Finite Group Databasebeta

← #13059554

Subgroups — #13059554

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×#66728C211yesmaximal, characteristic, complemented
2C2×#66686C211yesmaximal, characteristic, complemented
3C7×#929C211yesmaximal, characteristic, complemented
4C2×C3×Dic7⋊C4C211yesmaximal, characteristic, complemented
5#10621128C211yesmaximal, characteristic, complemented
6#10621114C211yesmaximal, characteristic, complemented
7#10621108C211yesmaximal, characteristic, complemented
8#10620995C211yesmaximal, characteristic, complemented
9#10620994C211yesmaximal, characteristic, complemented
10#10620982C211yesmaximal, characteristic, complemented
11#10620968C211yesmaximal, characteristic, complemented
12#10620966C211yesmaximal, characteristic, complemented
13#10620939C211yesmaximal, characteristic, complemented
14#10620917C211yesmaximal, characteristic, complemented
15#10620890C211yesmaximal, characteristic, complemented
16#90346—31nomaximal, Hall
17C22×C3×C4×C7C2211yescharacteristic
18C2×#4268C2211yescharacteristic
19C2×#4268C2211yescharacteristic
20#66728—24no—
21C2×D84C2211yescharacteristic
22C2×C4×D21C2211yescharacteristic
23C2×C4×D21C2211yescharacteristic
24C2×Dic42C2211yescharacteristic
25C2×C7×#67C2211yescharacteristic
26C22×C3×Dic7C2211yescharacteristic
27C22×C3×Dic7C2211yescharacteristic
28C2×#4248C2211yescharacteristic
29C2×#4247C2211yescharacteristic
30C2×#4247C2211yescharacteristic
31C2×D21⋊C4C2211yescharacteristic
32C2×D21⋊C4C2211yescharacteristic
33#66686—24no—
34C2×D3×Dic7C2211yescharacteristic
35C7×#217C2211yescharacteristic
36C7×(C2×D3)⋊C4C2211yescharacteristic
37C7×(C2×D3)⋊C4C2211yescharacteristic
38C7×Dic3⋊C4C2211yescharacteristic
39C7×Dic3⋊C4C2211yescharacteristic
40C3×Dic7⋊C4C2211yescharacteristic
41C3×Dic7⋊C4C2211yescharacteristic
42C3×Dic7⋊C4C2211yescharacteristic
43C3×Dic7⋊C4C2211yescharacteristic
44Dic3⋊Dic7C2211yescharacteristic
45Dic3⋊Dic7C2211yescharacteristic
46#66577C2211yescharacteristic
47Dic7⋊Dic3C2211yescharacteristic
48#66575C2211yescharacteristic
49#66575C2211yescharacteristic
50#66575C2211yescharacteristic
51#66575C2211yescharacteristic
52(C2×D3)⋊Dic7C2211yescharacteristic
53Dic3×Dic7C2211yescharacteristic
54C2×#1159—31no—
55C2×#1157—31no—
56C7×#123—31no—
57#6502—31no—
58C2×Dic7⋊C4D311yescharacteristic, complemented
59#6459—31no—
60#6457—31no—
61D7×C4⋊C4—31no—
62#6451—31no—
63#6449—31no—
64#6447—31no—
65#6446—31no—
66(C22⋊D7)⋊C4—31no—
67(C22⋊D7)⋊C4—31no—
68#6441—31no—
69#5507—71nomaximal, Hall
70C23×C3×C7C2311yescharacteristic
71C22×D21C2311yescharacteristic
72C22×D21C2311yescharacteristic
73C22×D3×C7C2311yescharacteristic
74C2×C3×C4×C7—22no—
75C2×C3×C4×C7C2311yescharacteristic
76C2×C3×C4×C7C2311yescharacteristic
77#4268—22no—
78#4268D414yescomplemented
79C2×Dic21C2311yescharacteristic
80C2×Dic21C2311yescharacteristic
81D84—22no—
82C4×D21—22no—
83C4×D21—22no—
84Dic42—22no—
85C7×#67—22no—
86C2×C7×Dic3C2311yescharacteristic
87C2×C7×Dic3C2311yescharacteristic
88C2×C7×Dic3C2311yescharacteristic
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—
99D21⋊C4—22no—
100D3×Dic7—22no—
101C2×C7×D4—31no—
102C22×C4×C7C2×D311yescharacteristic
103C2×C22⋊D7—31no—
104C2×C22⋊D7—31no—
105C2×C22⋊D7—31no—
106C2×C22⋊D7—31no—
107C22×Dic7—31no—
108C22×Dic7C2×D311yescharacteristic
109C22×Dic7C2×D311yescharacteristic
110#1159—64no—
111#1157—64no—
112C2×D28—31no—
113C2×C4×D7—31no—
114C2×C4×D7—31no—
115C2×C4×D7—31no—
116C2×C4×D7—31no—
117C2×Dic14—31no—
118C2×Dic14—31no—
119C7×C4⋊C4—31no—
120C7×C4⋊C4—31no—
121C7×C22⋊C4—31no—
122C7×C22⋊C4—31no—
123C7×C22⋊C4—31no—
124C22⋊Dic7—31no—
125(C2×D7)⋊C4—31no—
126(C2×D7)⋊C4—31no—
127(C2×D7)⋊C4—31no—
128(C2×D7)⋊C4—31no—
129C4⋊Dic7—31no—
130C4⋊Dic7—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×#235—71no—
140C2×C3×C4⋊C4—71no—
141#930—71no—
142#929—71no—
143#929D711yescharacteristic, complemented
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×D21—21no—
161C2×D21—21no—
162C2×D21C2×D412yes—
163C2×D3×C7—21no—
164C2×D3×C7—21no—
165C2×D3×C7—21no—
166C3×C4×C7—21no—
167C3×C4×C7—21no—
168Dic21—21no—
169Dic21C2×D412yes—
170C3×Dic7—21no—
171C3×Dic7—21no—
172C3×Dic7—21no—
173C3×Dic7#4112yescomplemented
174C7×Dic3—21no—
175C7×Dic3—21no—
176C7×Dic3—21no—
177#547—211noSylow
178C23×C7—31no—
179C23×C7C22×D311yescharacteristic
180C22×D7—31no—
181C22×D7—31no—
182C7×D4—62no—
183C2×C4×C7—22no—
184C2×C4×C7—31no—
185C2×C4×C7—31no—
186C2×C4×C7—31no—
187C2×C4×C7C22×D311yescharacteristic
188C2×C4×C7C22×D311yescharacteristic
189C22⋊D7—34no—
190C22⋊D7—62no—
191C22⋊D7—62no—
192C22⋊D7—62no—
193C2×Dic7—22no—
194C2×Dic7—22no—
195C2×Dic7—31no—
196C2×Dic7—31no—
197C2×Dic7—62no—
198C2×Dic7C22×D311yescharacteristic
199C2×Dic7C22×D311yescharacteristic
200C2×Dic7C22×D311yescharacteristic
201C2×Dic7C22×D311yescharacteristic
202D28—62no—
203C4×D7—62no—
204C4×D7—62no—
205C4×D7—62no—
206C4×D7—62no—
207Dic14—62no—
208Dic14—62no—
209C22×C3×C4—71no—
210C22×C3×C4—71no—
211C22×C3×C4C2×D711yescharacteristic
212C2×#67—71no—
213C2×#67—71no—
214C2×#67C2×D711yescharacteristic
215#235—144no—
216#235—144no—
217C2×D12—71no—
218C2×D12—71no—
219C2×D12—71no—
220C2×C4×D3—71no—
221C2×C4×D3—71no—
222C2×C4×D3—71no—
223C2×C4×D3—71no—
224C2×C4×D3—71no—
225C2×Dic6—71no—
226C2×Dic6—71no—
227C3×C4⋊C4—71no—
228C3×C4⋊C4—71no—
229C3×C4⋊C4—71no—
230C3×C4⋊C4—71no—
231#217C2×D711yescharacteristic
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)⋊C4C2×D711yescharacteristic
238(C2×D3)⋊C4C2×D711yescharacteristic
239C4⋊Dic3—71no—
240Dic3⋊C4—71no—
241Dic3⋊C4—71no—
242Dic3⋊C4—71no—
243Dic3⋊C4C2×D711yescharacteristic
244Dic3⋊C4C2×D711yescharacteristic
245C4×Dic3—71no—
246C2×C3×C7—22no—
247C2×C3×C7C22×D411yescharacteristic
248C2×C3×C7C2×#4111yescharacteristic
249C2×C3×C72−1+411yescharacteristic
250D21—22no—
251D21—41no—
252D3×C7—41no—
253C2×#41—211no—
254C2×#41—211no—
255C4⋊Q8—211no—
256#123—31no—
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—61no—
271C22×C7—61no—
272C22×C7—61no—
273C22×C7D3×D412yes—
274C22×C7C23×D311yescharacteristic
275C2×D7—32no—
276C2×D7—61no—
277C2×D7—61no—
278C2×D7—61no—
279C2×D7—61no—
280C2×D7—61no—
281C4×C7—21no—
282C4×C7—21no—
283C4×C7—61no—
284C4×C7—61no—
285C4×C7—61no—
286Dic7—21no—
287Dic7—21no—
288Dic7—21no—
289Dic7—32no—
290Dic7—61no—
291Dic7#23512yescomplemented
292C23×C3C22×D711yescharacteristic
293C22×D3—71no—
294C22×D3—71no—
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—74no—
307#67—142no—
308C2×Dic3—71no—
309C2×Dic3—71no—
310C2×Dic3C22×D711yescharacteristic
311C2×Dic3C22×D711yescharacteristic
312C2×Dic3C22×D711yescharacteristic
313D12—142no—
314D12—142no—
315D12—142no—
316C4×D3—142no—
317C4×D3—142no—
318C4×D3—142no—
319C4×D3—142no—
320C4×D3—142no—
321Dic6—142no—
322Dic6—142no—
323C3×C7#54711yescharacteristic, complemented, Hall
324#41—424no—
325#41—424no—
326C2×Q8—211no—
327C2×Q8—211no—
328C2×D4—31no—
329C2×D4—211no—
330C2×D4—211no—
331C2×D4—211no—
332C2×D4—211no—
333C2×D4—211no—
334C22×C4—71no—
335C22×C4—71no—
336C22×C4—211no—
337C22×C4—211no—
338C22×C4—211no—
339C22×C4—211no—
340C22×C4—211no—
341C22×C4D3×D711yescharacteristic
342C4⋊C4—31no—
343C4⋊C4—31no—
344C4⋊C4—71no—
345C4⋊C4—71no—
346C4⋊C4—71no—
347C4⋊C4—71no—
348C4⋊C4—211no—
349C4⋊C4—211no—
350C4⋊C4—211no—
351C4⋊C4—211no—
352C22⋊C4—31no—
353C22⋊C4—31no—
354C22⋊C4—31no—
355C22⋊C4—211no—
356C22⋊C4—211no—
357C22⋊C4—211no—
358C22⋊C4—211no—
359C22⋊C4—211no—
360C42—211no—
361C2×C7—22no—
362C2×C7—121no—
363C2×C7C2×#23511yescharacteristic
364C2×C7C2×D3×D411yescharacteristic
365C2×C7#100711yescharacteristic
366D7—62no—
367D7—121no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3D4×D712yes—
371C22×C3C23×D711yescharacteristic
372C2×D3—21no—
373C2×D3—21no—
374C2×D3—21no—
375C2×D3—72no—
376C2×D3—141no—
377C2×D3—141no—
378C2×D3—141no—
379C2×D3—141no—
380C2×D3—141no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—72no—
384C3×C4—141no—
385C3×C4—141no—
386C3×C4—141no—
387Dic3—21no—
388Dic3—21no—
389Dic3—21no—
390Dic3—72no—
391Dic3—141no—
392C23—31no—
393C23—211no—
394C23—211no—
395C23C2×D3×D711yescharacteristic
396Q8—422no—
397Q8—422no—
398D4—62no—
399D4—214no—
400D4—422no—
401D4—422no—
402D4—422no—
403D4—422no—
404C2×C4—22no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—71no—
409C2×C4—71no—
410C2×C4—71no—
411C2×C4—71no—
412C2×C4—142no—
413C2×C4—142no—
414C2×C4—211no—
415C2×C4—211no—
416C2×C4—422no—
417C2×C4—422no—
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×C3C2×D4×D711yescharacteristic
426C2×C3D7×#4111yescharacteristic
427C2×C3#655411yescharacteristic
428D3—41no—
429D3—142no—
430D3—281no—
431C22—21no—
432C22—21no—
433C22—61no—
434C22—61no—
435C22—61no—
436C22—212no—
437C22—421no—
438C22—421no—
439C22—421no—
440C22—421no—
441C22—421no—
442C22#6669412yes—
443C22C22×D3×D711yescharacteristic
444C4—21no—
445C4—21no—
446C4—61no—
447C4—61no—
448C4—61no—
449C4—72no—
450C4—141no—
451C4—141no—
452C4—141no—
453C4—212no—
454C4—421no—
455C3#9034611yescharacteristic, complemented, Sylow
456C2—22no—
457C2—121no—
458C2—422no—
459C2—841no—
460C2#1062155111yescharacteristic
461C2D7×#23511yescharacteristic
462C2C2×#6669411yescharacteristic
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×#66728C2semidirect
2. C2×#66686C2semidirect
3. C7×#929C2semidirect
4. C2×C3×Dic7⋊C4C2semidirect
5. #10621128C2semidirect
6. #10621114C2semidirect
7. #10621108C2semidirect
8. #10620995C2semidirect
9. #10620994C2semidirect
10. #10620982C2semidirect
11. #10620968C2semidirect
12. #10620966C2semidirect
13. #10620939C2semidirect
14. #10620917C2semidirect
15. #10620890C2semidirect
58. C2×Dic7⋊C4D3semidirect
78. #4268D4semidirect
143. #929D7semidirect
173. C3×Dic7#41semidirect
291. Dic7#235semidirect
323. C3×C7#547semidirect
423. C7#5507semidirect
455. C3#90346semidirect

Maximal subgroups

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

subgroupindex
C2×#667282
C2×#666862
C7×#9292
C2×C3×Dic7⋊C42
#106211282
#106211142
#106211082
#106209952
#106209942
#106209822
#106209682
#106209662
#106209392
#106209172
#106208902
#903463
#55077