Finite Group Databasebeta

← #11734186

Subgroups — #11734186

Order 896.

578 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6502C211yesmaximal, characteristic, complemented
2C2×#6498C211yesmaximal, characteristic, complemented
3C7×#392C211yesmaximal, characteristic, complemented
4#89995C211yesmaximal, characteristic, complemented
5#89995C211yesmaximal, characteristic, complemented
6#89994C211yesmaximal, characteristic, complemented
7#89994C211yesmaximal, characteristic, complemented
8#89733C211yesmaximal, characteristic, complemented
9#89731C211yesmaximal, characteristic, complemented
10#89731C211yesmaximal, characteristic, complemented
11#89721C211yesmaximal, characteristic, complemented
12#89720C211yesmaximal, characteristic, complemented
13#89714C211yesmaximal, characteristic, complemented
14#89448C211yesmaximal, characteristic, complemented
15#89430C211yesmaximal, characteristic, complemented
16C22×C7×D4C2211yescharacteristic
17C22×C7×D4C2211yescharacteristic
18C22×C7×D4C2211yescharacteristic
19C22×C22⋊D7C2211yescharacteristic
20C22×C22⋊D7C2211yescharacteristic
21C22×C22⋊D7C2211yescharacteristic
22C23×Dic7C2211yescharacteristic
23C2×C7×C22⋊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
34#6502—24no—
35#6498—24no—
36C2×(C2×D7)⋊C4C2211yescharacteristic
37C2×(C2×D7)⋊C4C2211yescharacteristic
38C2×(C2×D7)⋊C4C2211yescharacteristic
39C2×(C2×D7)⋊C4C2211yescharacteristic
40C2×C4⋊Dic7C2211yescharacteristic
41C2×Dic7⋊C4C2211yescharacteristic
42C2×Dic7⋊C4C2211yescharacteristic
43C2×Dic7⋊C4C2211yescharacteristic
44C2×Dic7⋊C4C2211yescharacteristic
45C2×Dic7⋊C4C2211yescharacteristic
46C2×Dic7⋊C4C2211yescharacteristic
47C7×#95C2211yescharacteristic
48C7⋊#95C2211yescharacteristic
49C7⋊#95C2211yescharacteristic
50C7⋊#95C2211yescharacteristic
51C7⋊#95C2211yescharacteristic
52C7⋊#95C2211yescharacteristic
53#2813—71nomaximal, Sylow
54C24×C7C2311yescharacteristic
55C24×C7C2311yescharacteristic
56C24×C7C2311yescharacteristic
57C23×D7C2311yescharacteristic
58C2×C7×D4—22no—
59C2×C7×D4—22no—
60C2×C7×D4—41no—
61C2×C7×D4—41no—
62C2×C7×D4—41no—
63C2×C7×D4—41no—
64C2×C7×D4—41no—
65C2×C7×D4—41no—
66C2×C7×D4—41no—
67C22×C4×C7C2311yescharacteristic
68C22×C4×C7C2311yescharacteristic
69C22×C4×C7C2311yescharacteristic
70C22×C4×C7C2311yescharacteristic
71C2×C22⋊D7—22no—
72C2×C22⋊D7—22no—
73C2×C22⋊D7—41no—
74C2×C22⋊D7—41no—
75C2×C22⋊D7—41no—
76C2×C22⋊D7—41no—
77C2×C22⋊D7—41no—
78C2×C22⋊D7—41no—
79C2×C22⋊D7—41no—
80C22×Dic7—41no—
81C22×Dic7—41no—
82C22×Dic7D414yescomplemented
83C22×Dic7C2311yescharacteristic
84C22×Dic7C2311yescharacteristic
85C22×Dic7C2311yescharacteristic
86C22×Dic7C2311yescharacteristic
87C22×Dic7C2311yescharacteristic
88C22×Dic7C2311yescharacteristic
89C22×Dic7C2311yescharacteristic
90C7×C22⋊C4—41no—
91C7×C22⋊C4—41no—
92C7×C22⋊C4—41no—
93C22⋊Dic7—22no—
94C22⋊Dic7—22no—
95C22⋊Dic7—22no—
96C22⋊Dic7—22no—
97C22⋊Dic7—41no—
98C22⋊Dic7—41no—
99C22⋊Dic7—41no—
100C22⋊Dic7—41no—
101(C2×D7)⋊C4—22no—
102(C2×D7)⋊C4—41no—
103(C2×D7)⋊C4—41no—
104(C2×D7)⋊C4—41no—
105C4⋊Dic7—41no—
106Dic7⋊C4—22no—
107Dic7⋊C4—22no—
108Dic7⋊C4—22no—
109Dic7⋊C4—41no—
110Dic7⋊C4—41no—
111Dic7⋊C4—41no—
112C2×#123—71no—
113C2×#121—71no—
114#400—71no—
115#399—71no—
116#396—71no—
117#396—71no—
118#394—71no—
119#394—71no—
120#394—71no—
121#394—71no—
122#394—71no—
123#392—71no—
124#392—71no—
125#392D711yescharacteristic, complemented
126#380—71no—
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×C7—21no—
140C23×C7—21no—
141C23×C7—21no—
142C23×C7—21no—
143C23×C7—21no—
144C23×C7—21no—
145C23×C7—21no—
146C23×C7—21no—
147C23×C7C2×D412yes—
148C23×C7C2411yescharacteristic
149C22×D7—21no—
150C22×D7—21no—
151C22×D7—21no—
152C22×D7—21no—
153C22×D7—21no—
154C22×D7—21no—
155C22×D7—21no—
156C7×D4—44no—
157C7×D4—44no—
158C7×D4—44no—
159C2×C4×C7—21no—
160C2×C4×C7—21no—
161C2×C4×C7—21no—
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—
171C22⋊D7—44no—
172C22⋊D7—44no—
173C22⋊D7—44no—
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—21no—
183C2×Dic7—21no—
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—44no—
194C2×Dic7C2×D412yes—
195C2×Dic7C2×D412yes—
196C22×D4—71no—
197C22×D4—71no—
198C22×D4—71no—
199C22×D4C2×D711yescharacteristic
200C22×D4C2×D711yescharacteristic
201C22×D4C2×D711yescharacteristic
202C23×C4—71no—
203#123—144no—
204#121—144no—
205C2×C4⋊C4—71no—
206C2×C4⋊C4—71no—
207C2×C4⋊C4—71no—
208C2×C4⋊C4—71no—
209C2×C4⋊C4—71no—
210C2×C4⋊C4—71no—
211C2×C4⋊C4—71no—
212C2×C22⋊C4—71no—
213C2×C22⋊C4—71no—
214C2×C22⋊C4—71no—
215C2×C22⋊C4—71no—
216C2×C22⋊C4—71no—
217C2×C22⋊C4—71no—
218C2×C22⋊C4—71no—
219C2×C22⋊C4—71no—
220C2×C22⋊C4—71no—
221C2×C22⋊C4—71no—
222C2×C22⋊C4—71no—
223C2×C22⋊C4—71no—
224C2×C22⋊C4C2×D711yescharacteristic
225C2×C22⋊C4C2×D711yescharacteristic
226C2×C22⋊C4C2×D711yescharacteristic
227#95—71no—
228#95—71no—
229#95—71no—
230#95—71no—
231#95—71no—
232#95C2×D711yescharacteristic
233C22×C7—22no—
234C22×C7—22no—
235C22×C7—22no—
236C22×C7—41no—
237C22×C7—41no—
238C22×C7—41no—
239C22×C7—41no—
240C22×C7—41no—
241C22×C7—41no—
242C22×C7—41no—
243C22×C7—41no—
244C22×C7—41no—
245C22×C7—41no—
246C22×C7—41no—
247C22×C7—41no—
248C22×C7—41no—
249C22×C7—41no—
250C22×C7—41no—
251C22×C7—41no—
252C22×C7—41no—
253C22×C7—41no—
254C22×C7C22×D411yescharacteristic
255C22×C7H(5,𝔽2)11yescharacteristic
256C22×C7H(5,𝔽2)11yescharacteristic
257C22×C7H(5,𝔽2)11yescharacteristic
258C22×C7H(5,𝔽2)11yescharacteristic
259C22×C7H(5,𝔽2)11yescharacteristic
260C22×C72−1+411yescharacteristic
261C2×D7—41no—
262C2×D7—41no—
263C2×D7—41no—
264C2×D7—41no—
265C2×D7—41no—
266C2×D7—41no—
267C2×D7—41no—
268C4×C7—41no—
269C4×C7—41no—
270C4×C7—41no—
271C4×C7—41no—
272Dic7—22no—
273Dic7—22no—
274Dic7—41no—
275Dic7—41no—
276Dic7—41no—
277Dic7—41no—
278Dic7—41no—
279C24—71no—
280C24C22×D711yescharacteristic
281C24C22×D711yescharacteristic
282C24C22×D711yescharacteristic
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—142no—
293C2×D4—142no—
294C2×D4—281no—
295C2×D4—281no—
296C2×D4—281no—
297C2×D4—281no—
298C2×D4—281no—
299C2×D4—281no—
300C2×D4—281no—
301C22×C4—71no—
302C22×C4—71no—
303C22×C4—74no—
304C22×C4—71no—
305C22×C4—71no—
306C22×C4—71no—
307C22×C4—71no—
308C22×C4—71no—
309C22×C4—281no—
310C22×C4—281no—
311C22×C4C22×D711yescharacteristic
312C22×C4C22×D711yescharacteristic
313C22×C4C22×D711yescharacteristic
314C22×C4C22×D711yescharacteristic
315C4⋊C4—142no—
316C4⋊C4—142no—
317C4⋊C4—142no—
318C4⋊C4—281no—
319C4⋊C4—281no—
320C4⋊C4—281no—
321C4⋊C4—281no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—142no—
326C22⋊C4—142no—
327C22⋊C4—142no—
328C22⋊C4—142no—
329C22⋊C4—142no—
330C22⋊C4—281no—
331C22⋊C4—281no—
332C22⋊C4—281no—
333C22⋊C4—281no—
334C22⋊C4—281no—
335C22⋊C4—281no—
336C22⋊C4—281no—
337C2×C7—42no—
338C2×C7—81no—
339C2×C7—81no—
340C2×C7#53411yescharacteristic
341C2×C7#53511yescharacteristic
342C2×C7#53711yescharacteristic
343C2×C7#56011yescharacteristic
344C2×C7#56011yescharacteristic
345C2×C7#56211yescharacteristic
346C2×C7#56211yescharacteristic
347D7—81no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—141no—
369C23—141no—
370C23—141no—
371C23—141no—
372C23—141no—
373C23—141no—
374C23—141no—
375C23D4×D712yes—
376C23C23×D711yescharacteristic
377D4—44no—
378D4—44no—
379D4—44no—
380D4—284no—
381D4—284no—
382D4—284no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—72no—
396C2×C4—72no—
397C2×C4—141no—
398C2×C4—141no—
399C2×C4—141no—
400C2×C4—141no—
401C2×C4—141no—
402C2×C4—141no—
403C2×C4—141no—
404C2×C4—141no—
405C2×C4—141no—
406C2×C4—141no—
407C2×C4—141no—
408C2×C4—141no—
409C2×C4—141no—
410C2×C4—141no—
411C2×C4—141no—
412C2×C4—141no—
413C2×C4—141no—
414C2×C4—141no—
415C2×C4—141no—
416C2×C4—284no—
417C7#281311yescharacteristic, complemented, Sylow
418C22—22no—
419C22—22no—
420C22—22no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—281no—
440C22—281no—
441C22—281no—
442C22—281no—
443C22—281no—
444C22—281no—
445C22—281no—
446C22C2×D4×D711yescharacteristic
447C22#654811yescharacteristic
448C22#654811yescharacteristic
449C22#654811yescharacteristic
450C22#654811yescharacteristic
451C22#654811yescharacteristic
452C22#655411yescharacteristic
453C4—41no—
454C4—41no—
455C4—41no—
456C4—41no—
457C4—142no—
458C4—142no—
459C4—281no—
460C4—281no—
461C4—281no—
462C4—281no—
463C4—281no—
464C2—42no—
465C2—81no—
466C2—81no—
467C2—561no—
468C2#9028011yescharacteristic
469C2#9028311yescharacteristic
470C2#9028611yescharacteristic
471C2#9028811yescharacteristic
472C2#9031211yescharacteristic
473C2#9031211yescharacteristic
474C2#9041111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D7
commutator, socle, cosocleC23×C7C24
FittingC7×#392C2
hypercenter#392D7
hypocenterC7#2813
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#6502C2semidirect
2. C2×#6498C2semidirect
3. C7×#392C2semidirect
4. #89995C2semidirect
5. #89995C2semidirect
6. #89994C2semidirect
7. #89994C2semidirect
8. #89733C2semidirect
9. #89731C2semidirect
10. #89731C2semidirect
11. #89721C2semidirect
12. #89720C2semidirect
13. #89714C2semidirect
14. #89448C2semidirect
15. #89430C2semidirect
82. C22×Dic7D4semidirect
125. #392D7semidirect
417. C7#2813semidirect

Maximal subgroups

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

subgroupindex
C2×#65022
C2×#64982
C7×#3922
#899952
#899942
#897332
#897312
#897212
#897202
#897142
#894482
#894302
#28137