Finite Group Databasebeta

← #11740139

Subgroups — #11740139

Order 896.

568 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#121C211yesmaximal, characteristic
2C2×#6498C211yesmaximal, characteristic, complemented
3#89994C211yesmaximal, characteristic, complemented
4#89994C211yesmaximal, characteristic, complemented
5#89992C211yesmaximal, characteristic, complemented
6#89992C211yesmaximal, characteristic, complemented
7#89992C211yesmaximal, characteristic, complemented
8#89982C211yesmaximal, characteristic, complemented
9#89982C211yesmaximal, characteristic, complemented
10#89754C211yesmaximal, characteristic, complemented
11#89752C211yesmaximal, characteristic, complemented
12#89724C211yesmaximal, characteristic, complemented
13#89724C211yesmaximal, characteristic, complemented
14#89718C211yesmaximal, characteristic, complemented
15#89714C211yesmaximal, characteristic, complemented
16C22×C7×D4C2211yescharacteristic
17C22×C7×D4C2211yescharacteristic
18C22×C7×D4C2211yescharacteristic
19C23×C4×C7C2211yescharacteristic
20C23×Dic7C2211yescharacteristic
21C23×Dic7C2211yescharacteristic
22C7×#121—24no—
23C2×C7×C4⋊C4C2211yescharacteristic
24C2×C7×C22⋊C4C2211yescharacteristic
25C2×C7×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic7C2211yescharacteristic
27C2×C22⋊Dic7C2211yescharacteristic
28C2×C22⋊Dic7C2211yescharacteristic
29C2×C22⋊Dic7C2211yescharacteristic
30C2×C22⋊Dic7C2211yescharacteristic
31C2×C22⋊Dic7C2211yescharacteristic
32C2×C22⋊Dic7C2211yescharacteristic
33C2×C22⋊Dic7C2211yescharacteristic
34C2×C22⋊Dic7C2211yescharacteristic
35C2×C22⋊Dic7C2211yescharacteristic
36#6498—24no—
37C2×Dic7⋊C4C2211yescharacteristic
38C2×Dic7⋊C4C2211yescharacteristic
39C2×Dic7⋊C4C2211yescharacteristic
40C2×Dic7⋊C4C2211yescharacteristic
41C2×Dic7⋊C4C2211yescharacteristic
42C2×Dic7⋊C4C2211yescharacteristic
43C7⋊#95C2211yescharacteristic
44C7⋊#95C2211yescharacteristic
45C7⋊#95C2211yescharacteristic
46C7⋊#95C2211yescharacteristic
47C7⋊#95C2211yescharacteristic
48C7⋊#95C2211yescharacteristic
49C7⋊#95C2211yescharacteristic
50C7⋊#95C2211yescharacteristic
51C7⋊#95C2211yescharacteristic
52C7⋊#95C2211yescharacteristic
53#2708—71nomaximal, Sylow
54C24×C7C2311yescharacteristic
55C24×C7C2311yescharacteristic
56C24×C7C2311yescharacteristic
57C2×C7×D4—22no—
58C2×C7×D4—22no—
59C2×C7×D4—22no—
60C2×C7×D4—22no—
61C2×C7×D4—41no—
62C2×C7×D4—41no—
63C2×C7×D4—41no—
64C2×C7×D4—41no—
65C2×C7×D4D414yes—
66C22×C4×C7—22no—
67C22×C4×C7—41no—
68C22×C4×C7—41no—
69C22×C4×C7C2311yescharacteristic
70C22×C4×C7C2311yescharacteristic
71C22×C4×C7C2311yescharacteristic
72C22×C4×C7C2311yescharacteristic
73C22×Dic7—22no—
74C22×Dic7—22no—
75C22×Dic7—41no—
76C22×Dic7—41no—
77C22×Dic7—41no—
78C22×Dic7—41no—
79C22×Dic7C2311yescharacteristic
80C22×Dic7C2311yescharacteristic
81C22×Dic7C2311yescharacteristic
82C22×Dic7C2311yescharacteristic
83C22×Dic7C2311yescharacteristic
84C22×Dic7C2311yescharacteristic
85C22×Dic7C2311yescharacteristic
86C22×Dic7C2311yescharacteristic
87C7×C4⋊C4—22no—
88C7×C22⋊C4—22no—
89C7×C22⋊C4—22no—
90C22⋊Dic7—22no—
91C22⋊Dic7—22no—
92C22⋊Dic7—22no—
93C22⋊Dic7—22no—
94C22⋊Dic7—22no—
95C22⋊Dic7—22no—
96C22⋊Dic7—41no—
97C22⋊Dic7—41no—
98C22⋊Dic7—41no—
99C22⋊Dic7—41no—
100Dic7⋊C4—22no—
101Dic7⋊C4—22no—
102Dic7⋊C4—41no—
103Dic7⋊C4—41no—
104Dic7⋊C4—41no—
105Dic7⋊C4—41no—
106C2×#123—71no—
107C2×#121D711yescharacteristic
108#400—71no—
109#398—71no—
110#397—71no—
111#397—71no—
112#394—71no—
113#394—71no—
114#386—71no—
115#386—71no—
116#386—71no—
117#385—71no—
118#385—71no—
119#385—71no—
120#380—71no—
121C23×C7—21no—
122C23×C7—21no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7—21no—
128C23×C7—21no—
129C23×C7—21no—
130C23×C7—21no—
131C23×C7—21no—
132C23×C7—21no—
133C23×C7—21no—
134C23×C7—21no—
135C23×C7—21no—
136C23×C7—21no—
137C23×C7—21no—
138C23×C7—21no—
139C23×C7C2×D412yes—
140C23×C7C2×D412yes—
141C23×C7#4112yes—
142C23×C7C2411yescharacteristic
143C7×D4—44no—
144C7×D4—44no—
145C7×D4—44no—
146C2×C4×C7—21no—
147C2×C4×C7—21no—
148C2×C4×C7—21no—
149C2×C4×C7—21no—
150C2×C4×C7—21no—
151C2×C4×C7—21no—
152C2×C4×C7—21no—
153C2×C4×C7—21no—
154C2×C4×C7—21no—
155C2×C4×C7—21no—
156C2×C4×C7—21no—
157C2×C4×C7—44no—
158C2×C4×C7C2×D412yes—
159C2×Dic7—21no—
160C2×Dic7—21no—
161C2×Dic7—21no—
162C2×Dic7—21no—
163C2×Dic7—21no—
164C2×Dic7—21no—
165C2×Dic7—21no—
166C2×Dic7—21no—
167C2×Dic7—21no—
168C2×Dic7—21no—
169C2×Dic7—21no—
170C2×Dic7—21no—
171C2×Dic7—21no—
172C2×Dic7—21no—
173C2×Dic7—21no—
174C2×Dic7—21no—
175C2×Dic7—21no—
176C2×Dic7—21no—
177C2×Dic7—21no—
178C2×Dic7—21no—
179C2×Dic7—21no—
180C2×Dic7—21no—
181C2×Dic7—21no—
182C2×Dic7—44no—
183C2×Dic7—44no—
184C2×Dic7#4112yes—
185C22×D4C2×D711yescharacteristic
186C22×D4C2×D711yescharacteristic
187C22×D4C2×D711yescharacteristic
188C23×C4—71no—
189C23×C4—71no—
190C23×C4C2×D711yescharacteristic
191#123—144no—
192#121—24no—
193C2×C4⋊C4—71no—
194C2×C4⋊C4—71no—
195C2×C4⋊C4—71no—
196C2×C4⋊C4—71no—
197C2×C4⋊C4—71no—
198C2×C4⋊C4—71no—
199C2×C4⋊C4C2×D711yescharacteristic
200C2×C22⋊C4—71no—
201C2×C22⋊C4—71no—
202C2×C22⋊C4—71no—
203C2×C22⋊C4—71no—
204C2×C22⋊C4—71no—
205C2×C22⋊C4—71no—
206C2×C22⋊C4—71no—
207C2×C22⋊C4—71no—
208C2×C22⋊C4—71no—
209C2×C22⋊C4—71no—
210C2×C22⋊C4C2×D711yescharacteristic
211C2×C22⋊C4C2×D711yescharacteristic
212#95—71no—
213#95—71no—
214#95—71no—
215#95—71no—
216#95—71no—
217#95—71no—
218#95—71no—
219#95—71no—
220#95—71no—
221#95—71no—
222C22×C7—22no—
223C22×C7—22no—
224C22×C7—22no—
225C22×C7—22no—
226C22×C7—22no—
227C22×C7—22no—
228C22×C7—22no—
229C22×C7—22no—
230C22×C7—22no—
231C22×C7—41no—
232C22×C7—41no—
233C22×C7—41no—
234C22×C7—41no—
235C22×C7—41no—
236C22×C7—41no—
237C22×C7—41no—
238C22×C7—41no—
239C22×C7—41no—
240C22×C7—41no—
241C22×C7—41no—
242C22×C7—41no—
243C22×C7C22×D411yescharacteristic
244C22×C7C2×#4111yescharacteristic
245C22×C7C2×#4111yescharacteristic
246C22×C7H(5,𝔽2)11yescharacteristic
247C22×C7H(5,𝔽2)11yescharacteristic
248C22×C7H(5,𝔽2)11yescharacteristic
249C22×C72−1+411yescharacteristic
250C4×C7—22no—
251C4×C7—41no—
252C4×C7—41no—
253C4×C7—41no—
254Dic7—22no—
255Dic7—41no—
256Dic7—41no—
257Dic7—41no—
258Dic7—41no—
259Dic7—41no—
260Dic7—41no—
261Dic7—41no—
262C24C22×D711yescharacteristic
263C24C22×D711yescharacteristic
264C24C22×D711yescharacteristic
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4C22⋊D714yes—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—71no—
278C22×C4—71no—
279C22×C4—71no—
280C22×C4—71no—
281C22×C4—71no—
282C22×C4—71no—
283C22×C4—71no—
284C22×C4—71no—
285C22×C4—142no—
286C22×C4—142no—
287C22×C4—281no—
288C22×C4—281no—
289C22×C4—281no—
290C22×C4—281no—
291C22×C4C22×D711yescharacteristic
292C22×C4C22×D711yescharacteristic
293C22×C4C22×D711yescharacteristic
294C22×C4C22×D711yescharacteristic
295C4⋊C4—22no—
296C4⋊C4—142no—
297C4⋊C4—142no—
298C4⋊C4—281no—
299C4⋊C4—281no—
300C4⋊C4—281no—
301C4⋊C4—281no—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—142no—
305C22⋊C4—142no—
306C22⋊C4—142no—
307C22⋊C4—142no—
308C22⋊C4—142no—
309C22⋊C4—142no—
310C22⋊C4—281no—
311C22⋊C4—281no—
312C22⋊C4—281no—
313C22⋊C4—281no—
314C2×C7—42no—
315C2×C7—42no—
316C2×C7—42no—
317C2×C7#53411yescharacteristic
318C2×C7#53811yescharacteristic
319C2×C7#53911yescharacteristic
320C2×C7#54611yescharacteristic
321C2×C7#54711yescharacteristic
322C2×C7#55311yescharacteristic
323C2×C7#56211yescharacteristic
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23#115912yes—
343C23C2×C22⋊D712yes—
344C23C2×C22⋊D712yes—
345C23C23×D711yescharacteristic
346D4—44no—
347D4—44no—
348D4—44no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—44no—
361C2×C4—72no—
362C2×C4—141no—
363C2×C4—141no—
364C2×C4—141no—
365C2×C4—141no—
366C2×C4—141no—
367C2×C4—141no—
368C2×C4—141no—
369C2×C4—141no—
370C2×C4—141no—
371C2×C4—141no—
372C2×C4—141no—
373C2×C4—141no—
374C2×C4—141no—
375C2×C4—141no—
376C2×C4—141no—
377C2×C4—141no—
378C2×C4—141no—
379C2×C4—141no—
380C2×C4—141no—
381C2×C4—141no—
382C2×C4—141no—
383C2×C4—141no—
384C2×C4—141no—
385C2×C4—284no—
386C2×C4—284no—
387C2×C4C2×C22⋊D712yes—
388C7#270811yescharacteristic, complemented, Sylow
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22C2×#115911yescharacteristic
411C22#654811yescharacteristic
412C22#654811yescharacteristic
413C22#654811yescharacteristic
414C22D7×#4111yescharacteristic
415C22#655411yescharacteristic
416C22C22×C22⋊D711yescharacteristic
417C4—22no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—142no—
422C4—281no—
423C4—281no—
424C4—281no—
425C4—281no—
426C4—281no—
427C4—281no—
428C4—281no—
429C2—42no—
430C2—42no—
431C2—42no—
432C2#9029211yescharacteristic
433C2#9029311yescharacteristic
434C2#9030411yescharacteristic
435C2#9031211yescharacteristic
436C2#9049511yescharacteristic
437C2#9049711yescharacteristic
438C2#9051511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D7
commutator, socle, cosocleC23×C7C24
Fitting, prime radicalC2×C7×#121C2
hypercenterC2×#121D7
hypocenterC7#2708
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#6498C2semidirect
3. #89994C2semidirect
4. #89994C2semidirect
5. #89992C2semidirect
6. #89992C2semidirect
7. #89992C2semidirect
8. #89982C2semidirect
9. #89982C2semidirect
10. #89754C2semidirect
11. #89752C2semidirect
12. #89724C2semidirect
13. #89724C2semidirect
14. #89718C2semidirect
15. #89714C2semidirect
388. C7#2708semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#1212
C2×#64982
#899942
#899922
#899822
#897542
#897522
#897242
#897182
#897142
#27087