Finite Group Databasebeta

← C3×#89729 #13055376

Subgroups — C3×#89729 #13055376

Order 1344.

516 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊D7C211yesmaximal, characteristic
2C2×C3×C7×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×C22⋊Dic7C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
6C2×C3×Dic7⋊C4C211yesmaximal, characteristic, complemented
7C2×C3×C4×Dic7C211yesmaximal, characteristic, complemented
8#89729C311yesmaximal, characteristic, direct product factor, Hall
9C24×C3×C7C2211yescharacteristic
10C23×C3×D7C2211yescharacteristic
11C22×C3×C4×C7C2211yescharacteristic
12C22×C3×C4×C7C2211yescharacteristic
13C2×C3×C22⋊D7—22no—
14C2×C3×C22⋊D7—22no—
15C2×C3×C22⋊D7C414yescomplemented
16C22×C3×Dic7C2211yescharacteristic
17C22×C3×Dic7C2211yescharacteristic
18C22×C3×Dic7C2211yescharacteristic
19C3×C7×C22⋊C4—22no—
20C3×C22⋊Dic7—22no—
21C3×(C2×D7)⋊C4—22no—
22C3×(C2×D7)⋊C4—22no—
23C3×Dic7⋊C4—22no—
24C3×C4×Dic7—22no—
25C22×C22⋊D7C2×C311yescharacteristic
26C2×C7×C22⋊C4C2×C311yescharacteristic, complemented
27C2×C22⋊Dic7C2×C311yescharacteristic, complemented
28C2×(C2×D7)⋊C4C2×C311yescharacteristic, complemented
29C2×(C2×D7)⋊C4C2×C311yescharacteristic, complemented
30C2×Dic7⋊C4C2×C311yescharacteristic, complemented
31C2×C4×Dic7C2×C311yescharacteristic, complemented
32C3×#390—71nomaximal, Hall
33C23×C3×C7—21no—
34C23×C3×C7—21no—
35C23×C3×C7—21no—
36C23×C3×C7—21no—
37C23×C3×C7—21no—
38C23×C3×C7—21no—
39C23×C3×C7C2×C412yes—
40C23×C3×C7C2311yescharacteristic
41C22×C3×D7—21no—
42C22×C3×D7—21no—
43C22×C3×D7—21no—
44C22×C3×D7—21no—
45C22×C3×D7—21no—
46C22×C3×D7—21no—
47C22×C3×D7C2×C412yes—
48C2×C3×C4×C7—21no—
49C2×C3×C4×C7—21no—
50C2×C3×C4×C7—21no—
51C2×C3×C4×C7—21no—
52C2×C3×C4×C7—21no—
53C2×C3×C4×C7D412yescomplemented
54C3×C22⋊D7—28no—
55C2×C3×Dic7—21no—
56C2×C3×Dic7—21no—
57C2×C3×Dic7—21no—
58C2×C3×Dic7—21no—
59C2×C3×Dic7—21no—
60C2×C3×Dic7C2×C412yes—
61C2×C3×Dic7D412yes—
62C2×C3×Dic7D412yes—
63C2×C3×Dic7D412yescomplemented
64C24×C7C22×C311yescharacteristic
65C23×D7C22×C311yescharacteristic
66C22×C4×C7C22×C311yescharacteristic
67C22×C4×C7C22×C311yescharacteristic
68C2×C22⋊D7—22no—
69C2×C22⋊D7—22no—
70C2×C22⋊D7C3×C414yescomplemented
71C22×Dic7C22×C311yescharacteristic
72C22×Dic7C22×C311yescharacteristic
73C22×Dic7C22×C311yescharacteristic
74C7×C22⋊C4—22no—
75C22⋊Dic7—22no—
76(C2×D7)⋊C4—22no—
77(C2×D7)⋊C4—22no—
78Dic7⋊C4—22no—
79C4×Dic7—22no—
80C22×C3×D4—71no—
81C2×C3×C4⋊C4—71no—
82C2×C3×C22⋊C4—71no—
83C2×C3×C22⋊C4—71no—
84C2×C3×C22⋊C4—71no—
85C2×C3×C22⋊C4D711yescharacteristic, complemented
86C2×C3×C42—71no—
87C22×C3×C7—22no—
88C22×C3×C7—22no—
89C22×C3×C7—22no—
90C22×C3×C7—41no—
91C22×C3×C7—41no—
92C22×C3×C7—41no—
93C22×C3×C7—41no—
94C22×C3×C7C22×C411yescharacteristic
95C22×C3×C7C2×D411yescharacteristic
96C22×C3×C7C2×D411yescharacteristic
97C22×C3×C7C2×D411yescharacteristic
98C22×C3×C7C2×D411yescharacteristic
99C22×C3×C7#4111yescharacteristic
100C22×C3×C7#4111yescharacteristic
101C2×C3×D7—22no—
102C2×C3×D7—22no—
103C2×C3×D7—22no—
104C2×C3×D7—41no—
105C2×C3×D7—41no—
106C2×C3×D7—41no—
107C2×C3×D7—41no—
108C3×C4×C7—22no—
109C3×C4×C7—41no—
110C3×Dic7—22no—
111C3×Dic7—41no—
112C3×Dic7C22⋊C414yescomplemented
113#390—71noSylow
114C23×C7—21no—
115C23×C7—21no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7C2×C3×C412yes—
121C23×C7C23×C311yescharacteristic
122C22×D7—21no—
123C22×D7—21no—
124C22×D7—21no—
125C22×D7—21no—
126C22×D7—21no—
127C22×D7—21no—
128C22×D7C2×C3×C412yes—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7C3×D412yescomplemented
135C22⋊D7—28no—
136C2×Dic7—21no—
137C2×Dic7—21no—
138C2×Dic7—21no—
139C2×Dic7—21no—
140C2×Dic7—21no—
141C2×Dic7C2×C3×C412yes—
142C2×Dic7C3×D412yes—
143C2×Dic7C3×D412yes—
144C2×Dic7C3×D412yescomplemented
145C24×C3—71no—
146C24×C3C2×D711yescharacteristic
147C2×C3×D4—74no—
148C2×C3×D4—142no—
149C2×C3×D4—142no—
150C22×C3×C4—71no—
151C22×C3×C4—71no—
152C22×C3×C4—71no—
153C22×C3×C4C2×D711yescharacteristic
154C22×C3×C4C2×D711yescharacteristic
155C3×C4⋊C4—142no—
156C3×C22⋊C4—22no—
157C3×C22⋊C4—142no—
158C3×C22⋊C4—142no—
159C3×C22⋊C4—142no—
160C3×C42—142no—
161C2×C3×C7—42no—
162C2×C3×C7C2×C22⋊C411yescharacteristic
163C2×C3×C7C4×D411yescharacteristic
164C2×C3×C7C4×D411yescharacteristic
165C2×C3×C7#12111yescharacteristic
166C2×C3×C7#12111yescharacteristic
167C2×C3×C7#12411yescharacteristic
168C2×C3×C7#12711yescharacteristic
169C3×D7—42no—
170C22×D4—71no—
171C2×C4⋊C4—71no—
172C2×C22⋊C4—71no—
173C2×C22⋊C4—71no—
174C2×C22⋊C4—71no—
175C2×C22⋊C4C3×D711yescharacteristic, complemented
176C2×C42—71no—
177C22×C7—22no—
178C22×C7—22no—
179C22×C7—22no—
180C22×C7—41no—
181C22×C7—41no—
182C22×C7—41no—
183C22×C7—41no—
184C22×C7C22×C3×C411yescharacteristic
185C22×C7C2×C3×D411yescharacteristic
186C22×C7C2×C3×D411yescharacteristic
187C22×C7C2×C3×D411yescharacteristic
188C22×C7C2×C3×D411yescharacteristic
189C22×C7C3×#4111yescharacteristic
190C22×C7C3×#4111yescharacteristic
191C2×D7—22no—
192C2×D7—22no—
193C2×D7—22no—
194C2×D7—41no—
195C2×D7—41no—
196C2×D7—41no—
197C2×D7—41no—
198C4×C7—22no—
199C4×C7—41no—
200Dic7—22no—
201Dic7—41no—
202Dic7C3×C22⋊C414yescomplemented
203C23×C3—21no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—21no—
208C23×C3—21no—
209C23×C3—72no—
210C23×C3—141no—
211C23×C3—141no—
212C23×C3—141no—
213C23×C3—141no—
214C23×C3—141no—
215C23×C3—141no—
216C23×C3C4×D712yes—
217C23×C3C22×D711yescharacteristic
218C3×D4—148no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—72no—
225C2×C3×C4—72no—
226C2×C3×C4—72no—
227C2×C3×C4—72no—
228C2×C3×C4—141no—
229C2×C3×C4—141no—
230C2×C3×C4—141no—
231C2×C3×C4—141no—
232C2×C3×C4—141no—
233C2×C3×C4C22⋊D712yescomplemented
234C3×C7#39011yescharacteristic, complemented, Hall
235C24—71no—
236C24C2×C3×D711yescharacteristic
237C2×D4—74no—
238C2×D4—142no—
239C2×D4—142no—
240C22×C4—71no—
241C22×C4—71no—
242C22×C4—71no—
243C22×C4C2×C3×D711yescharacteristic
244C22×C4C2×C3×D711yescharacteristic
245C4⋊C4—142no—
246C22⋊C4—22no—
247C22⋊C4—142no—
248C22⋊C4—142no—
249C22⋊C4—142no—
250C42—142no—
251C2×C7—42no—
252C2×C7C2×C3×C22⋊C411yescharacteristic
253C2×C7C3×C4×D411yescharacteristic
254C2×C7C3×C4×D411yescharacteristic
255C2×C7C3×#12111yescharacteristic
256C2×C7C3×#12111yescharacteristic
257C2×C7C3×#12411yescharacteristic
258C2×C7C3×#12711yescharacteristic
259D7—42no—
260C22×C3—22no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—142no—
268C22×C3—142no—
269C22×C3—142no—
270C22×C3—281no—
271C22×C3—281no—
272C22×C3—281no—
273C22×C3—281no—
274C22×C3C2×C4×D711yescharacteristic
275C22×C3#115711yescharacteristic
276C22×C3D4×D711yescharacteristic
277C22×C3D4×D711yescharacteristic
278C22×C3D4×D711yescharacteristic
279C22×C3#115911yescharacteristic
280C22×C3C2×C22⋊D711yescharacteristic
281C3×C4—22no—
282C3×C4—41no—
283C3×C4—74no—
284C3×C4—142no—
285C3×C4—281no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—72no—
293C23—141no—
294C23—141no—
295C23—141no—
296C23—141no—
297C23—141no—
298C23—141no—
299C23C3×C4×D712yes—
300C23C22×C3×D711yescharacteristic
301D4—148no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—72no—
308C2×C4—72no—
309C2×C4—72no—
310C2×C4—72no—
311C2×C4—141no—
312C2×C4—141no—
313C2×C4—141no—
314C2×C4—141no—
315C2×C4—141no—
316C2×C4C3×C22⋊D712yescomplemented
317C7C3×#39011yescharacteristic, complemented, Sylow
318C2×C3—42no—
319C2×C3—282no—
320C2×C3D7×C22⋊C411yescharacteristic
321C2×C3(C22⋊D7)⋊C411yescharacteristic
322C2×C3#644711yescharacteristic
323C2×C3#644811yescharacteristic
324C2×C3C4×C22⋊D711yescharacteristic
325C2×C3#650211yescharacteristic
326C2×C3#650311yescharacteristic
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—142no—
335C22—142no—
336C22—142no—
337C22—281no—
338C22—281no—
339C22—281no—
340C22—281no—
341C22C2×C3×C4×D711yescharacteristic
342C22C3×#115711yescharacteristic
343C22C3×D4×D711yescharacteristic
344C22C3×D4×D711yescharacteristic
345C22C3×D4×D711yescharacteristic
346C22C3×#115911yescharacteristic
347C22C2×C3×C22⋊D711yescharacteristic
348C4—22no—
349C4—41no—
350C4—74no—
351C4—142no—
352C4—281no—
353C3#8972911yescharacteristic, direct product factor, Sylow
354C2—42no—
355C2—282no—
356C2C3×D7×C22⋊C411yescharacteristic
357C2C3×(C22⋊D7)⋊C411yescharacteristic
358C2C3×#644711yescharacteristic
359C2C3×#644811yescharacteristic
360C2C3×C4×C22⋊D711yescharacteristic
361C2C3×#650211yescharacteristic
362C2C3×#650311yescharacteristic
subgroupG/H
centerC23×C3C22×D7
commutatorC22×C7C22×C3×C4
FrattiniC23C22×C3×D7
FittingC2×C3×C7×C22⋊C4C2
socleC23×C3×C7C23
prime radicalC22×C3×C22⋊D7C2
cosocleC23×C7C23×C3
hypercenterC2×C3×C22⋊C4D7
hypocenterC7C3×#390
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C7×C22⋊C4C2semidirect
3. C2×C3×C22⋊Dic7C2semidirect
4. C2×C3×(C2×D7)⋊C4C2semidirect
5. C2×C3×(C2×D7)⋊C4C2semidirect
6. C2×C3×Dic7⋊C4C2semidirect
7. C2×C3×C4×Dic7C2semidirect
8. #89729C3direct (N × H)
15. C2×C3×C22⋊D7C4semidirect
26. C2×C7×C22⋊C4C2×C3semidirect
27. C2×C22⋊Dic7C2×C3semidirect
28. C2×(C2×D7)⋊C4C2×C3semidirect
29. C2×(C2×D7)⋊C4C2×C3semidirect
30. C2×Dic7⋊C4C2×C3semidirect
31. C2×C4×Dic7C2×C3semidirect
53. C2×C3×C4×C7D4semidirect
63. C2×C3×Dic7D4semidirect
70. C2×C22⋊D7C3×C4semidirect
85. C2×C3×C22⋊C4D7semidirect
112. C3×Dic7C22⋊C4semidirect
134. C2×C4×C7C3×D4semidirect
144. C2×Dic7C3×D4semidirect
175. C2×C22⋊C4C3×D7semidirect
202. Dic7C3×C22⋊C4semidirect
233. C2×C3×C4C22⋊D7semidirect
234. C3×C7#390semidirect
316. C2×C4C3×C22⋊D7semidirect
317. C7C3×#390semidirect
353. C3#89729direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊D72
C2×C3×C7×C22⋊C42
C2×C3×C22⋊Dic72
C2×C3×(C2×D7)⋊C42
C2×C3×Dic7⋊C42
C2×C3×C4×Dic72
#897293
C3×#3907