Finite Group Databasebeta

← #13058679

Subgroups — #13058679

Order 1344.

480 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
1#10621378C211yesmaximal, characteristic, complemented
2C7×#894C211yesmaximal, characteristic, complemented
3C3×#6452C211yesmaximal, characteristic, complemented
4#10621022C211yesmaximal, characteristic, complemented
5#10621013C211yesmaximal, characteristic, complemented
6#10621008C211yesmaximal, characteristic, complemented
7#10620995C211yesmaximal, characteristic, complemented
8#10620989C211yesmaximal, characteristic, complemented
9#10620982C211yesmaximal, characteristic, complemented
10#10620982C211yesmaximal, characteristic, complemented
11#10620982C211yesmaximal, characteristic, complemented
12#10620978C211yesmaximal, characteristic, complemented
13#10620968C211yesmaximal, characteristic, complemented
14#10620964C211yesmaximal, characteristic, complemented
15#10620917C211yesmaximal, characteristic, complemented
16#90354—31nomaximal, Hall
17C2×D84C2211yescharacteristic
18C2×D84C2211yescharacteristic
19C2×D84C2211yescharacteristic
20C2×C4×D21C2211yescharacteristic
21C2×C7×D12C2211yescharacteristic
22C2×C4×D3×C7C2211yescharacteristic
23C2×#4247C2211yescharacteristic
24C2×#4247C2211yescharacteristic
25C2×#4247C2211yescharacteristic
26C2×#4247C2211yescharacteristic
27C2×#4247C2211yescharacteristic
28C2×#4247C2211yescharacteristic
29C2×D21⋊C4C2211yescharacteristic
30C2×D21⋊C4C2211yescharacteristic
31C2×D3×Dic7C2211yescharacteristic
32C3×C7×C4⋊C4C2211yescharacteristic
33#66631C2211yescharacteristic
34#66631C2211yescharacteristic
35C7×(C2×D3)⋊C4C2211yescharacteristic
36C7×(C2×D3)⋊C4C2211yescharacteristic
37C7×(C2×D3)⋊C4C2211yescharacteristic
38C7×Dic3⋊C4C2211yescharacteristic
39C3×C4⋊Dic7C2211yescharacteristic
40C3×Dic7⋊C4C2211yescharacteristic
41C3×Dic7⋊C4C2211yescharacteristic
42C3×Dic7⋊C4C2211yescharacteristic
43C3×Dic7⋊C4C2211yescharacteristic
44C3×C4×Dic7C2211yescharacteristic
45Dic3⋊Dic7C2211yescharacteristic
46#66575C2211yescharacteristic
47#66575C2211yescharacteristic
48#66575C2211yescharacteristic
49#66575C2211yescharacteristic
50(C2×D3)⋊Dic7C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic
52C7×#123—31no—
53#6503—31no—
54#6502—31no—
55#6493—31no—
56C4×C22⋊D7—31no—
57#6458—31no—
58#6457—31no—
59#6455—31no—
60#6452D311yescharacteristic, complemented
61#6449—31no—
62#6447—31no—
63#6447—31no—
64#6447—31no—
65#6446—31no—
66(C22⋊D7)⋊C4—31no—
67#5697—71nomaximal, Hall
68C22×D21C2311yescharacteristic
69C22×D21C2311yescharacteristic
70C22×D21C2311yescharacteristic
71C22×D3×C7C2311yescharacteristic
72C22×D3×C7C2311yescharacteristic
73C2×C3×C4×C7C2311yescharacteristic
74C2×C3×C4×C7C2311yescharacteristic
75C2×C3×C4×C7C2311yescharacteristic
76C2×Dic21C2311yescharacteristic
77D84—41no—
78D84—41no—
79D84—41no—
80C4×D21—41no—
81C2×C7×Dic3C2311yescharacteristic
82C2×C7×Dic3C2311yescharacteristic
83C7×D12—41no—
84C4×D3×C7—41no—
85C2×C3×Dic7C2311yescharacteristic
86C2×C3×Dic7C2311yescharacteristic
87C2×C3×Dic7C2311yescharacteristic
88C2×C3×Dic7C2311yescharacteristic
89#4247—22no—
90#4247—22no—
91#4247—41no—
92#4247—41no—
93#4247—41no—
94#4247—41no—
95D21⋊C4—22no—
96D21⋊C4—41no—
97D3×Dic7—41no—
98C2×C7×D4—31no—
99C22×C4×C7—31no—
100C2×C22⋊D7—31no—
101C2×C22⋊D7—31no—
102C2×C22⋊D7—31no—
103C2×C22⋊D7—31no—
104C2×C22⋊D7—31no—
105C2×C22⋊D7—31no—
106C22×Dic7—31no—
107C2×D28—31no—
108C2×D28—31no—
109C2×D28—31no—
110C2×C4×D7—31no—
111C2×C4×D7—31no—
112C2×C4×D7—31no—
113C7×C4⋊C4—31no—
114C7×C4⋊C4C2×D311yescharacteristic
115C7×C22⋊C4—31no—
116C7×C22⋊C4—31no—
117C7×C22⋊C4—31no—
118C22⋊Dic7—31no—
119(C2×D7)⋊C4—31no—
120(C2×D7)⋊C4—31no—
121(C2×D7)⋊C4—31no—
122(C2×D7)⋊C4—31no—
123(C2×D7)⋊C4—31no—
124(C2×D7)⋊C4—31no—
125C4⋊Dic7—31no—
126C4⋊Dic7C2×D311yescharacteristic
127Dic7⋊C4C2×D311yescharacteristic
128Dic7⋊C4C2×D311yescharacteristic
129Dic7⋊C4C2×D311yescharacteristic
130Dic7⋊C4C2×D311yescharacteristic
131C4×Dic7—31no—
132C4×Dic7C2×D311yescharacteristic
133C3×#125—71no—
134#895—71no—
135#895—71no—
136#895—71no—
137#895—71no—
138#895—71no—
139#895—71no—
140#894—71no—
141#894—71no—
142#894—71no—
143#894D711yescharacteristic, complemented
144#893—71no—
145#893—71no—
146#874—71no—
147#872—71no—
148C22×C3×C7C2411yescharacteristic
149C2×D21—21no—
150C2×D21—21no—
151C2×D21—21no—
152C2×D21—21no—
153C2×D21—21no—
154C2×D21—21no—
155C2×D21—21no—
156C2×D21—21no—
157C2×D21—21no—
158C2×D3×C7—21no—
159C2×D3×C7—21no—
160C2×D3×C7—21no—
161C2×D3×C7—21no—
162C2×D3×C7—21no—
163C2×D3×C7—21no—
164C3×C4×C7—21no—
165C3×C4×C7—21no—
166C3×C4×C7—21no—
167Dic21—21no—
168C3×Dic7—21no—
169C3×Dic7—21no—
170C3×Dic7—21no—
171C3×Dic7#4112yes—
172C7×Dic3—21no—
173C7×Dic3—21no—
174#540—211noSylow
175C23×C7—31no—
176C23×C7—31no—
177C22×D7—31no—
178C22×D7—31no—
179C22×D7—31no—
180C7×D4—121no—
181C2×C4×C7—31no—
182C2×C4×C7—31no—
183C2×C4×C7—121no—
184C2×C4×C7C22×D311yescharacteristic
185C2×C4×C7C22×D311yescharacteristic
186C2×C4×C7C22×D311yescharacteristic
187C22⋊D7—62no—
188C22⋊D7—62no—
189C22⋊D7—121no—
190C22⋊D7—121no—
191C22⋊D7—121no—
192C22⋊D7—121no—
193C2×Dic7—31no—
194C2×Dic7—121no—
195C2×Dic7C22×D311yescharacteristic
196C2×Dic7C22×D311yescharacteristic
197C2×Dic7C22×D311yescharacteristic
198C2×Dic7C22×D311yescharacteristic
199D28—121no—
200D28—121no—
201D28—121no—
202C4×D7—62no—
203C4×D7—121no—
204C4×D7—121no—
205C2×D12—71no—
206C2×D12—71no—
207C2×D12—71no—
208C2×D12—71no—
209C2×D12—71no—
210C2×D12—71no—
211C2×D12—71no—
212C2×D12—71no—
213C2×D12—71no—
214C2×D12C2×D711yescharacteristic
215C2×C4×D3—71no—
216C2×C4×D3—71no—
217C2×C4×D3—71no—
218C2×C4×D3—71no—
219C2×C4×D3C2×D711yescharacteristic
220C3×C4⋊C4—71no—
221C3×C4⋊C4—71no—
222C3×C4⋊C4—71no—
223C3×C4⋊C4—71no—
224C3×C4⋊C4—71no—
225C3×C4⋊C4C2×D711yescharacteristic
226C3×C42—71no—
227(C2×D3)⋊C4—71no—
228(C2×D3)⋊C4—71no—
229(C2×D3)⋊C4—71no—
230(C2×D3)⋊C4—71no—
231(C2×D3)⋊C4—71no—
232(C2×D3)⋊C4—71no—
233(C2×D3)⋊C4—71no—
234(C2×D3)⋊C4C2×D711yescharacteristic
235(C2×D3)⋊C4C2×D711yescharacteristic
236(C2×D3)⋊C4C2×D711yescharacteristic
237Dic3⋊C4—71no—
238Dic3⋊C4C2×D711yescharacteristic
239C4×Dic3—71no—
240C2×C3×C7C2×#4111yescharacteristic
241C2×C3×C7H(5,𝔽2)11yescharacteristic
242C2×C3×C7H(5,𝔽2)11yescharacteristic
243D21—41no—
244D21—41no—
245D21—41no—
246D3×C7—41no—
247D3×C7—41no—
248#127—211no—
249#125—71no—
250#123—31no—
251#123—211no—
252#123—211no—
253#123—211no—
254#121—211no—
255#121—211no—
256#121—211no—
257#121—211no—
258#121—211no—
259#121—211no—
260C4×D4—211no—
261C4×D4—211no—
262#117—211no—
263C22×C7—61no—
264C22×C7—61no—
265C22×C7—61no—
266C22×C7—61no—
267C22×C7—61no—
268C22×C7—61no—
269C22×C7C23×D311yescharacteristic
270C2×D7—61no—
271C2×D7—61no—
272C2×D7—61no—
273C2×D7—61no—
274C2×D7—61no—
275C2×D7—61no—
276C2×D7—61no—
277C2×D7—61no—
278C2×D7—61no—
279C4×C7—21no—
280C4×C7—21no—
281C4×C7—21no—
282C4×C7—61no—
283C4×C7—61no—
284Dic7—21no—
285Dic7—21no—
286Dic7—21no—
287Dic7—61no—
288Dic7#23912yes—
289C22×D3—71no—
290C22×D3—71no—
291C22×D3—71no—
292C22×D3C22×D711yescharacteristic
293C22×D3C22×D711yescharacteristic
294C2×C3×C4—71no—
295C2×C3×C4—71no—
296C2×C3×C4—71no—
297C2×C3×C4—71no—
298C2×C3×C4C22×D711yescharacteristic
299C2×C3×C4C22×D711yescharacteristic
300C2×C3×C4C22×D711yescharacteristic
301C2×Dic3—71no—
302C2×Dic3C22×D711yescharacteristic
303C2×Dic3C22×D711yescharacteristic
304D12—41no—
305D12—142no—
306D12—142no—
307D12—281no—
308D12—281no—
309D12—281no—
310D12—281no—
311D12—281no—
312D12—281no—
313D12—281no—
314C4×D3—41no—
315C4×D3—142no—
316C4×D3—281no—
317C4×D3—281no—
318C4×D3—281no—
319C3×C7#54011yescharacteristic, complemented, Hall
320C2×D4—31no—
321C2×D4—211no—
322C2×D4—211no—
323C2×D4—211no—
324C2×D4—211no—
325C2×D4—211no—
326C2×D4—211no—
327C2×D4—211no—
328C2×D4—211no—
329C2×D4—211no—
330C22×C4—31no—
331C22×C4—211no—
332C22×C4—211no—
333C22×C4—211no—
334C22×C4—211no—
335C4⋊C4—31no—
336C4⋊C4—71no—
337C4⋊C4—71no—
338C4⋊C4—71no—
339C4⋊C4—71no—
340C4⋊C4—71no—
341C4⋊C4—211no—
342C4⋊C4D3×D711yescharacteristic
343C22⋊C4—31no—
344C22⋊C4—31no—
345C22⋊C4—31no—
346C22⋊C4—211no—
347C22⋊C4—211no—
348C22⋊C4—211no—
349C22⋊C4—211no—
350C22⋊C4—211no—
351C22⋊C4—211no—
352C22⋊C4—211no—
353C42—71no—
354C42—211no—
355C2×C7—121no—
356C2×C7—121no—
357C2×C7C2×#23911yescharacteristic
358C2×C7#100911yescharacteristic
359C2×C7#100911yescharacteristic
360D7—121no—
361D7—121no—
362D7—121no—
363C22×C3C23×D711yescharacteristic
364C2×D3—21no—
365C2×D3—21no—
366C2×D3—21no—
367C2×D3—21no—
368C2×D3—21no—
369C2×D3—21no—
370C2×D3—141no—
371C2×D3—141no—
372C2×D3—141no—
373C2×D3—141no—
374C2×D3—141no—
375C2×D3—141no—
376C2×D3—141no—
377C2×D3—141no—
378C2×D3—141no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—72no—
383C3×C4—141no—
384C3×C4—141no—
385C3×C4—141no—
386Dic3—21no—
387Dic3—21no—
388Dic3—141no—
389C23—31no—
390C23—31no—
391C23—211no—
392C23—211no—
393C23—211no—
394D4—121no—
395D4—422no—
396D4—422no—
397D4—841no—
398D4—841no—
399D4—841no—
400D4—841no—
401D4—841no—
402D4—841no—
403D4—841no—
404C2×C4—31no—
405C2×C4—31no—
406C2×C4—71no—
407C2×C4—71no—
408C2×C4—71no—
409C2×C4—71no—
410C2×C4—121no—
411C2×C4—211no—
412C2×C4—422no—
413C2×C4—841no—
414C2×C4—841no—
415C2×C4—841no—
416C2×C4C2×D3×D711yescharacteristic
417C2×C4C2×D3×D711yescharacteristic
418C2×C4C2×D3×D711yescharacteristic
419C7#569711yescharacteristic, complemented, Sylow
420C2×C3#654811yescharacteristic
421C2×C3D7×#4111yescharacteristic
422C2×C3#655311yescharacteristic
423D3—41no—
424D3—41no—
425D3—281no—
426D3—281no—
427D3—281no—
428C22—61no—
429C22—61no—
430C22—61no—
431C22—61no—
432C22—61no—
433C22—61no—
434C22—421no—
435C22—421no—
436C22—421no—
437C22—421no—
438C22—421no—
439C22—421no—
440C22—421no—
441C22—421no—
442C22—421no—
443C22C22×D3×D711yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—61no—
448C4—61no—
449C4—72no—
450C4—141no—
451C4—141no—
452C4—141no—
453C4—421no—
454C3#9035411yescharacteristic, complemented, Sylow
455C2—121no—
456C2—121no—
457C2—841no—
458C2—841no—
459C2—841no—
460C2#1062156611yescharacteristic
461C2#1062157411yescharacteristic
462C2D7×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C4⋊C4C22
hypercenterC4⋊C4D3×D7
hypocenterC3×C7#540
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10621378C2semidirect
2. C7×#894C2semidirect
3. C3×#6452C2semidirect
4. #10621022C2semidirect
5. #10621013C2semidirect
6. #10621008C2semidirect
7. #10620995C2semidirect
8. #10620989C2semidirect
9. #10620982C2semidirect
10. #10620982C2semidirect
11. #10620982C2semidirect
12. #10620978C2semidirect
13. #10620968C2semidirect
14. #10620964C2semidirect
15. #10620917C2semidirect
60. #6452D3semidirect
143. #894D7semidirect
319. C3×C7#540semidirect
419. C7#5697semidirect
454. C3#90354semidirect

Maximal subgroups

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

subgroupindex
#106213782
C7×#8942
C3×#64522
#106210222
#106210132
#106210082
#106209952
#106209892
#106209822
#106209782
#106209682
#106209642
#106209172
#903543
#56977