Finite Group Databasebeta

← #13284050

Subgroups — #13284050

Order 1792.

1282 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89755C211yesmaximal, characteristic
2C2×#89744C212yesmaximal
3C7×C4⋊#95C211yesmaximal, characteristic
4#11729319C211yesmaximal, characteristic
5#11729290C212yesmaximal
6#11727174C212yesmaximal
7#11727165C212yesmaximal
8#11727159C212yesmaximal
9#11727156C212yesmaximal
10C22×C7×C4⋊C4C2211yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C42×C7C2211yescharacteristic
13C22×C4⋊Dic7C2211yescharacteristic
14C22×C4⋊Dic7C2211yescharacteristic
15C22×Dic7⋊C4C2212yes—
16C22×Dic7⋊C4C2212yes—
17C22×Dic7⋊C4C2212yes—
18C22×C4×Dic7C2212yes—
19C2×C7×#95C2212yes—
20C2×C7×#95C2212yes—
21C2×C7⋊#95C2212yes—
22C2×C7⋊#95C2212yes—
23C2×C7⋊#95C2212yes—
24C2×C7⋊#95C2211yescharacteristic
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31#89755C418yescomplemented
32#89744—28no—
33#14587—71nomaximal, Sylow
34C23×C4×C7C2311yescharacteristic
35C23×C4×C7C2311yescharacteristic
36C23×C4×C7C2312yes—
37C23×C4×C7C2312yes—
38C23×C4×C7C2311yescharacteristic
39C23×Dic7C2312yes—
40C23×Dic7C2312yes—
41C23×Dic7C2312yes—
42C23×Dic7C2312yes—
43C2×C7×C4⋊C4—41no—
44C2×C7×C4⋊C4—41no—
45C2×C7×C4⋊C4—41no—
46C2×C7×C4⋊C4—41no—
47C2×C7×C4⋊C4C2×C414yes—
48C2×C7×C4⋊C4D414yes—
49C2×C42×C7—22no—
50C2×C42×C7—41no—
51C2×C42×C7—41no—
52C2×C4⋊Dic7—41no—
53C2×C4⋊Dic7—41no—
54C2×C4⋊Dic7—42no—
55C2×C4⋊Dic7—41no—
56C2×C4⋊Dic7C2×C414yes—
57C2×Dic7⋊C4—24no—
58C2×Dic7⋊C4—24no—
59C2×Dic7⋊C4—24no—
60C2×Dic7⋊C4—24no—
61C2×Dic7⋊C4—24no—
62C2×Dic7⋊C4—42no—
63C2×Dic7⋊C4—42no—
64C2×Dic7⋊C4—42no—
65C2×Dic7⋊C4C2×C418yes—
66C2×C4×Dic7—24no—
67C2×C4×Dic7—24no—
68C2×C4×Dic7—42no—
69C7×#95—42no—
70C7×#95—42no—
71C7⋊#95—24no—
72C7⋊#95—24no—
73C7⋊#95—24no—
74C7⋊#95—41no—
75C7⋊#95—42no—
76C7⋊#95—42no—
77C7⋊#95—42no—
78C7⋊#95C2×C418yes—
79C7⋊#95C2×C414yes—
80C7⋊#95Q818yes—
81C2×#398—71no—
82C2×#389—72no—
83#1444—72no—
84#1441—72no—
85#1441—71no—
86#1436—72no—
87#1436—72no—
88C4⋊#95D711yescharacteristic
89#1434—72no—
90C24×C7C2411yescharacteristic
91C22×C4×C7—21no—
92C22×C4×C7—21no—
93C22×C4×C7—21no—
94C22×C4×C7—21no—
95C22×C4×C7—22no—
96C22×C4×C7—22no—
97C22×C4×C7—22no—
98C22×C4×C7—22no—
99C22×C4×C7—22no—
100C22×C4×C7—22no—
101C22×C4×C7—22no—
102C22×C4×C7—21no—
103C22×C4×C7—22no—
104C22×C4×C7—22no—
105C22×C4×C7—22no—
106C22×C4×C7—22no—
107C22×C4×C7—22no—
108C22×C4×C7—22no—
109C22×C4×C7—21no—
110C22×C4×C7—21no—
111C22×C4×C7—21no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7C22×C412yes—
116C22×C4×C7C22×C412yes—
117C22×C4×C7C22×C412yes—
118C22×C4×C7C2×D414yes—
119C22×C4×C7C2×D412yes—
120C22×C4×C7C2×Q814yes—
121C22×C4×C7#4112yes—
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×Dic7—22no—
144C22×Dic7—22no—
145C22×Dic7C22×C414yes—
146C22×Dic7C22×C414yes—
147C22×Dic7C2×Q814yes—
148C22×Dic7C2×Q814yes—
149C22×Dic7#4114yes—
150C7×C4⋊C4—44no—
151C7×C4⋊C4—44no—
152C42×C7—44no—
153C4⋊Dic7—44no—
154C4⋊Dic7—44no—
155Dic7⋊C4—216no—
156Dic7⋊C4—48no—
157Dic7⋊C4—48no—
158C4×Dic7—48no—
159C22×C4⋊C4—72no—
160C22×C4⋊C4—71no—
161C22×C4⋊C4—72no—
162C22×C4⋊C4—72no—
163C22×C4⋊C4—71no—
164C22×C4⋊C4C2×D711yescharacteristic
165C22×C4⋊C4C2×D711yescharacteristic
166C22×C42—72no—
167C22×C42C2×D711yescharacteristic
168#398—78no—
169#389—148no—
170C2×#95—72no—
171C2×#95—71no—
172C2×#95—72no—
173C2×#95—72no—
174C2×#95—72no—
175C2×#95—72no—
176C2×#95—71no—
177C2×#95—72no—
178C2×#95—72no—
179C2×#95—72no—
180C2×#95C2×D712yes—
181C2×#95C2×D712yes—
182C23×C7C23×C411yescharacteristic
183C23×C7C22×D411yescharacteristic
184C23×C7C22×Q812yes—
185C23×C7C2×#4111yescharacteristic
186C23×C7C2×#4112yes—
187C23×C7H(5,𝔽2)11yescharacteristic
188C23×C7H(5,𝔽2)11yescharacteristic
189C23×C7H(5,𝔽2)11yescharacteristic
190C23×C7H(5,𝔽2)12yes—
191C23×C72−1+411yescharacteristic
192C23×C72−1+412yes—
193C2×C4×C7—22no—
194C2×C4×C7—22no—
195C2×C4×C7—22no—
196C2×C4×C7—22no—
197C2×C4×C7—22no—
198C2×C4×C7—22no—
199C2×C4×C7—22no—
200C2×C4×C7—22no—
201C2×C4×C7—24no—
202C2×C4×C7—24no—
203C2×C4×C7—24no—
204C2×C4×C7—24no—
205C2×C4×C7—24no—
206C2×C4×C7—24no—
207C2×C4×C7—24no—
208C2×C4×C7—24no—
209C2×C4×C7—42no—
210C2×C4×C7—42no—
211C2×C4×C7—42no—
212C2×C4×C7—42no—
213C2×C4×C7—42no—
214C2×C4×C7—42no—
215C2×C4×C7—41no—
216C2×C4×C7—41no—
217C2×C4×C7—42no—
218C2×C4×C7—42no—
219C2×C4×C7—42no—
220C2×C4×C7—42no—
221C2×C4×C7—41no—
222C2×C4×C7—41no—
223C2×C4×C7C4×D414yes—
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—24no—
235C2×Dic7—24no—
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×Dic7—42no—
250C2×Dic7—42no—
251C2×Dic7C4×Q818yes—
252C23×C4—72no—
253C23×C4—72no—
254C23×C4—72no—
255C23×C4—72no—
256C23×C4C22×D711yescharacteristic
257C23×C4C22×D711yescharacteristic
258C23×C4C22×D712yes—
259C23×C4C22×D712yes—
260C23×C4C22×D711yescharacteristic
261C2×C4⋊C4—41no—
262C2×C4⋊C4—41no—
263C2×C4⋊C4—41no—
264C2×C4⋊C4—41no—
265C2×C4⋊C4—78no—
266C2×C4⋊C4—74no—
267C2×C4⋊C4—144no—
268C2×C4⋊C4—144no—
269C2×C4⋊C4—144no—
270C2×C4⋊C4—144no—
271C2×C4⋊C4—144no—
272C2×C4⋊C4—282no—
273C2×C4⋊C4—282no—
274C2×C4⋊C4—282no—
275C2×C4⋊C4—281no—
276C2×C4⋊C4—281no—
277C2×C4⋊C4—282no—
278C2×C4⋊C4—281no—
279C2×C4⋊C4C4×D714yes—
280C2×C4⋊C4D2814yes—
281C2×C42—22no—
282C2×C42—41no—
283C2×C42—41no—
284C2×C42—144no—
285C2×C42—144no—
286C2×C42—282no—
287#95—42no—
288#95—42no—
289#95—74no—
290#95—78no—
291#95—78no—
292#95—144no—
293#95—144no—
294#95—144no—
295#95—282no—
296#95—282no—
297#95—282no—
298#95—281no—
299C22×C7C2×C4×D411yescharacteristic
300C22×C7C2×C4×Q812yes—
301C22×C7#51811yescharacteristic
302C22×C7#52011yescharacteristic
303C22×C7#52012yes—
304C22×C7#53411yescharacteristic
305C22×C7#53711yescharacteristic
306C22×C7#53811yescharacteristic
307C22×C7#53911yescharacteristic
308C22×C7#54012yes—
309C22×C7#54112yes—
310C22×C7#54412yes—
311C22×C7#54412yes—
312C22×C7#54612yes—
313C22×C7D4×Q812yes—
314C22×C7#55212yes—
315C22×C7#55412yes—
316C22×C7#55412yes—
317C22×C7#55511yescharacteristic
318C22×C7Q8211yescharacteristic
319C22×C7#56011yescharacteristic
320C22×C7#56212yes—
321C22×C7#56311yescharacteristic
322C4×C7—24no—
323C4×C7—42no—
324C4×C7—42no—
325C4×C7—44no—
326C4×C7—44no—
327Dic7—28no—
328Dic7—44no—
329Dic7—44no—
330Dic7—82no—
331C24C23×D711yescharacteristic
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—74no—
357C22×C4—74no—
358C22×C4—74no—
359C22×C4—74no—
360C22×C4—74no—
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×C4—142no—
381C22×C4—142no—
382C22×C4—142no—
383C22×C4—142no—
384C22×C4C2×C4×D712yes—
385C22×C4C2×C4×D712yes—
386C22×C4C2×C4×D712yes—
387C22×C4C2×D2814yes—
388C22×C4C2×D2812yes—
389C22×C4#115712yes—
390C22×C4Q8×D714yes—
391C4⋊C4—44no—
392C4⋊C4—44no—
393C4⋊C4—1416no—
394C4⋊C4—284no—
395C4⋊C4—288no—
396C4⋊C4—288no—
397C4⋊C4—284no—
398C42—44no—
399C42—288no—
400C2×C7#232511yescharacteristic
401C2×C7#233012yes—
402C2×C7#236012yes—
403C2×C7#236911yescharacteristic
404C2×C7#237611yescharacteristic
405C2×C7#269911yescharacteristic
406C2×C7#270412yes—
407C2×C7#273411yescharacteristic
408C2×C7#276812yes—
409C2×C7#276911yescharacteristic
410C2×C7#279211yescharacteristic
411C23C22×C4×D711yescharacteristic
412C23C22×D2811yescharacteristic
413C23C2×#115711yescharacteristic
414C23#654811yescharacteristic
415C23#654812yes—
416C23#654811yescharacteristic
417C23#654811yescharacteristic
418C23C2×Q8×D712yes—
419C23#655111yescharacteristic
420C23D7×#4112yes—
421C23#655412yes—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—78no—
453C2×C4—144no—
454C2×C4—144no—
455C2×C4—144no—
456C2×C4—144no—
457C2×C4—144no—
458C2×C4—144no—
459C2×C4—144no—
460C2×C4—144no—
461C2×C4—144no—
462C2×C4—144no—
463C2×C4—144no—
464C2×C4—144no—
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—282no—
475C2×C4—282no—
476C2×C4—282no—
477C2×C4—282no—
478C2×C4—282no—
479C2×C4—282no—
480C2×C4C4×D2814yes—
481C7#1458711yescharacteristic, complemented, Sylow
482C22C2×C4×D2811yescharacteristic
483C22#9017711yescharacteristic
484C22#9018411yescharacteristic
485C22#9018511yescharacteristic
486C22#9019511yescharacteristic
487C22#9020111yescharacteristic
488C22#9020212yes—
489C22#9020611yescharacteristic
490C22#9022012yes—
491C22#9023712yes—
492C22#9024512yes—
493C22C4×Q8×D712yes—
494C22Q8×D2812yes—
495C22#9030612yes—
496C22#9031212yes—
497C22#9031412yes—
498C22#9032712yes—
499C22#9036111yescharacteristic
500C22#9036311yescharacteristic
501C22#9038712yes—
502C22#9041111yescharacteristic
503C22#9041311yescharacteristic
504C22#9042012yes—
505C4—24no—
506C4—44no—
507C4—44no—
508C4—42no—
509C4—42no—
510C4—148no—
511C4—284no—
512C4—284no—
513C4—562no—
514C2#1173077811yescharacteristic
515C2#1173121812yes—
516C2#1173143312yes—
517C2#1173165411yescharacteristic
518C2#1173179511yescharacteristic
519C2#1173341812yes—
520C2#1173371212yes—
521C2#1173375411yescharacteristic
522C2#1173383011yescharacteristic
523C2#1173393911yescharacteristic
524C2#1173401911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, prime radical, cosocleC24×C7C24
hypercenterC4⋊#95D7
hypocenterC7#14587
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
31. #89755C4semidirect
481. C7#14587semidirect

Maximal subgroups

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

subgroupindex
C2×#897552
C2×#897442
C7×C4⋊#952
#117293192
#117292902
#117271742
#117271652
#117271592
#117271562
#145877