Finite Group Databasebeta

← #13059524

Subgroups — #13059524

Order 1344.

584 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#235C211yesmaximal, characteristic, complemented
2C2×#66686C211yesmaximal, characteristic, complemented
3#10621412C211yesmaximal, characteristic, complemented
4C2×C3×Dic7⋊C4C211yesmaximal, characteristic, complemented
5#10621128C211yesmaximal, characteristic, complemented
6#67×Dic7C211yesmaximal, characteristic, complemented
7#10621101C211yesmaximal, characteristic, complemented
8#10621008C211yesmaximal, characteristic, complemented
9#10620986C211yesmaximal, characteristic, complemented
10#10620985C211yesmaximal, characteristic, complemented
11#10620978C211yesmaximal, characteristic, complemented
12D3×Dic7⋊C4C211yesmaximal, characteristic, complemented
13#10620914C211yesmaximal, characteristic, complemented
14#10620913C211yesmaximal, characteristic, complemented
15#10620891C211yesmaximal, characteristic, complemented
16#90515—31nomaximal, Hall
17C22×C3×C4×C7C2211yescharacteristic
18C2×#4268C2211yescharacteristic
19C2×C7×#67C2211yescharacteristic
20C2×C7×#67C2211yescharacteristic
21C7×#235—24no—
22C2×C7×D12C2211yescharacteristic
23C2×C4×D3×C7C2211yescharacteristic
24C2×C4×D3×C7C2211yescharacteristic
25C2×C7×Dic6C2211yescharacteristic
26C22×C3×Dic7C2211yescharacteristic
27C22×C3×Dic7C2211yescharacteristic
28C2×#4248C2211yescharacteristic
29C2×#4247C2211yescharacteristic
30C2×#4247C2211yescharacteristic
31C2×D21⋊C4C2211yescharacteristic
32#66686—24no—
33C2×D3×Dic7C2211yescharacteristic
34C2×D3×Dic7C2211yescharacteristic
35#66636C2211yescharacteristic
36#66631C2211yescharacteristic
37#66631C2211yescharacteristic
38#66629C2211yescharacteristic
39#66629C2211yescharacteristic
40C3×Dic7⋊C4C2211yescharacteristic
41C3×Dic7⋊C4C2211yescharacteristic
42C3×Dic7⋊C4C2211yescharacteristic
43C3×Dic7⋊C4C2211yescharacteristic
44Dic3⋊Dic7C2211yescharacteristic
45#66577C2211yescharacteristic
46#66577C2211yescharacteristic
47Dic7⋊Dic3C2211yescharacteristic
48#66575C2211yescharacteristic
49(C2×D3)⋊Dic7C2211yescharacteristic
50(C2×D3)⋊Dic7C2211yescharacteristic
51(C2×D3)⋊Dic7C2211yescharacteristic
52(C2×D3)⋊Dic7C2211yescharacteristic
53Dic3×Dic7C2211yescharacteristic
54C2×C7×#41—31no—
55C2×#1159—31no—
56#6509—31no—
57#6507—31no—
58#6502—31no—
59#6502—31no—
60#6498—31no—
61#6498—31no—
62D4×Dic7—31no—
63#6492—31no—
64#6492—31no—
65C4×C22⋊D7—31no—
66#6487—31no—
67C2×Dic7⋊C4—31no—
68C2×Dic7⋊C4D311yescharacteristic, complemented
69#5507—71nomaximal, Hall
70C23×C3×C7C2311yescharacteristic
71C22×D21C2311yescharacteristic
72C22×D3×C7C2311yescharacteristic
73C22×D3×C7C2311yescharacteristic
74C2×C3×C4×C7—22no—
75C2×C3×C4×C7C2311yescharacteristic
76C2×C3×C4×C7C2311yescharacteristic
77#4268—22no—
78C2×Dic21C2311yescharacteristic
79C2×Dic21C2311yescharacteristic
80C2×Dic21C2311yescharacteristic
81C7×#67—22no—
82C7×#67D414yescomplemented
83C2×C7×Dic3C2311yescharacteristic
84C2×C7×Dic3C2311yescharacteristic
85C7×D12—22no—
86C4×D3×C7—22no—
87C4×D3×C7—22no—
88C7×Dic6—22no—
89C2×C3×Dic7—22no—
90C2×C3×Dic7—22no—
91C2×C3×Dic7C2311yescharacteristic
92C2×C3×Dic7C2311yescharacteristic
93C2×C3×Dic7C2311yescharacteristic
94C2×C3×Dic7C2311yescharacteristic
95#4248—22no—
96#4247—22no—
97#4247—22no—
98D21⋊C4—22no—
99D3×Dic7—22no—
100D3×Dic7—22no—
101C7×#41—64no—
102C2×C7×Q8—31no—
103C2×C7×D4—31no—
104C2×C7×D4—31no—
105C2×C7×D4—31no—
106C22×C4×C7—31no—
107C22×C4×C7—31no—
108C22×C4×C7C2×D311yescharacteristic
109C2×C22⋊D7—31no—
110C2×C22⋊D7—31no—
111C2×C22⋊D7—31no—
112C22×Dic7—31no—
113C22×Dic7—31no—
114C22×Dic7C2×D311yescharacteristic
115C22×Dic7C2×D311yescharacteristic
116#1159—64no—
117C2×C4×D7—31no—
118C2×Dic14—31no—
119C22⋊Dic7—31no—
120C22⋊Dic7—31no—
121C22⋊Dic7—31no—
122C22⋊Dic7—31no—
123C22⋊Dic7—31no—
124(C2×D7)⋊C4—31no—
125(C2×D7)⋊C4—31no—
126(C2×D7)⋊C4—31no—
127C4⋊Dic7—31no—
128Dic7⋊C4—31no—
129Dic7⋊C4—31no—
130Dic7⋊C4—31no—
131Dic7⋊C4—31no—
132Dic7⋊C4—31no—
133Dic7⋊C4C2×D311yescharacteristic
134Dic7⋊C4C2×D311yescharacteristic
135Dic7⋊C4C2×D311yescharacteristic
136Dic7⋊C4C2×D311yescharacteristic
137C4×Dic7—31no—
138C2×#235—71no—
139C2×#235D711yescharacteristic, complemented
140C2×C3×C4⋊C4—71no—
141#930—71no—
142#929—71no—
143#929—71no—
144C4×#67—71no—
145#896—71no—
146#896—71no—
147#895—71no—
148#894—71no—
149#894—71no—
150#893—71no—
151D3×C4⋊C4—71no—
152#888—71no—
153C22×C3×C7—21no—
154C22×C3×C7—21no—
155C22×C3×C7C2×D412yes—
156C22×C3×C7C2411yescharacteristic
157C2×D21—21no—
158C2×D21—21no—
159C2×D21—21no—
160C2×D3×C7—21no—
161C2×D3×C7—21no—
162C2×D3×C7—21no—
163C2×D3×C7—21no—
164C2×D3×C7—21no—
165C2×D3×C7C2×D412yes—
166C3×C4×C7—21no—
167C3×C4×C7—21no—
168Dic21—21no—
169Dic21—21no—
170Dic21—21no—
171C3×Dic7—21no—
172C3×Dic7—21no—
173C3×Dic7—21no—
174C3×Dic7#4112yescomplemented
175C7×Dic3—21no—
176C7×Dic3C2×D412yes—
177#547—211noSylow
178C23×C7—31no—
179C23×C7—31no—
180C23×C7C22×D311yescharacteristic
181C22×D7—31no—
182C7×Q8—62no—
183C7×D4—34no—
184C7×D4—62no—
185C7×D4—62no—
186C2×C4×C7—22no—
187C2×C4×C7—31no—
188C2×C4×C7—31no—
189C2×C4×C7—62no—
190C2×C4×C7—62no—
191C2×C4×C7C22×D311yescharacteristic
192C2×C4×C7C22×D311yescharacteristic
193C22⋊D7—62no—
194C22⋊D7—62no—
195C22⋊D7—62no—
196C2×Dic7—22no—
197C2×Dic7—22no—
198C2×Dic7—31no—
199C2×Dic7—31no—
200C2×Dic7—31no—
201C2×Dic7—62no—
202C2×Dic7—62no—
203C2×Dic7C22×D311yescharacteristic
204C2×Dic7C22×D311yescharacteristic
205C2×Dic7C22×D311yescharacteristic
206C2×Dic7C22×D311yescharacteristic
207C4×D7—62no—
208Dic14—62no—
209C22×C3×C4—71no—
210C22×C3×C4—71no—
211C22×C3×C4C2×D711yescharacteristic
212C2×#67—71no—
213C2×#67C2×D711yescharacteristic
214C2×#67C2×D711yescharacteristic
215#235—24no—
216#235—144no—
217C2×D12—71no—
218C2×D12—71no—
219C2×D12C2×D711yescharacteristic
220C2×C4×D3—71no—
221C2×C4×D3—71no—
222C2×C4×D3—71no—
223C2×C4×D3C2×D711yescharacteristic
224C2×C4×D3C2×D711yescharacteristic
225C2×Dic6—71no—
226C2×Dic6C2×D711yescharacteristic
227C3×C4⋊C4—71no—
228C3×C4⋊C4—71no—
229C3×C4⋊C4—71no—
230C3×C4⋊C4—71no—
231#217—71no—
232(C2×D3)⋊C4—71no—
233(C2×D3)⋊C4—71no—
234(C2×D3)⋊C4—71no—
235(C2×D3)⋊C4—71no—
236(C2×D3)⋊C4—71no—
237(C2×D3)⋊C4—71no—
238(C2×D3)⋊C4—71no—
239C4⋊Dic3—71no—
240Dic3⋊C4—71no—
241Dic3⋊C4—71no—
242Dic3⋊C4—71no—
243Dic3⋊C4—71no—
244Dic3⋊C4—71no—
245C4×Dic3—71no—
246C2×C3×C7—22no—
247C2×C3×C7C22×D411yescharacteristic
248C2×C3×C7C2×#4111yescharacteristic
249C2×C3×C72−1+411yescharacteristic
250D21—41no—
251D3×C7—22no—
252D3×C7—41no—
253C2×#41—31no—
254C2×#41—211no—
255C4⋊Q8—211no—
256#123—211no—
257#123—211no—
258#123—211no—
259#123—211no—
260C22⋊Q8—211no—
261C22⋊Q8—211no—
262#121—211no—
263#121—211no—
264C4×D4—211no—
265C4×D4—211no—
266C2×C4⋊C4—71no—
267C2×C4⋊C4—211no—
268C22×C7—21no—
269C22×C7—21no—
270C22×C7—32no—
271C22×C7—61no—
272C22×C7—61no—
273C22×C7—61no—
274C22×C7—61no—
275C22×C7—61no—
276C22×C7D3×D412yes—
277C22×C7C23×D311yescharacteristic
278C2×D7—61no—
279C2×D7—61no—
280C2×D7—61no—
281C4×C7—21no—
282C4×C7—21no—
283C4×C7—32no—
284C4×C7—61no—
285Dic7—21no—
286Dic7—21no—
287Dic7—21no—
288Dic7—61no—
289Dic7—61no—
290Dic7—61no—
291Dic7#23512yescomplemented
292C23×C3C22×D711yescharacteristic
293C22×D3—71no—
294C22×D3C22×D711yescharacteristic
295C22×D3C22×D711yescharacteristic
296C2×C3×C4—22no—
297C2×C3×C4—71no—
298C2×C3×C4—71no—
299C2×C3×C4—71no—
300C2×C3×C4—71no—
301C2×C3×C4—142no—
302C2×C3×C4—142no—
303C2×C3×C4C22×D711yescharacteristic
304C2×C3×C4C22×D711yescharacteristic
305#67—22no—
306#67—142no—
307#67C22⋊D714yescomplemented
308C2×Dic3—71no—
309C2×Dic3—71no—
310C2×Dic3—71no—
311C2×Dic3C22×D711yescharacteristic
312C2×Dic3C22×D711yescharacteristic
313D12—22no—
314D12—142no—
315D12—142no—
316C4×D3—22no—
317C4×D3—22no—
318C4×D3—142no—
319C4×D3—142no—
320C4×D3—142no—
321Dic6—22no—
322Dic6—142no—
323C3×C7#54711yescharacteristic, complemented, Hall
324#41—64no—
325#41—424no—
326C2×Q8—31no—
327C2×Q8—211no—
328C2×D4—31no—
329C2×D4—31no—
330C2×D4—31no—
331C2×D4—211no—
332C2×D4—211no—
333C2×D4—211no—
334C22×C4—31no—
335C22×C4—31no—
336C22×C4—71no—
337C22×C4—71no—
338C22×C4—211no—
339C22×C4—211no—
340C22×C4—211no—
341C22×C4D3×D711yescharacteristic
342C4⋊C4—71no—
343C4⋊C4—71no—
344C4⋊C4—71no—
345C4⋊C4—71no—
346C4⋊C4—211no—
347C4⋊C4—211no—
348C4⋊C4—211no—
349C4⋊C4—211no—
350C4⋊C4—211no—
351C4⋊C4—211no—
352C22⋊C4—211no—
353C22⋊C4—211no—
354C22⋊C4—211no—
355C22⋊C4—211no—
356C22⋊C4—211no—
357C22⋊C4—211no—
358C22⋊C4—211no—
359C22⋊C4—211no—
360C42—211no—
361C2×C7—22no—
362C2×C7—62no—
363C2×C7—121no—
364C2×C7C2×#23511yescharacteristic
365C2×C7C2×D3×D411yescharacteristic
366C2×C7#100711yescharacteristic
367D7—121no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3C2×C22⋊D712yes—
371C22×C3C23×D711yescharacteristic
372C2×D3—21no—
373C2×D3—21no—
374C2×D3—21no—
375C2×D3—21no—
376C2×D3—21no—
377C2×D3—141no—
378C2×D3—141no—
379C2×D3—141no—
380C2×D3C2×C22⋊D712yes—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—72no—
384C3×C4—141no—
385C3×C4—141no—
386C3×C4—141no—
387Dic3—21no—
388Dic3—141no—
389Dic3—141no—
390Dic3—141no—
391Dic3C2×C22⋊D712yes—
392C23—31no—
393C23—31no—
394C23—211no—
395C23C2×D3×D711yescharacteristic
396Q8—62no—
397Q8—422no—
398D4—34no—
399D4—62no—
400D4—62no—
401D4—422no—
402D4—422no—
403D4—422no—
404C2×C4—22no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—62no—
408C2×C4—62no—
409C2×C4—71no—
410C2×C4—71no—
411C2×C4—71no—
412C2×C4—71no—
413C2×C4—142no—
414C2×C4—142no—
415C2×C4—211no—
416C2×C4—211no—
417C2×C4—211no—
418C2×C4—422no—
419C2×C4—422no—
420C2×C4—422no—
421C2×C4C2×D3×D711yescharacteristic
422C2×C4C2×D3×D711yescharacteristic
423C7#550711yescharacteristic, complemented, Sylow
424C2×C3—22no—
425C2×C3D7×#4111yescharacteristic
426C2×C3#655411yescharacteristic
427C2×C3C22×C22⋊D711yescharacteristic
428D3—22no—
429D3—41no—
430D3—281no—
431C22—21no—
432C22—21no—
433C22—32no—
434C22—61no—
435C22—61no—
436C22—61no—
437C22—61no—
438C22—61no—
439C22—421no—
440C22—421no—
441C22—421no—
442C22D3×C22⋊D712yes—
443C22C22×D3×D711yescharacteristic
444C4—21no—
445C4—21no—
446C4—32no—
447C4—61no—
448C4—72no—
449C4—141no—
450C4—141no—
451C4—141no—
452C4—421no—
453C4—421no—
454C4—421no—
455C3#9051511yescharacteristic, complemented, Sylow
456C2—22no—
457C2—62no—
458C2—121no—
459C2—841no—
460C2#1062155111yescharacteristic
461C2D7×#23511yescharacteristic
462C2C2×D3×C22⋊D711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC22×C3×C4×C7C22
hypercenterC22×C4D3×D7
hypocenterC3×C7#547
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C7×#235C2semidirect
2. C2×#66686C2semidirect
3. #10621412C2semidirect
4. C2×C3×Dic7⋊C4C2semidirect
5. #10621128C2semidirect
6. #67×Dic7C2semidirect
7. #10621101C2semidirect
8. #10621008C2semidirect
9. #10620986C2semidirect
10. #10620985C2semidirect
11. #10620978C2semidirect
12. D3×Dic7⋊C4C2semidirect
13. #10620914C2semidirect
14. #10620913C2semidirect
15. #10620891C2semidirect
68. C2×Dic7⋊C4D3semidirect
82. C7×#67D4semidirect
139. C2×#235D7semidirect
174. C3×Dic7#41semidirect
291. Dic7#235semidirect
307. #67C22⋊D7semidirect
323. C3×C7#547semidirect
423. C7#5507semidirect
455. C3#90515semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#2352
C2×#666862
#106214122
C2×C3×Dic7⋊C42
#106211282
#67×Dic72
#106211012
#106210082
#106209862
#106209852
#106209782
D3×Dic7⋊C42
#106209142
#106209132
#106208912
#905153
#55077