C7#232712yes—
396C2×C7#234412yes—
397C2×C7#236611yescharacteristic
398C2×C7#238111yescharacteristic
399C2×C7#268011yescharacteristic
400C2×C7#268011yescharacteristic
401C2×C7#272112yes—
402C2×C7#272112yes—
403C2×C7#279411yescharacteristic
404C2×C7#279411yescharacteristic
405C23C22×C4×D711yescharacteristic
406C23C2×D4×D712yes—
407C23C2×#115911yescharacteristic
408C23#654811yescharacteristic
409C23#654811yescharacteristic
410C23C2×#116111yescharacteristic
411C23#655112yes—
412C23D7×#4112yes—
413C23#655412yes—
414C23#655411yescharacteristic
415C23#655411yescharacteristic
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—78no—
447C2×C4—144no—
448C2×C4—144no—
449C2×C4—144no—
450C2×C4—144no—
451C2×C4—144no—
452C2×C4—144no—
453C2×C4—144no—
454C2×C4—144no—
455C2×C4—144no—
456C2×C4—144no—
457C2×C4—144no—
458C2×C4—144no—
459C2×C4—282no—
460C2×C4—282no—
461C2×C4—282no—
462C2×C4—282no—
463C2×C4—282no—
464C2×C4—282no—
465C2×C4—282no—
466C2×C4—282no—
467C2×C4—282no—
468C2×C4—282no—
469C2×C4—282no—
470C2×C4—282no—
471C2×C4—282no—
472C2×C4—282no—
473C2×C4—282no—
474C2×C4#645514yes—
475C7#1442411yescharacteristic, complemented, Sylow
476C22#9017711yescharacteristic
477C22C2×#645511yescharacteristic
478C22#9020711yescharacteristic
479C22C4×D4×D712yes—
480C22#9026312yes—
481C22#9028111yescharacteristic
482C22#9029012yes—
483C22#9029311yescharacteristic
484C22#9029311yescharacteristic
485C22#9030212yes—
486C22#9031912yes—
487C22#9033012yes—
488C22#9033611yescharacteristic
489C22#9033611yescharacteristic
490C22#9033712yes—
491C22#9033912yes—
492C22#9035511yescharacteristic
493C22#9036311yescharacteristic
494C22#9038512yes—
495C22#9038712yes—
496C22#9039212yes—
497C22#9041712yes—
498C22#9042611yescharacteristic
499C4—24no—
500C4—42no—
501C4—42no—
502C4—44no—
503C4—82no—
504C4—148no—
505C4—284no—
506C4—284no—
507C4—562no—
508C2#1173131211yescharacteristic
509C2#1173212411yescharacteristic
510C2#1173239312yes—
511C2#1173364512yes—
512C2#1173394211yescharacteristic
513C2#1173444911yescharacteristic
514C2#1173470711yescharacteristic
515C2#1173480912yes—
516C2#1173530712yes—
517C2#1173536011yescharacteristic
518C2#1173574511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1441C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1441D7
hypocenterC7#14424
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
32. #89748C4semidirect
475. C7#14424semidirect

Maximal subgroups

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

subgroupindex
C2×#897502
C2×#897482
C2×#894272
C7×#14412
#117293192
#117271752
#117271612
#117271562
#144247