Finite Group Databasebeta

← #13060063

Subgroups — #13060063

Order 1344.

436 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic21C211yesmaximal, characteristic, complemented
2C7×#939C211yesmaximal, characteristic
3C3×#6498C211yesmaximal, characteristic, complemented
4#10621138C211yesmaximal, characteristic, complemented
5#10621137C211yesmaximal, characteristic, complemented
6#67⋊Dic7C211yesmaximal, characteristic, complemented
7#10621117C211yesmaximal, characteristic, complemented
8#10621105C211yesmaximal, characteristic, complemented
9C2×Dic7⋊Dic3C211yesmaximal, characteristic, complemented
10#10621101C211yesmaximal, characteristic, complemented
11#10621092C211yesmaximal, characteristic, complemented
12#10620979C211yesmaximal, characteristic, complemented
13#10620944C211yesmaximal, characteristic, complemented
14#10620929C211yesmaximal, characteristic, complemented
15#10620896C211yesmaximal, characteristic, complemented
16#90293—31nomaximal, Hall
17C2×C3×C7×D4C2211yescharacteristic
18C22×Dic21C2211yescharacteristic
19C22×Dic21C2211yescharacteristic
20C2×C7×#67C2211yescharacteristic
21C2×C7×#67C2211yescharacteristic
22C22×C7×Dic3C2211yescharacteristic
23C22×C3×Dic7C2211yescharacteristic
24C2×#4248C2211yescharacteristic
25C2×D3×Dic7C2211yescharacteristic
26#66636C2211yescharacteristic
27#66636C2211yescharacteristic
28C4⋊Dic21C2211yescharacteristic
29C4×Dic21C2211yescharacteristic
30C7×#217C2211yescharacteristic
31C7×(C2×D3)⋊C4C2211yescharacteristic
32C7×Dic3⋊C4C2211yescharacteristic
33C3×C22⋊Dic7C2211yescharacteristic
34C3×C22⋊Dic7C2211yescharacteristic
35C3×C22⋊Dic7C2211yescharacteristic
36C3×Dic7⋊C4C2211yescharacteristic
37C3×Dic7⋊C4C2211yescharacteristic
38Dic3⋊Dic7C2211yescharacteristic
39Dic3⋊Dic7C2211yescharacteristic
40#66577C2211yescharacteristic
41#66577C2211yescharacteristic
42#66577C2211yescharacteristic
43Dic7⋊Dic3C2211yescharacteristic
44Dic7⋊Dic3C2211yescharacteristic
45Dic7⋊Dic3C2211yescharacteristic
46Dic7⋊Dic3C2211yescharacteristic
47Dic7⋊Dic3C2211yescharacteristic
48(C2×D3)⋊Dic7C2211yescharacteristic
49(C2×D3)⋊Dic7C2211yescharacteristic
50(C2×D3)⋊Dic7C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic
52C7×#121—31no—
53#6498—31no—
54#6498—31no—
55#6498—31no—
56#6498D311yescharacteristic, complemented
57D4×Dic7—31no—
58D4×Dic7—31no—
59#6487—31no—
60C2×Dic7⋊C4—31no—
61#6452—31no—
62#6452—31no—
63#6442—31no—
64#6442—31no—
65#6441—31no—
66#6441—31no—
67#5665—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C23×C3×C7C2311yescharacteristic
70C22×D3×C7C2311yescharacteristic
71C3×C7×D4—22no—
72C2×C3×C4×C7C2311yescharacteristic
73C2×Dic21—41no—
74C2×Dic21—41no—
75C2×Dic21C2311yescharacteristic
76C2×Dic21C2311yescharacteristic
77C2×Dic21C2311yescharacteristic
78C2×Dic21C2311yescharacteristic
79C7×#67—22no—
80C7×#67—41no—
81C2×C7×Dic3—41no—
82C2×C7×Dic3C2311yescharacteristic
83C2×C7×Dic3C2311yescharacteristic
84C2×C7×Dic3C2311yescharacteristic
85C2×C3×Dic7—22no—
86C2×C3×Dic7C2311yescharacteristic
87C2×C3×Dic7C2311yescharacteristic
88C2×C3×Dic7C2311yescharacteristic
89C2×C3×Dic7C2311yescharacteristic
90#4248—41no—
91D3×Dic7—41no—
92C2×C7×D4—31no—
93C2×C7×D4—31no—
94C2×C7×D4C2×D311yescharacteristic
95C22×C4×C7—31no—
96C22×Dic7—31no—
97C22×Dic7—31no—
98C22×Dic7—31no—
99C22×Dic7C2×D311yescharacteristic
100C2×Dic14—31no—
101C7×C4⋊C4—31no—
102C7×C22⋊C4—31no—
103C7×C22⋊C4—31no—
104C22⋊Dic7—31no—
105C22⋊Dic7—31no—
106C22⋊Dic7—31no—
107C22⋊Dic7—31no—
108C22⋊Dic7—31no—
109C22⋊Dic7C2×D311yescharacteristic
110C22⋊Dic7C2×D311yescharacteristic
111C22⋊Dic7C2×D311yescharacteristic
112C4⋊Dic7—31no—
113C4⋊Dic7—31no—
114C4⋊Dic7—31no—
115Dic7⋊C4—31no—
116Dic7⋊C4—31no—
117Dic7⋊C4—31no—
118Dic7⋊C4—31no—
119Dic7⋊C4—31no—
120Dic7⋊C4—31no—
121Dic7⋊C4—31no—
122Dic7⋊C4—31no—
123Dic7⋊C4C2×D311yescharacteristic
124Dic7⋊C4C2×D311yescharacteristic
125C4×Dic7—31no—
126C4×Dic7—31no—
127C3×#123—71no—
128#939D711yescharacteristic
129D4×Dic3—71no—
130#929—71no—
131C2×C4⋊Dic3—71no—
132#898—71no—
133#897—71no—
134#890—71no—
135#889—71no—
136#886—71no—
137#883—71no—
138#67⋊C4—71no—
139#879—71no—
140#878—71no—
141#878—71no—
142C22×C3×C7—21no—
143C22×C3×C7—21no—
144C22×C3×C7—21no—
145C22×C3×C7—21no—
146C22×C3×C7—21no—
147C22×C3×C7#4112yes—
148C22×C3×C7C2411yescharacteristic
149C2×D3×C7—21no—
150C2×D3×C7—21no—
151C2×D3×C7—21no—
152C3×C4×C7—21no—
153Dic21—21no—
154Dic21—21no—
155Dic21—21no—
156Dic21—21no—
157C3×Dic7—21no—
158C3×Dic7—21no—
159C3×Dic7—21no—
160C3×Dic7—21no—
161C7×Dic3—21no—
162C7×Dic3—21no—
163C7×Dic3—21no—
164#539—211noSylow
165C23×C7—31no—
166C23×C7C22×D311yescharacteristic
167C23×C7C22×D311yescharacteristic
168C7×D4—22no—
169C7×D4—62no—
170C7×D4—121no—
171C2×C4×C7—31no—
172C2×C4×C7—31no—
173C2×C4×C7—31no—
174C2×C4×C7—121no—
175C2×C4×C7C22×D311yescharacteristic
176C2×Dic7—22no—
177C2×Dic7—31no—
178C2×Dic7—31no—
179C2×Dic7—31no—
180C2×Dic7—31no—
181C2×Dic7—121no—
182C2×Dic7—121no—
183C2×Dic7—121no—
184C2×Dic7C22×D311yescharacteristic
185C2×Dic7C22×D311yescharacteristic
186C2×Dic7C22×D311yescharacteristic
187C2×Dic7C22×D311yescharacteristic
188Dic14—121no—
189C2×C3×D4C2×D711yescharacteristic
190C22×C3×C4—71no—
191C2×#67C2×D711yescharacteristic
192C2×#67C2×D711yescharacteristic
193C22×Dic3—71no—
194C22×Dic3—71no—
195C22×Dic3C2×D711yescharacteristic
196C2×C4×D3—71no—
197C2×Dic6—71no—
198C3×C4⋊C4—71no—
199C3×C4⋊C4—71no—
200C3×C22⋊C4—71no—
201C3×C22⋊C4—71no—
202C3×C22⋊C4—71no—
203#217—71no—
204#217—71no—
205#217C2×D711yescharacteristic
206(C2×D3)⋊C4—71no—
207(C2×D3)⋊C4—71no—
208(C2×D3)⋊C4—71no—
209(C2×D3)⋊C4C2×D711yescharacteristic
210C4⋊Dic3—71no—
211C4⋊Dic3—71no—
212C4⋊Dic3—71no—
213C4⋊Dic3—71no—
214C4⋊Dic3—71no—
215C4⋊Dic3—71no—
216Dic3⋊C4—71no—
217Dic3⋊C4—71no—
218Dic3⋊C4—71no—
219Dic3⋊C4—71no—
220Dic3⋊C4—71no—
221Dic3⋊C4C2×D711yescharacteristic
222C4×Dic3—71no—
223C4×Dic3—71no—
224C2×C3×C7—22no—
225C2×C3×C7—41no—
226C2×C3×C7C2×#4111yescharacteristic
227C2×C3×C7H(5,𝔽2)11yescharacteristic
228C2×C3×C72−1+411yescharacteristic
229D3×C7—41no—
230#126—211no—
231#126—211no—
232#125—211no—
233#125—211no—
234#123—71no—
235#123—211no—
236#123—211no—
237#123—211no—
238C22⋊Q8—211no—
239C22⋊Q8—211no—
240C22⋊Q8—211no—
241#121—31no—
242C4×D4—211no—
243C4×D4—211no—
244C2×C4⋊C4—211no—
245C22×C7—21no—
246C22×C7—21no—
247C22×C7—21no—
248C22×C7—21no—
249C22×C7—21no—
250C22×C7—61no—
251C22×C7—61no—
252C22×C7—61no—
253C22×C7#23712yes—
254C22×C7C23×D311yescharacteristic
255C4×C7—21no—
256C4×C7—61no—
257C4×C7—61no—
258C4×C7—61no—
259Dic7—21no—
260Dic7—21no—
261Dic7—21no—
262Dic7—21no—
263Dic7—61no—
264Dic7—61no—
265Dic7—61no—
266Dic7—61no—
267C23×C3C22×D711yescharacteristic
268C23×C3C22×D711yescharacteristic
269C22×D3C22×D711yescharacteristic
270C3×D4—22no—
271C2×C3×C4—71no—
272C2×C3×C4—71no—
273C2×C3×C4—71no—
274C2×C3×C4—71no—
275C2×C3×C4—142no—
276C2×C3×C4C22×D711yescharacteristic
277#67—22no—
278#67—41no—
279C2×Dic3—41no—
280C2×Dic3—71no—
281C2×Dic3—71no—
282C2×Dic3—71no—
283C2×Dic3—71no—
284C2×Dic3—281no—
285C2×Dic3—281no—
286C2×Dic3C22×D711yescharacteristic
287C2×Dic3C22×D711yescharacteristic
288C2×Dic3C22×D711yescharacteristic
289C4×D3—281no—
290Dic6—281no—
291C3×C7#53911yescharacteristic, complemented, Hall
292C2×Q8—211no—
293C2×D4—31no—
294C2×D4—31no—
295C2×D4D3×D711yescharacteristic
296C22×C4—31no—
297C22×C4—71no—
298C22×C4—211no—
299C22×C4—211no—
300C22×C4—211no—
301C4⋊C4—31no—
302C4⋊C4—71no—
303C4⋊C4—71no—
304C4⋊C4—211no—
305C4⋊C4—211no—
306C4⋊C4—211no—
307C4⋊C4—211no—
308C4⋊C4—211no—
309C4⋊C4—211no—
310C4⋊C4—211no—
311C4⋊C4—211no—
312C4⋊C4—211no—
313C4⋊C4—211no—
314C4⋊C4—211no—
315C22⋊C4—31no—
316C22⋊C4—31no—
317C22⋊C4—71no—
318C22⋊C4—71no—
319C22⋊C4—71no—
320C22⋊C4—211no—
321C22⋊C4—211no—
322C22⋊C4—211no—
323C22⋊C4—211no—
324C22⋊C4—211no—
325C42—211no—
326C42—211no—
327C2×C7—22no—
328C2×C7—41no—
329C2×C7—121no—
330C2×C7C2×#23711yescharacteristic
331C2×C7#100911yescharacteristic
332C2×C7#101011yescharacteristic
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3#115912yes—
339C22×C3C23×D711yescharacteristic
340C2×D3—21no—
341C2×D3—21no—
342C2×D3—21no—
343C3×C4—21no—
344C3×C4—141no—
345C3×C4—141no—
346C3×C4—141no—
347C3×C4—141no—
348Dic3—21no—
349Dic3—21no—
350Dic3—21no—
351Dic3—141no—
352Dic3—141no—
353Dic3—141no—
354Dic3—141no—
355C23—31no—
356C23C2×D3×D711yescharacteristic
357C23C2×D3×D711yescharacteristic
358Q8—841no—
359D4—22no—
360D4—62no—
361D4—121no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—71no—
366C2×C4—71no—
367C2×C4—71no—
368C2×C4—71no—
369C2×C4—121no—
370C2×C4—142no—
371C2×C4—211no—
372C2×C4—211no—
373C2×C4—211no—
374C2×C4—211no—
375C2×C4—841no—
376C2×C4—841no—
377C2×C4—841no—
378C2×C4C2×D3×D711yescharacteristic
379C7#566511yescharacteristic, complemented, Sylow
380C2×C3—22no—
381C2×C3—41no—
382C2×C3C2×#115911yescharacteristic
383C2×C3#654811yescharacteristic
384C2×C3#655411yescharacteristic
385D3—41no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—61no—
392C22—61no—
393C22—61no—
394C22#6668412yes—
395C22C22×D3×D711yescharacteristic
396C4—21no—
397C4—61no—
398C4—61no—
399C4—61no—
400C4—141no—
401C4—141no—
402C4—141no—
403C4—141no—
404C4—421no—
405C4—421no—
406C4—421no—
407C4—421no—
408C3#9029311yescharacteristic, complemented, Sylow
409C2—22no—
410C2—41no—
411C2—121no—
412C2#1062156711yescharacteristic
413C2#1062157411yescharacteristic
414C2C2×#6668411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC2×C3×C7×D4C22
prime radicalC7×#939C2
hypercenterC2×D4D3×D7
hypocenterC3×C7#539
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. D4×Dic21C2semidirect
3. C3×#6498C2semidirect
4. #10621138C2semidirect
5. #10621137C2semidirect
6. #67⋊Dic7C2semidirect
7. #10621117C2semidirect
8. #10621105C2semidirect
9. C2×Dic7⋊Dic3C2semidirect
10. #10621101C2semidirect
11. #10621092C2semidirect
12. #10620979C2semidirect
13. #10620944C2semidirect
14. #10620929C2semidirect
15. #10620896C2semidirect
56. #6498D3semidirect
291. C3×C7#539semidirect
379. C7#5665semidirect
408. C3#90293semidirect

Maximal subgroups

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

subgroupindex
D4×Dic212
C7×#9392
C3×#64982
#106211382
#106211372
#67⋊Dic72
#106211172
#106211052
C2×Dic7⋊Dic32
#106211012
#106210922
#106209792
#106209442
#106209292
#106208962
#902933
#56657