Finite Group Databasebeta

← #13058064

Subgroups — #13058064

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×#66686C211yesmaximal, characteristic, complemented
2C2×#66684C211yesmaximal, characteristic, complemented
3#10621369C211yesmaximal, characteristic, complemented
4C7×#67⋊C4C211yesmaximal, characteristic, complemented
5C3×#6449C211yesmaximal, characteristic, complemented
6#10621131C211yesmaximal, characteristic, complemented
7C2×Dic3⋊Dic7C211yesmaximal, characteristic, complemented
8#10621031C211yesmaximal, characteristic, complemented
9#10621019C211yesmaximal, characteristic, complemented
10#10621016C211yesmaximal, characteristic, complemented
11#10620991C211yesmaximal, characteristic, complemented
12#10620989C211yesmaximal, characteristic, complemented
13D3×C4⋊Dic7C211yesmaximal, characteristic, complemented
14#10620984C211yesmaximal, characteristic, complemented
15#10620957C211yesmaximal, characteristic, complemented
16#90246—31nomaximal, Hall
17C2×#4268C2211yescharacteristic
18C22×Dic21C2211yescharacteristic
19C2×C7×#67C2211yescharacteristic
20C22×C7×Dic3C2211yescharacteristic
21C2×C4×D3×C7C2211yescharacteristic
22C2×C3×C22⋊D7C2211yescharacteristic
23C22×C3×Dic7C2211yescharacteristic
24C2×#4248C2211yescharacteristic
25C2×#4248C2211yescharacteristic
26C2×#4247C2211yescharacteristic
27C2×#4246C2211yescharacteristic
28C2×#4245C2211yescharacteristic
29C2×D21⋊C4C2211yescharacteristic
30#66686—24no—
31C2×D3×Dic7C2211yescharacteristic
32C2×D3×Dic7C2211yescharacteristic
33#66684—24no—
34C2×Dic3×D7C2211yescharacteristic
35C3×C7×C22⋊C4C2211yescharacteristic
36#66631C2211yescharacteristic
37#66631C2211yescharacteristic
38C4⋊Dic21C2211yescharacteristic
39C4⋊Dic21C2211yescharacteristic
40C7×(C2×D3)⋊C4C2211yescharacteristic
41C7×Dic3⋊C4C2211yescharacteristic
42C4×C7×Dic3C2211yescharacteristic
43C3×(C2×D7)⋊C4C2211yescharacteristic
44C3×(C2×D7)⋊C4C2211yescharacteristic
45C3×C4⋊Dic7C2211yescharacteristic
46C3×C4⋊Dic7C2211yescharacteristic
47Dic3⋊Dic7C2211yescharacteristic
48Dic3⋊Dic7C2211yescharacteristic
49Dic3⋊Dic7C2211yescharacteristic
50Dic3⋊Dic7C2211yescharacteristic
51Dic3⋊Dic7C2211yescharacteristic
52#66575C2211yescharacteristic
53(C2×D7)⋊Dic3C2211yescharacteristic
54C2×#1159—31no—
55C2×#1159—31no—
56C4×C7×D4—31no—
57#6493—31no—
58#6493—31no—
59C2×C4⋊Dic7—31no—
60C2×C4⋊Dic7—31no—
61#6460—31no—
62#6460—31no—
63#6449—31no—
64#6449—31no—
65#6449—31no—
66#6449D311yescharacteristic, complemented
67C4×D28—31no—
68#6432—31no—
69#5655—71nomaximal, Hall
70C23×C3×C7C2311yescharacteristic
71C22×D21C2311yescharacteristic
72C22×D3×C7C2311yescharacteristic
73C22×C3×D7C2311yescharacteristic
74C2×C3×C4×C7C2311yescharacteristic
75C2×C3×C4×C7C2311yescharacteristic
76#4268—22no—
77C2×Dic21—22no—
78C2×Dic21C2311yescharacteristic
79C2×Dic21C2311yescharacteristic
80C2×Dic21C2311yescharacteristic
81C7×#67D414yescomplemented
82C2×C7×Dic3—22no—
83C2×C7×Dic3C2311yescharacteristic
84C2×C7×Dic3C2311yescharacteristic
85C2×C7×Dic3C2311yescharacteristic
86C4×D3×C7—22no—
87C3×C22⋊D7—22no—
88C2×C3×Dic7—22no—
89C2×C3×Dic7C2311yescharacteristic
90C2×C3×Dic7C2311yescharacteristic
91C2×C3×Dic7C2311yescharacteristic
92#4248—22no—
93#4248—22no—
94#4247—22no—
95#4246—22no—
96#4245—22no—
97D21⋊C4—22no—
98D3×Dic7—22no—
99D3×Dic7—22no—
100Dic3×D7—22no—
101C2×C7×D4—31no—
102C22×C4×C7—31no—
103C22×C4×C7—31no—
104C2×C22⋊D7—31no—
105C2×C22⋊D7—31no—
106C2×C22⋊D7—31no—
107C2×C22⋊D7C2×D311yescharacteristic
108C22×Dic7—31no—
109C22×Dic7—31no—
110C22×Dic7—31no—
111C22×Dic7C2×D311yescharacteristic
112#1159—64no—
113#1159—64no—
114C2×D28—31no—
115C2×C4×D7—31no—
116C2×C4×D7—31no—
117C2×Dic14—31no—
118C2×Dic14—31no—
119C7×C4⋊C4—31no—
120C7×C22⋊C4—31no—
121C7×C22⋊C4C2×D311yescharacteristic
122C42×C7—31no—
123(C2×D7)⋊C4—31no—
124(C2×D7)⋊C4—31no—
125(C2×D7)⋊C4—31no—
126(C2×D7)⋊C4—31no—
127(C2×D7)⋊C4C2×D311yescharacteristic
128(C2×D7)⋊C4C2×D311yescharacteristic
129C4⋊Dic7—31no—
130C4⋊Dic7—31no—
131C4⋊Dic7—31no—
132C4⋊Dic7—31no—
133C4⋊Dic7—31no—
134C4⋊Dic7—31no—
135C4⋊Dic7—31no—
136C4⋊Dic7C2×D311yescharacteristic
137C4⋊Dic7C2×D311yescharacteristic
138C2×#237—71no—
139C2×#235—71no—
140C3×#123—71no—
141#939—71no—
142C2×Dic3⋊C4—71no—
143#896—71no—
144#894—71no—
145D3×C4⋊C4—71no—
146#888—71no—
147#886—71no—
148#884—71no—
149#883—71no—
150#67⋊C4—71no—
151#67⋊C4D711yescharacteristic, complemented
152#878—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×C7C2×D412yes—
163C2×C3×D7—21no—
164C2×C3×D7—21no—
165C2×C3×D7—21no—
166C3×C4×C7—21no—
167C3×C4×C7—21no—
168Dic21—21no—
169Dic21—21no—
170Dic21—21no—
171C3×Dic7—21no—
172C3×Dic7—21no—
173C3×Dic7—21no—
174C7×Dic3—21no—
175C7×Dic3C2×D412yes—
176C7×Dic3#4112yescomplemented
177#547—211noSylow
178C23×C7—31no—
179C23×C7C22×D311yescharacteristic
180C22×D7—31no—
181C22×D7C22×D311yescharacteristic
182C7×D4—34no—
183C2×C4×C7—31no—
184C2×C4×C7—31no—
185C2×C4×C7—31no—
186C2×C4×C7—62no—
187C2×C4×C7—62no—
188C2×C4×C7C22×D311yescharacteristic
189C2×C4×C7C22×D311yescharacteristic
190C22⋊D7—22no—
191C22⋊D7—62no—
192C22⋊D7—62no—
193C22⋊D7—62no—
194C2×Dic7—22no—
195C2×Dic7—31no—
196C2×Dic7—31no—
197C2×Dic7—31no—
198C2×Dic7—62no—
199C2×Dic7—62no—
200C2×Dic7—62no—
201C2×Dic7C22×D311yescharacteristic
202C2×Dic7C22×D311yescharacteristic
203C2×Dic7C22×D311yescharacteristic
204D28—62no—
205C4×D7—62no—
206C4×D7—62no—
207Dic14—62no—
208Dic14—62no—
209C2×C3×D4—71no—
210C22×C3×C4—71no—
211C2×#67—71no—
212C2×#67—71no—
213C2×#67—71no—
214C2×#67C2×D711yescharacteristic
215C22×Dic3—71no—
216C22×Dic3—71no—
217C22×Dic3C2×D711yescharacteristic
218#237—144no—
219#235—144no—
220C2×D12—71no—
221C2×C4×D3—71no—
222C2×C4×D3—71no—
223C2×C4×D3—71no—
224C2×C4×D3C2×D711yescharacteristic
225C2×Dic6—71no—
226C2×Dic6—71no—
227C3×C4⋊C4—71no—
228C3×C4⋊C4—71no—
229C3×C22⋊C4—71no—
230C3×C22⋊C4—71no—
231C3×C22⋊C4C2×D711yescharacteristic
232#217—71no—
233(C2×D3)⋊C4—71no—
234(C2×D3)⋊C4—71no—
235(C2×D3)⋊C4—71no—
236(C2×D3)⋊C4C2×D711yescharacteristic
237C4⋊Dic3—71no—
238C4⋊Dic3—71no—
239Dic3⋊C4—71no—
240Dic3⋊C4—71no—
241Dic3⋊C4—71no—
242Dic3⋊C4—71no—
243Dic3⋊C4—71no—
244Dic3⋊C4C2×D711yescharacteristic
245C4×Dic3C2×D711yescharacteristic
246C2×C3×C7—22no—
247C2×C3×C7C22×D411yescharacteristic
248C2×C3×C7C2×#4111yescharacteristic
249C2×C3×C72−1+411yescharacteristic
250D21—41no—
251C3×D7—41no—
252D3×C7—22no—
253C2×#41—211no—
254C2×#41—211no—
255C4⋊Q8—211no—
256#123—71no—
257#123—211no—
258#123—211no—
259#123—211no—
260C22⋊Q8—211no—
261C22⋊Q8—211no—
262#121—211no—
263#121—211no—
264C4×D4—31no—
265C4×D4—211no—
266C2×C4⋊C4—211no—
267C2×C4⋊C4—211no—
268C22×C7—21no—
269C22×C7—21no—
270C22×C7—32no—
271C22×C7—61no—
272C22×C7—61no—
273C22×C7D3×D412yes—
274C22×C7C23×D311yescharacteristic
275C2×D7—21no—
276C2×D7—21no—
277C2×D7—21no—
278C2×D7—61no—
279C2×D7—61no—
280C2×D7—61no—
281C4×C7—21no—
282C4×C7—21no—
283C4×C7—32no—
284C4×C7—32no—
285C4×C7—61no—
286Dic7—21no—
287Dic7—21no—
288Dic7—21no—
289Dic7—61no—
290Dic7—61no—
291Dic7—61no—
292C23×C3—71no—
293C23×C3C22×D711yescharacteristic
294C22×D3—71no—
295C22×D3C22×D711yescharacteristic
296C3×D4—142no—
297C2×C3×C4—71no—
298C2×C3×C4—71no—
299C2×C3×C4—71no—
300C2×C3×C4—142no—
301C2×C3×C4C22×D711yescharacteristic
302C2×C3×C4C22×D711yescharacteristic
303#67—142no—
304#67—142no—
305#67—142no—
306#67D2814yescomplemented
307C2×Dic3—22no—
308C2×Dic3—71no—
309C2×Dic3—71no—
310C2×Dic3—71no—
311C2×Dic3—142no—
312C2×Dic3—142no—
313C2×Dic3C22×D711yescharacteristic
314C2×Dic3C22×D711yescharacteristic
315C2×Dic3C22×D711yescharacteristic
316D12—142no—
317C4×D3—22no—
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—71no—
330C2×D4—211no—
331C2×D4—211no—
332C2×D4—211no—
333C2×D4—211no—
334C22×C4—31no—
335C22×C4—31no—
336C22×C4—71no—
337C22×C4—211no—
338C22×C4—211no—
339C22×C4—211no—
340C22×C4—211no—
341C22×C4—211no—
342C4⋊C4—31no—
343C4⋊C4—71no—
344C4⋊C4—71no—
345C4⋊C4—211no—
346C4⋊C4—211no—
347C4⋊C4—211no—
348C4⋊C4—211no—
349C4⋊C4—211no—
350C4⋊C4—211no—
351C4⋊C4—211no—
352C22⋊C4—31no—
353C22⋊C4—71no—
354C22⋊C4—71no—
355C22⋊C4—211no—
356C22⋊C4—211no—
357C22⋊C4—211no—
358C22⋊C4—211no—
359C22⋊C4D3×D711yescharacteristic
360C42—31no—
361C2×C7—22no—
362C2×C7—62no—
363C2×C7C2×D3×D411yescharacteristic
364C2×C7D3×#4111yescharacteristic
365C2×C7#101011yescharacteristic
366D7—41no—
367D7—121no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—141no—
371C22×C3—141no—
372C22×C3—141no—
373C22×C3C2×D2812yes—
374C22×C3C23×D711yescharacteristic
375C2×D3—21no—
376C2×D3—21no—
377C2×D3—141no—
378C2×D3—141no—
379C2×D3—141no—
380C2×D3C2×D2812yes—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—141no—
384C3×C4—141no—
385C3×C4—141no—
386Dic3—21no—
387Dic3—141no—
388Dic3—141no—
389Dic3—141no—
390Dic3C2×D2812yes—
391Dic3#115912yescomplemented
392C23—31no—
393C23—71no—
394C23—211no—
395C23C2×D3×D711yescharacteristic
396Q8—422no—
397Q8—422no—
398D4—34no—
399D4—142no—
400D4—422no—
401D4—422no—
402D4—422no—
403D4—422no—
404C2×C4—31no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—62no—
408C2×C4—62no—
409C2×C4—71no—
410C2×C4—71no—
411C2×C4—71no—
412C2×C4—142no—
413C2×C4—211no—
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#565511yescharacteristic, complemented, Sylow
424C2×C3—22no—
425C2×C3—281no—
426C2×C3C22×D2811yescharacteristic
427C2×C3C2×#115911yescharacteristic
428C2×C3#655411yescharacteristic
429D3—22no—
430D3—281no—
431C22—21no—
432C22—21no—
433C22—32no—
434C22—61no—
435C22—61no—
436C22—141no—
437C22—141no—
438C22—141no—
439C22—421no—
440C22—421no—
441C22—421no—
442C22D3×D2812yes—
443C22C22×D3×D711yescharacteristic
444C4—21no—
445C4—21no—
446C4—32no—
447C4—32no—
448C4—61no—
449C4—141no—
450C4—141no—
451C4—141no—
452C4—421no—
453C4—421no—
454C4—421no—
455C3#9024611yescharacteristic, complemented, Sylow
456C2—22no—
457C2—62no—
458C2—281no—
459C2—841no—
460C2C2×D3×D2811yescharacteristic
461C2#1062156711yescharacteristic
462C2D3×#115911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C22⋊C4C22
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×#66686C2semidirect
2. C2×#66684C2semidirect
3. #10621369C2semidirect
4. C7×#67⋊C4C2semidirect
5. C3×#6449C2semidirect
6. #10621131C2semidirect
7. C2×Dic3⋊Dic7C2semidirect
8. #10621031C2semidirect
9. #10621019C2semidirect
10. #10621016C2semidirect
11. #10620991C2semidirect
12. #10620989C2semidirect
13. D3×C4⋊Dic7C2semidirect
14. #10620984C2semidirect
15. #10620957C2semidirect
66. #6449D3semidirect
81. C7×#67D4semidirect
151. #67⋊C4D7semidirect
176. C7×Dic3#41semidirect
306. #67D28semidirect
323. C3×C7#547semidirect
391. Dic3#1159semidirect
423. C7#5655semidirect
455. C3#90246semidirect

Maximal subgroups

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

subgroupindex
C2×#666862
C2×#666842
#106213692
C7×#67⋊C42
C3×#64492
#106211312
C2×Dic3⋊Dic72
#106210312
#106210192
#106210162
#106209912
#106209892
D3×C4⋊Dic72
#106209842
#106209572
#902463
#56557