Finite Group Databasebeta

← #11731036

Subgroups — #11731036

Order 896.

710 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6493C211yesmaximal, characteristic, complemented
2C2×#6447C211yesmaximal, characteristic, complemented
3C2×#6446C211yesmaximal, characteristic, complemented
4C2×C4×D28C211yesmaximal, characteristic, complemented
5C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
6#89985C211yesmaximal, characteristic, complemented
7#89733C211yesmaximal, characteristic, complemented
8#89732C211yesmaximal, characteristic, complemented
9#89712C211yesmaximal, characteristic, complemented
10#89712C211yesmaximal, characteristic, complemented
11#89711C211yesmaximal, characteristic, complemented
12#89443C211yesmaximal, characteristic, complemented
13#89440C211yesmaximal, characteristic, complemented
14#89437C211yesmaximal, characteristic, complemented
15#89433C211yesmaximal, characteristic, complemented
16C23×C4×C7C2211yescharacteristic
17C22×C22⋊D7C2211yescharacteristic
18C22×C22⋊D7C2211yescharacteristic
19C22×C22⋊D7C2211yescharacteristic
20C22×D28C2211yescharacteristic
21C22×D28C2211yescharacteristic
22C22×D28C2211yescharacteristic
23C22×C4×D7C2211yescharacteristic
24C22×C4×D7C2211yescharacteristic
25C2×C7×C22⋊C4C2211yescharacteristic
26C2×C7×C22⋊C4C2211yescharacteristic
27C2×C42×C7C2211yescharacteristic
28C2×C42×C7C2211yescharacteristic
29C2×C22⋊Dic7C2211yescharacteristic
30#6493—24no—
31C2×(C2×D7)⋊C4C2211yescharacteristic
32C2×(C2×D7)⋊C4C2211yescharacteristic
33C2×(C2×D7)⋊C4C2211yescharacteristic
34C2×(C2×D7)⋊C4C2211yescharacteristic
35C2×(C2×D7)⋊C4C2211yescharacteristic
36C2×(C2×D7)⋊C4C2211yescharacteristic
37C2×(C2×D7)⋊C4C2211yescharacteristic
38C2×(C2×D7)⋊C4C2211yescharacteristic
39C2×(C2×D7)⋊C4C2211yescharacteristic
40C2×(C2×D7)⋊C4C2211yescharacteristic
41C2×C4⋊Dic7C2211yescharacteristic
42C2×C4⋊Dic7C2211yescharacteristic
43C2×C4⋊Dic7C2211yescharacteristic
44C2×Dic7⋊C4C2211yescharacteristic
45C2×Dic7⋊C4C2211yescharacteristic
46#6447—24no—
47#6446—24no—
48C4×D28—24no—
49C7×#95C2211yescharacteristic
50C7×#95C2211yescharacteristic
51C7⋊#95C2211yescharacteristic
52C7⋊#95C2211yescharacteristic
53C7⋊#95C2211yescharacteristic
54C7⋊#95C2211yescharacteristic
55#2464—71nomaximal, Sylow
56C24×C7C2311yescharacteristic
57C23×D7C2311yescharacteristic
58C23×D7C2311yescharacteristic
59C23×D7C2311yescharacteristic
60C22×C4×C7—22no—
61C22×C4×C7—22no—
62C22×C4×C7—41no—
63C22×C4×C7C2311yescharacteristic
64C22×C4×C7C2311yescharacteristic
65C22×C4×C7C2311yescharacteristic
66C22×C4×C7C2311yescharacteristic
67C22×C4×C7C2311yescharacteristic
68C22×C4×C7C2311yescharacteristic
69C2×C22⋊D7—22no—
70C2×C22⋊D7—22no—
71C2×C22⋊D7—22no—
72C2×C22⋊D7—22no—
73C2×C22⋊D7—22no—
74C2×C22⋊D7—22no—
75C2×C22⋊D7—41no—
76C2×C22⋊D7—41no—
77C2×C22⋊D7—41no—
78C22×Dic7C2311yescharacteristic
79C22×Dic7C2311yescharacteristic
80C22×Dic7C2311yescharacteristic
81C22×Dic7C2311yescharacteristic
82C22×Dic7C2311yescharacteristic
83C2×D28—22no—
84C2×D28—22no—
85C2×D28—22no—
86C2×D28—22no—
87C2×D28—22no—
88C2×D28—22no—
89C2×D28—22no—
90C2×D28—41no—
91C2×D28—41no—
92C2×C4×D7—22no—
93C2×C4×D7—22no—
94C2×C4×D7—22no—
95C2×C4×D7—22no—
96C2×C4×D7—41no—
97C2×C4×D7—41no—
98C7×C22⋊C4—22no—
99C7×C22⋊C4D414yescomplemented
100C42×C7—22no—
101C42×C7—41no—
102C22⋊Dic7—22no—
103(C2×D7)⋊C4—22no—
104(C2×D7)⋊C4—22no—
105(C2×D7)⋊C4—22no—
106(C2×D7)⋊C4—22no—
107(C2×D7)⋊C4—22no—
108(C2×D7)⋊C4—22no—
109(C2×D7)⋊C4—41no—
110(C2×D7)⋊C4—41no—
111(C2×D7)⋊C4—41no—
112(C2×D7)⋊C4D414yescomplemented
113C4⋊Dic7—22no—
114C4⋊Dic7—22no—
115C4⋊Dic7—22no—
116Dic7⋊C4—22no—
117Dic7⋊C4—22no—
118C2×#123—71no—
119C2×#121—71no—
120C2×#121—71no—
121C2×C4×D4—71no—
122#398—71no—
123#394—71no—
124#392—71no—
125#392—71no—
126#390—71no—
127#388—71no—
128#388—71no—
129#386—71no—
130#386—71no—
131#385—71no—
132C4×C22⋊C4D711yescharacteristic, complemented
133C23×C7—21no—
134C23×C7—21no—
135C23×C7—21no—
136C23×C7—21no—
137C23×C7—21no—
138C23×C7—21no—
139C23×C7C2×D412yes—
140C23×C7C2411yescharacteristic
141C22×D7—21no—
142C22×D7—21no—
143C22×D7—21no—
144C22×D7—21no—
145C22×D7—21no—
146C22×D7—21no—
147C22×D7—21no—
148C22×D7—21no—
149C22×D7—21no—
150C22×D7—21no—
151C22×D7—21no—
152C22×D7—21no—
153C22×D7—21no—
154C22×D7—21no—
155C22×D7—21no—
156C22×D7—21no—
157C22×D7—21no—
158C22×D7—21no—
159C22×D7—21no—
160C22×D7C2×D412yes—
161C22×D7#4112yes—
162C2×C4×C7—21no—
163C2×C4×C7—21no—
164C2×C4×C7—21no—
165C2×C4×C7—21no—
166C2×C4×C7—21no—
167C2×C4×C7—21no—
168C2×C4×C7—21no—
169C2×C4×C7—21no—
170C2×C4×C7—21no—
171C2×C4×C7—21no—
172C2×C4×C7—21no—
173C2×C4×C7—21no—
174C2×C4×C7—21no—
175C2×C4×C7—44no—
176C2×C4×C7C2×D412yes—
177C2×C4×C7C2×D412yes—
178C2×C4×C7C2×D412yes—
179C2×C4×C7#4112yes—
180C2×C4×C7#4112yes—
181C22⋊D7—44no—
182C22⋊D7—44no—
183C22⋊D7—44no—
184C2×Dic7—21no—
185C2×Dic7—21no—
186C2×Dic7—21no—
187C2×Dic7—21no—
188C2×Dic7—21no—
189C2×Dic7—21no—
190C2×Dic7—21no—
191C2×Dic7—21no—
192C2×Dic7—21no—
193C2×Dic7—21no—
194C2×Dic7—21no—
195C2×Dic7—21no—
196C2×Dic7—21no—
197C2×Dic7—21no—
198C2×Dic7C2×D412yes—
199D28—28no—
200D28—44no—
201D28—44no—
202C4×D7—44no—
203C4×D7—44no—
204C22×D4—71no—
205C22×D4—71no—
206C22×D4—71no—
207C22×D4—71no—
208C22×D4—71no—
209C22×D4—71no—
210C23×C4—71no—
211C23×C4—71no—
212C23×C4C2×D711yescharacteristic
213#123—144no—
214#121—144no—
215#121—144no—
216C4×D4—144no—
217C2×C4⋊C4—71no—
218C2×C4⋊C4—71no—
219C2×C4⋊C4—71no—
220C2×C4⋊C4—71no—
221C2×C4⋊C4—71no—
222C2×C22⋊C4—71no—
223C2×C22⋊C4—71no—
224C2×C22⋊C4—71no—
225C2×C22⋊C4—71no—
226C2×C22⋊C4—71no—
227C2×C22⋊C4—71no—
228C2×C22⋊C4—71no—
229C2×C22⋊C4—71no—
230C2×C22⋊C4—71no—
231C2×C22⋊C4—71no—
232C2×C22⋊C4—71no—
233C2×C22⋊C4C2×D711yescharacteristic
234C2×C22⋊C4C2×D711yescharacteristic
235C2×C42C2×D711yescharacteristic
236C2×C42C2×D711yescharacteristic
237#95—71no—
238#95—71no—
239#95—71no—
240#95—71no—
241#95C2×D711yescharacteristic
242#95C2×D711yescharacteristic
243C22×C7—22no—
244C22×C7—22no—
245C22×C7—22no—
246C22×C7—41no—
247C22×C7—41no—
248C22×C7—41no—
249C22×C7—41no—
250C22×C7C22×D411yescharacteristic
251C22×C7C22×D411yescharacteristic
252C22×C7C2×#4111yescharacteristic
253C22×C7C2×#4111yescharacteristic
254C22×C7C2×#4111yescharacteristic
255C22×C7H(5,𝔽2)11yescharacteristic
256C22×C7H(5,𝔽2)11yescharacteristic
257C2×D7—22no—
258C2×D7—22no—
259C2×D7—22no—
260C2×D7—22no—
261C2×D7—22no—
262C2×D7—22no—
263C2×D7—41no—
264C2×D7—41no—
265C2×D7—41no—
266C2×D7—41no—
267C2×D7—41no—
268C2×D7—41no—
269C2×D7—41no—
270C2×D7—41no—
271C2×D7—41no—
272C2×D7—41no—
273C2×D7—41no—
274C2×D7—41no—
275C2×D7—41no—
276C2×D7—41no—
277C2×D7—41no—
278C4×C7—22no—
279C4×C7—22no—
280C4×C7—22no—
281C4×C7—22no—
282C4×C7—22no—
283C4×C7—41no—
284Dic7—22no—
285Dic7—41no—
286Dic7—41no—
287Dic7—41no—
288Dic7—41no—
289C24—71no—
290C24—71no—
291C24—71no—
292C24C22×D711yescharacteristic
293C2×D4—142no—
294C2×D4—142no—
295C2×D4—142no—
296C2×D4—142no—
297C2×D4—142no—
298C2×D4—142no—
299C2×D4—142no—
300C2×D4—142no—
301C2×D4—142no—
302C2×D4—142no—
303C2×D4—142no—
304C2×D4—142no—
305C2×D4—142no—
306C2×D4—281no—
307C2×D4—281no—
308C2×D4—281no—
309C2×D4—281no—
310C2×D4—281no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—71no—
315C22×C4—71no—
316C22×C4—71no—
317C22×C4—71no—
318C22×C4—71no—
319C22×C4—142no—
320C22×C4—142no—
321C22×C4—142no—
322C22×C4—142no—
323C22×C4—281no—
324C22×C4—281no—
325C22×C4C22×D711yescharacteristic
326C22×C4C22×D711yescharacteristic
327C22×C4C22×D711yescharacteristic
328C22×C4C22×D711yescharacteristic
329C22×C4C22×D711yescharacteristic
330C22×C4C22×D711yescharacteristic
331C4⋊C4—142no—
332C4⋊C4—142no—
333C4⋊C4—142no—
334C4⋊C4—142no—
335C4⋊C4—142no—
336C22⋊C4—22no—
337C22⋊C4—74no—
338C22⋊C4—142no—
339C22⋊C4—142no—
340C22⋊C4—142no—
341C22⋊C4—142no—
342C22⋊C4—142no—
343C22⋊C4—142no—
344C22⋊C4—142no—
345C22⋊C4—281no—
346C22⋊C4—281no—
347C22⋊C4—281no—
348C22⋊C4D2814yescomplemented
349C42—22no—
350C42—41no—
351C2×C7—42no—
352C2×C7#52511yescharacteristic
353C2×C7#53211yescharacteristic
354C2×C7#54011yescharacteristic
355C2×C7D4211yescharacteristic
356C2×C7#54611yescharacteristic
357C2×C7#54611yescharacteristic
358C2×C7#55311yescharacteristic
359D7—42no—
360D7—42no—
361D7—81no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—72no—
369C23—72no—
370C23—141no—
371C23—141no—
372C23—141no—
373C23—141no—
374C23—141no—
375C23—141no—
376C23—141no—
377C23—141no—
378C23—141no—
379C23—141no—
380C23—141no—
381C23—141no—
382C23—141no—
383C23—141no—
384C23—141no—
385C23—141no—
386C23—141no—
387C23—141no—
388C23—141no—
389C23C2×D2812yes—
390C23C23×D711yescharacteristic
391D4—148no—
392D4—284no—
393D4—284no—
394D4—284no—
395D4—284no—
396D4—284no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—44no—
411C2×C4—72no—
412C2×C4—141no—
413C2×C4—141no—
414C2×C4—141no—
415C2×C4—141no—
416C2×C4—141no—
417C2×C4—141no—
418C2×C4—141no—
419C2×C4—141no—
420C2×C4—141no—
421C2×C4—141no—
422C2×C4—141no—
423C2×C4—141no—
424C2×C4—141no—
425C2×C4—141no—
426C2×C4—284no—
427C2×C4—284no—
428C2×C4C2×D2812yes—
429C2×C4C2×D2812yes—
430C2×C4#115712yes—
431C2×C4#115712yes—
432C2×C4D4×D712yes—
433C7#246411yescharacteristic, complemented, Sylow
434C22—22no—
435C22—22no—
436C22—22no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—142no—
442C22—142no—
443C22—142no—
444C22—142no—
445C22—142no—
446C22—142no—
447C22—281no—
448C22—281no—
449C22—281no—
450C22—281no—
451C22—281no—
452C22—281no—
453C22—281no—
454C22—281no—
455C22—281no—
456C22—281no—
457C22—281no—
458C22—281no—
459C22—281no—
460C22—281no—
461C22—281no—
462C22C22×D2811yescharacteristic
463C22C2×#115711yescharacteristic
464C22C2×#115711yescharacteristic
465C22C2×D4×D711yescharacteristic
466C22#654811yescharacteristic
467C22D7×#4111yescharacteristic
468C22#655311yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—22no—
473C4—22no—
474C4—41no—
475C4—142no—
476C4—281no—
477C4—281no—
478C4—281no—
479C4—281no—
480C2—42no—
481C2—282no—
482C2—282no—
483C2—561no—
484C2#9016811yescharacteristic
485C2#9018111yescharacteristic
486C2#9022111yescharacteristic
487C2#9023811yescharacteristic
488C2D4×D2811yescharacteristic
489C2#9024511yescharacteristic
490C2#9025311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D7
commutator, socle, cosocleC23×C7C24
FittingC4×C7×C22⋊C4C2
hypercenterC4×C22⋊C4D7
hypocenterC7#2464
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#6493C2semidirect
2. C2×#6447C2semidirect
3. C2×#6446C2semidirect
4. C2×C4×D28C2semidirect
5. C4×C7×C22⋊C4C2semidirect
6. #89985C2semidirect
7. #89733C2semidirect
8. #89732C2semidirect
9. #89712C2semidirect
10. #89712C2semidirect
11. #89711C2semidirect
12. #89443C2semidirect
13. #89440C2semidirect
14. #89437C2semidirect
15. #89433C2semidirect
99. C7×C22⋊C4D4semidirect
112. (C2×D7)⋊C4D4semidirect
132. C4×C22⋊C4D7semidirect
348. C22⋊C4D28semidirect
433. C7#2464semidirect

Maximal subgroups

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

subgroupindex
C2×#64932
C2×#64472
C2×#64462
C2×C4×D282
C4×C7×C22⋊C42
#899852
#897332
#897322
#897122
#897112
#894432
#894402
#894372
#894332
#24647