Finite Group Databasebeta

← #11732151

Subgroups — #11732151

Order 896.

610 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6502C211yesmaximal, characteristic
2C2×D4×Dic7C211yesmaximal, characteristic, complemented
3C7×#386C211yesmaximal, characteristic, complemented
4#89985C211yesmaximal, characteristic, complemented
5C2×C7⋊#95C211yesmaximal, characteristic, complemented
6#89733C211yesmaximal, characteristic, complemented
7#89730C211yesmaximal, characteristic, complemented
8#89730C211yesmaximal, characteristic, complemented
9#89725C211yesmaximal, characteristic, complemented
10#89722C211yesmaximal, characteristic, complemented
11#89715C211yesmaximal, characteristic, complemented
12#89446C211yesmaximal, characteristic, complemented
13#89442C211yesmaximal, characteristic, complemented
14#89431C211yesmaximal, characteristic, complemented
15#89425C211yesmaximal, characteristic, complemented
16C22×C7×D4C2211yescharacteristic
17C23×C4×C7C2211yescharacteristic
18C22×C22⋊D7C2211yescharacteristic
19C22×C22⋊D7C2211yescharacteristic
20C23×Dic7C2211yescharacteristic
21C23×Dic7C2211yescharacteristic
22C23×Dic7C2211yescharacteristic
23C2×C7×C22⋊C4C2211yescharacteristic
24C2×C7×C22⋊C4C2211yescharacteristic
25C2×C7×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic7C2211yescharacteristic
27C2×C22⋊Dic7C2211yescharacteristic
28C2×C22⋊Dic7C2211yescharacteristic
29#6502—24no—
30D4×Dic7—24no—
31C2×(C2×D7)⋊C4C2211yescharacteristic
32C2×(C2×D7)⋊C4C2211yescharacteristic
33C2×(C2×D7)⋊C4C2211yescharacteristic
34C2×(C2×D7)⋊C4C2211yescharacteristic
35C2×(C2×D7)⋊C4C2211yescharacteristic
36C2×C4⋊Dic7C2211yescharacteristic
37C2×C4⋊Dic7C2211yescharacteristic
38C2×C4⋊Dic7C2211yescharacteristic
39C2×Dic7⋊C4C2211yescharacteristic
40C2×C4×Dic7C2211yescharacteristic
41C7×#95C2211yescharacteristic
42C7×#95C2211yescharacteristic
43C7⋊#95C2211yescharacteristic
44C7⋊#95C2211yescharacteristic
45C7⋊#95C2211yescharacteristic
46C7⋊#95C2211yescharacteristic
47C7⋊#95C2211yescharacteristic
48C7⋊#95C2211yescharacteristic
49C7⋊#95C2211yescharacteristic
50C7⋊#95C2211yescharacteristic
51C7⋊#95C2211yescharacteristic
52C7⋊#95C2211yescharacteristic
53#2444—71nomaximal, Sylow
54C24×C7C2311yescharacteristic
55C24×C7C2311yescharacteristic
56C23×D7C2311yescharacteristic
57C2×C7×D4—22no—
58C2×C7×D4—22no—
59C2×C7×D4D414yes—
60C22×C4×C7—22no—
61C22×C4×C7—41no—
62C22×C4×C7—41no—
63C22×C4×C7C2311yescharacteristic
64C22×C4×C7C2311yescharacteristic
65C22×C4×C7C2311yescharacteristic
66C22×C4×C7C2311yescharacteristic
67C22×C4×C7C2311yescharacteristic
68C2×C22⋊D7—22no—
69C2×C22⋊D7—22no—
70C2×C22⋊D7—22no—
71C2×C22⋊D7—22no—
72C2×C22⋊D7—22no—
73C2×C22⋊D7—41no—
74C22×Dic7—22no—
75C22×Dic7—22no—
76C22×Dic7—22no—
77C22×Dic7—22no—
78C22×Dic7—22no—
79C22×Dic7—22no—
80C22×Dic7—41no—
81C22×Dic7—41no—
82C22×Dic7—41no—
83C22×Dic7C2311yescharacteristic
84C22×Dic7C2311yescharacteristic
85C22×Dic7C2311yescharacteristic
86C22×Dic7C2311yescharacteristic
87C22×Dic7C2311yescharacteristic
88C22×Dic7C2311yescharacteristic
89C22×Dic7C2311yescharacteristic
90C7×C22⋊C4—22no—
91C7×C22⋊C4—41no—
92C7×C22⋊C4—41no—
93C22⋊Dic7—22no—
94C22⋊Dic7—22no—
95C22⋊Dic7—22no—
96(C2×D7)⋊C4—22no—
97(C2×D7)⋊C4—22no—
98(C2×D7)⋊C4—41no—
99(C2×D7)⋊C4—41no—
100(C2×D7)⋊C4—41no—
101C4⋊Dic7—22no—
102C4⋊Dic7—22no—
103C4⋊Dic7—41no—
104Dic7⋊C4—22no—
105C4×Dic7—22no—
106C2×#121—71no—
107C2×C4×D4—71no—
108#400—71no—
109#397—71no—
110#397—71no—
111#394—71no—
112#388—71no—
113#387—71no—
114#386—71no—
115#386—71no—
116#386—71no—
117#386D711yescharacteristic, complemented
118#385—71no—
119#381—71no—
120C2×#95—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×C7C2×D412yes—
132C23×C7C2×D412yes—
133C23×C7#4112yes—
134C23×C7#4112yes—
135C23×C7C2411yescharacteristic
136C22×D7—21no—
137C22×D7—21no—
138C22×D7—21no—
139C22×D7—21no—
140C22×D7—21no—
141C22×D7—21no—
142C22×D7—21no—
143C7×D4—28no—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
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—21no—
158C2×C4×C7—44no—
159C2×C4×C7C2×D412yes—
160C22⋊D7—44no—
161C22⋊D7—44no—
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—44no—
182C2×Dic7—44no—
183C2×Dic7—44no—
184C2×Dic7#4112yes—
185C2×Dic7#4112yes—
186C22×D4—71no—
187C22×D4—71no—
188C22×D4C2×D711yescharacteristic
189C23×C4—71no—
190C23×C4—71no—
191C23×C4—71no—
192C23×C4C2×D711yescharacteristic
193#121—144no—
194C4×D4—144no—
195C2×C4⋊C4—71no—
196C2×C4⋊C4—71no—
197C2×C4⋊C4—71no—
198C2×C4⋊C4—71no—
199C2×C22⋊C4—71no—
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⋊C4C2×D711yescharacteristic
208C2×C22⋊C4C2×D711yescharacteristic
209C2×C22⋊C4C2×D711yescharacteristic
210C2×C42—71no—
211#95—71no—
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#95C2×D711yescharacteristic
222#95C2×D711yescharacteristic
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—22no—
232C22×C7—41no—
233C22×C7—41no—
234C22×C7—41no—
235C22×C7—41no—
236C22×C7#12314yes—
237C22×C7C22×D411yescharacteristic
238C22×C7C2×#4111yescharacteristic
239C22×C7C2×#4111yescharacteristic
240C22×C7C2×#4111yescharacteristic
241C22×C7C2×#4111yescharacteristic
242C22×C7H(5,𝔽2)11yescharacteristic
243C22×C7H(5,𝔽2)11yescharacteristic
244C2×D7—41no—
245C2×D7—41no—
246C2×D7—41no—
247C2×D7—41no—
248C2×D7—41no—
249C2×D7—41no—
250C2×D7—41no—
251C4×C7—22no—
252C4×C7—41no—
253C4×C7—41no—
254C4×C7—41no—
255C4×C7—41no—
256Dic7—22no—
257Dic7—22no—
258Dic7—41no—
259Dic7—41no—
260Dic7—41no—
261Dic7—41no—
262Dic7—41no—
263C24—71no—
264C24C22×D711yescharacteristic
265C24C22×D711yescharacteristic
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—142no—
269C2×D4—142no—
270C2×D4—142no—
271C2×D4—142no—
272C2×D4—142no—
273C2×D4—281no—
274C2×D4D2814yes—
275C22×C4—22no—
276C22×C4—41no—
277C22×C4—41no—
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—142no—
288C22×C4—142no—
289C22×C4—142no—
290C22×C4—142no—
291C22×C4—281no—
292C22×C4—281no—
293C22×C4—281no—
294C22×C4C22×D711yescharacteristic
295C22×C4C22×D711yescharacteristic
296C22×C4C22×D711yescharacteristic
297C22×C4C22×D711yescharacteristic
298C22×C4C22×D711yescharacteristic
299C4⋊C4—142no—
300C4⋊C4—142no—
301C4⋊C4—142no—
302C4⋊C4—281no—
303C22⋊C4—22no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—142no—
307C22⋊C4—142no—
308C22⋊C4—142no—
309C22⋊C4—142no—
310C22⋊C4—142no—
311C22⋊C4—281no—
312C22⋊C4—281no—
313C22⋊C4—281no—
314C42—142no—
315C2×C7—24no—
316C2×C7—42no—
317C2×C7C2×#12311yescharacteristic
318C2×C7#52911yescharacteristic
319C2×C7#53811yescharacteristic
320C2×C7#54611yescharacteristic
321C2×C7#54611yescharacteristic
322C2×C7#55311yescharacteristic
323C2×C7#55311yescharacteristic
324D7—81no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—141no—
336C23—141no—
337C23—141no—
338C23—141no—
339C23—141no—
340C23—141no—
341C23—141no—
342C23C2×D2812yes—
343C23C2×D2812yes—
344C23#115912yes—
345C23#115912yes—
346C23C23×D711yescharacteristic
347D4—28no—
348D4—284no—
349D4—284no—
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—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—44no—
365C2×C4—72no—
366C2×C4—72no—
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—141no—
386C2×C4—284no—
387C2×C4—284no—
388C2×C4—284no—
389C2×C4C2×D2812yes—
390C7#244411yescharacteristic, complemented, Sylow
391C22—22no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—281no—
405C22—281no—
406C22—281no—
407C22—281no—
408C22—281no—
409C22—281no—
410C22—281no—
411C22#644914yes—
412C22C22×D2811yescharacteristic
413C22C2×#115911yescharacteristic
414C22C2×#115911yescharacteristic
415C22#654811yescharacteristic
416C22#654811yescharacteristic
417C22D7×#4111yescharacteristic
418C22D7×#4111yescharacteristic
419C4—22no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—142no—
425C4—142no—
426C4—281no—
427C4—281no—
428C4—281no—
429C4—281no—
430C4—281no—
431C2—24no—
432C2—42no—
433C2—561no—
434C2C2×#644911yescharacteristic
435C2#9024511yescharacteristic
436C2#9024511yescharacteristic
437C2#9028411yescharacteristic
438C2#9029211yescharacteristic
439C2#9029211yescharacteristic
440C2#9034011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D7
commutator, socle, cosocleC23×C7C24
FittingC7×#386C2
prime radicalC2×#6502C2
hypercenter#386D7
hypocenterC7#2444
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic7C2semidirect
3. C7×#386C2semidirect
4. #89985C2semidirect
5. C2×C7⋊#95C2semidirect
6. #89733C2semidirect
7. #89730C2semidirect
8. #89730C2semidirect
9. #89725C2semidirect
10. #89722C2semidirect
11. #89715C2semidirect
12. #89446C2semidirect
13. #89442C2semidirect
14. #89431C2semidirect
15. #89425C2semidirect
117. #386D7semidirect
390. C7#2444semidirect

Maximal subgroups

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

subgroupindex
C2×#65022
C2×D4×Dic72
C7×#3862
#899852
C2×C7⋊#952
#897332
#897302
#897252
#897222
#897152
#894462
#894422
#894312
#894252
#24447