Finite Group Databasebeta

← #13247221

Subgroups — #13247221

Order 1792.

514 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11731763C211yesmaximal, characteristic
2#11728229C211yesmaximal, characteristic
3#11728229C211yesmaximal, characteristic
4C7×#1296C211yesmaximal, characteristic, complemented
5#11725508C211yesmaximal, characteristic, complemented
6#11725508C211yesmaximal, characteristic, complemented
7#11725440C211yesmaximal, characteristic, complemented
8C2×#6455—21no—
9C2×C42×D7C2211yescharacteristic
10C2×C7×C4⋊C8C2211yescharacteristic
11C2×C7×C4⋊C8C2211yescharacteristic
12C7×#384C2211yescharacteristic
13C2×(C2×D7)⋊C8—21no—
14C2×(C2×D7)⋊C8—21no—
15#89759—21no—
16#89759C412yes—
17#89749—21no—
18C4⋊C4×Dic7—21no—
19C4⋊C4×Dic7C412yes—
20#89707C2211yescharacteristic
21C2×C4⋊(C7⋊C8)C2211yescharacteristic
22C2×C4⋊(C7⋊C8)C2211yescharacteristic
23#89345—21no—
24#89345—21no—
25#8726—71nomaximal, Sylow
26C22×C4×D7C2×C411yescharacteristic
27C22×C4×D7D411yescharacteristic
28C22×C4×D7D411yescharacteristic
29C22×C7×C8—21no—
30C22×C7×C8—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4C2×C412yes—
34C2×C42×C7C2311yescharacteristic
35C2×(C2×D7)⋊C4—22no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—21no—
38C2×C4⋊Dic7C2×C412yes—
39C2×C4×Dic7—22no—
40C2×C4×Dic7C2×C411yescharacteristic
41C2×C4×Dic7D411yescharacteristic
42C2×C4×Dic7D411yescharacteristic
43C22×C7⋊C8—21no—
44C22×C7⋊C8—21no—
45#6455—42no—
46#6455—42no—
47C42×D7—21no—
48C42×D7—21no—
49C42×D7—21no—
50C42×D7—21no—
51C7×C4⋊C8—21no—
52C7×C4⋊C8—21no—
53C7×C4⋊C8—21no—
54C7×C4⋊C8—21no—
55C7⋊#95—22no—
56C7⋊#95—22no—
57(C2×D7)⋊C8—42no—
58(C2×D7)⋊C8—42no—
59C4⋊(C7⋊C8)—21no—
60C4⋊(C7⋊C8)—21no—
61C4⋊(C7⋊C8)—21no—
62C4⋊(C7⋊C8)—21no—
63#2285—71no—
64#1797—71no—
65#1797—71no—
66#1296—71no—
67#1296—71no—
68#1296—71no—
69#1296D711yescharacteristic, complemented
70C23×D7C22⋊C411yescharacteristic
71C22×C4×C7—22no—
72C22×C4×C7C22×C411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C22×C4×C7C2×D411yescharacteristic
75C22×Dic7—22no—
76C22×Dic7C22⋊C411yescharacteristic
77C22×Dic7C22⋊C411yescharacteristic
78C22×Dic7C22⋊C411yescharacteristic
79C2×C4×D7—21no—
80C2×C4×D7—21no—
81C2×C4×D7—21no—
82C2×C4×D7—21no—
83C2×C4×D7—21no—
84C2×C4×D7—21no—
85C2×C4×D7—21no—
86C2×C4×D7—21no—
87C2×C4×D7—21no—
88C2×C4×D7—21no—
89C2×C4×D7—21no—
90C2×C4×D7—21no—
91C2×C4×D7—41no—
92C2×C4×D7—41no—
93C2×C4×D7D812yes—
94C2×C4×D7SD1612yes—
95C2×C7×C8—41no—
96C2×C7×C8—41no—
97C2×C7×C8—41no—
98C2×C7×C8—41no—
99C2×C7×C8—41no—
100C2×C7×C8—41no—
101C7×C4⋊C4—42no—
102C7×C4⋊C4—41no—
103C7×C4⋊C4—41no—
104C7×C4⋊C4—41no—
105C7×C4⋊C4—41no—
106C42×C7#4111yescharacteristic
107C42×C7#4111yescharacteristic
108C42×C7#4111yescharacteristic
109C42×C7#4111yescharacteristic
110(C2×D7)⋊C4—44no—
111C4⋊Dic7—41no—
112C4⋊Dic7—41no—
113C4⋊Dic7—41no—
114C4⋊Dic7—41no—
115C4⋊Dic7—42no—
116C4×Dic7—21no—
117C4×Dic7—21no—
118C4×Dic7—21no—
119C4×Dic7—21no—
120C4×Dic7—21no—
121C4×Dic7—21no—
122C4×Dic7—44no—
123C2×C7⋊C8—41no—
124C2×C7⋊C8—41no—
125C2×C7⋊C8—41no—
126C2×C7⋊C8—41no—
127C2×C7⋊C8—41no—
128C2×C7⋊C8—41no—
129C2×#117—141no—
130C22×C42—71no—
131C2×C4⋊C8—71no—
132C2×C4⋊C8—71no—
133C2×C4⋊C8C2×D711yescharacteristic
134C2×C4⋊C8C2×D711yescharacteristic
135C2×C22⋊C8—141no—
136C2×C22⋊C8—141no—
137#384—71no—
138#384C2×D711yescharacteristic
139#382—141no—
140#380—72no—
141#380—141no—
142C4×C4⋊C4—72no—
143C4×C4⋊C4—141no—
144#336—141no—
145#336—141no—
146C23×C7C2×C22⋊C411yescharacteristic
147C22×D7—21no—
148C22×D7—21no—
149C22×D7—21no—
150C22×D7—21no—
151C22×D7—21no—
152C22×D7—21no—
153C22×D7#10212yes—
154C2×C4×C7—21no—
155C2×C4×C7—21no—
156C2×C4×C7—42no—
157C2×C4×C7—42no—
158C2×C4×C7—42no—
159C2×C4×C7#11711yescharacteristic
160C2×C4×C7#11711yescharacteristic
161C2×C4×C7#12311yescharacteristic
162C2×C4×C7#12311yescharacteristic
163C2×C4×C7#12311yescharacteristic
164C2×C4×C7#12311yescharacteristic
165C2×C4×C7C2×D811yescharacteristic
166C2×C4×C7C2×SD1611yescharacteristic
167C2×C4×C7#13511yescharacteristic
168C2×C4×C7#13511yescharacteristic
169C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C7#13711yescharacteristic
171C2×C4×C7#13711yescharacteristic
172C2×C4×C7#13711yescharacteristic
173C2×Dic7—21no—
174C2×Dic7—21no—
175C2×Dic7—21no—
176C2×Dic7—21no—
177C2×Dic7—21no—
178C2×Dic7—21no—
179C2×Dic7—21no—
180C2×Dic7—21no—
181C2×Dic7—42no—
182C2×Dic7—42no—
183C2×Dic7—42no—
184C2×Dic7#10212yes—
185C4×D7—22no—
186C4×D7—22no—
187C4×D7—22no—
188C4×D7—22no—
189C4×D7—42no—
190C4×D7—42no—
191C4×D7—41no—
192C4×D7—41no—
193C4×D7—41no—
194C4×D7—41no—
195C7×C8—81no—
196C7×C8—81no—
197C7⋊C8—81no—
198C7⋊C8—81no—
199C23×C4—71no—
200C23×C4—71no—
201C23×C4—71no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—141no—
205C22×C8—141no—
206#117—282no—
207#117—282no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—72no—
211C2×C4⋊C4—141no—
212C2×C4⋊C4—141no—
213C2×C4⋊C4C4×D712yes—
214C2×C22⋊C4—142no—
215C2×C42—71no—
216C2×C42—71no—
217C2×C42—71no—
218C2×C42—141no—
219C2×C42—141no—
220C2×C42—141no—
221C2×C42—141no—
222C2×C42—142no—
223C2×C42C22×D711yescharacteristic
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—141no—
229C4⋊C8—141no—
230C4⋊C8—141no—
231C4⋊C8—141no—
232C22⋊C8—282no—
233C22⋊C8—282no—
234#95—142no—
235#95—142no—
236C22×C7#38111yescharacteristic
237C22×C7#41311yescharacteristic
238C22×C7#41311yescharacteristic
239C22×C7C2×#10211yescharacteristic
240C22×C7#41611yescharacteristic
241C22×C7#41711yescharacteristic
242C22×C7#41911yescharacteristic
243C2×D7—22no—
244C2×D7—22no—
245C2×D7—22no—
246C2×D7—41no—
247C2×D7—41no—
248C2×D7—41no—
249C2×D7—41no—
250C4×C7—21no—
251C4×C7—21no—
252C4×C7—82no—
253C4×C7#48011yescharacteristic
254C4×C7#48011yescharacteristic
255C4×C7#48211yescharacteristic
256C4×C7#48211yescharacteristic
257C4×C7#48311yescharacteristic
258C4×C7#48311yescharacteristic
259C4×C7#48511yescharacteristic
260C4×C7#48511yescharacteristic
261Dic7—22no—
262Dic7—41no—
263Dic7—41no—
264Dic7—82no—
265C24—71no—
266C22×C4—22no—
267C22×C4—71no—
268C22×C4—72no—
269C22×C4—72no—
270C22×C4—71no—
271C22×C4—71no—
272C22×C4—141no—
273C22×C4—141no—
274C22×C4—141no—
275C22×C4—141no—
276C22×C4—141no—
277C22×C4—141no—
278C22×C4—141no—
279C22×C4—141no—
280C22×C4—141no—
281C22×C4—141no—
282C22×C4—141no—
283C22×C4—141no—
284C22×C4—142no—
285C22×C4—281no—
286C22×C4—281no—
287C22×C4C2×C4×D711yescharacteristic
288C22×C4D4×D711yescharacteristic
289C22×C4D4×D711yescharacteristic
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—281no—
297C2×C8—281no—
298C2×C8—281no—
299C2×C8—281no—
300C2×C8—281no—
301C2×C8—281no—
302C4⋊C4—42no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—282no—
308C4⋊C4—281no—
309C4⋊C4—281no—
310C4⋊C4—281no—
311C4⋊C4—281no—
312C22⋊C4—284no—
313C42—141no—
314C42—141no—
315C42—141no—
316C42—141no—
317C42—141no—
318C42—141no—
319C42—284no—
320C42#115711yescharacteristic
321C42#115711yescharacteristic
322C42#115911yescharacteristic
323C42#116111yescharacteristic
324C2×C7#154011yescharacteristic
325C2×C7#154711yescharacteristic
326C2×C7#155411yescharacteristic
327C2×C7#155911yescharacteristic
328C2×C7#182211yescharacteristic
329C2×C7#182311yescharacteristic
330C2×C7#182511yescharacteristic
331D7—42no—
332C23—72no—
333C23—141no—
334C23—141no—
335C23—141no—
336C23—141no—
337C23—141no—
338C23—141no—
339C23D7×C22⋊C411yescharacteristic
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—72no—
346C2×C4—141no—
347C2×C4—141no—
348C2×C4—142no—
349C2×C4—142no—
350C2×C4—142no—
351C2×C4—142no—
352C2×C4—141no—
353C2×C4—141no—
354C2×C4—141no—
355C2×C4—141no—
356C2×C4—141no—
357C2×C4—141no—
358C2×C4—282no—
359C2×C4—282no—
360C2×C4—281no—
361C2×C4—281no—
362C2×C4—281no—
363C2×C4—281no—
364C2×C4—282no—
365C2×C4—282no—
366C2×C4—282no—
367C2×C4#643511yescharacteristic
368C2×C4#644611yescharacteristic
369C2×C4#644611yescharacteristic
370C2×C4#645511yescharacteristic
371C2×C4#645711yescharacteristic
372C2×C4#645711yescharacteristic
373C2×C4D7×D811yescharacteristic
374C2×C4#647511yescharacteristic
375C2×C4D7×SD1611yescharacteristic
376C2×C4#647711yescharacteristic
377C2×C4#647811yescharacteristic
378C2×C4#647911yescharacteristic
379C2×C4#648111yescharacteristic
380C2×C4#648111yescharacteristic
381C8—81no—
382C8—81no—
383C8—561no—
384C8—561no—
385C7#872611yescharacteristic, complemented, Sylow
386C22—142no—
387C22—142no—
388C22—142no—
389C22—281no—
390C22—281no—
391C22—281no—
392C22—281no—
393C22#8943611yescharacteristic
394C22#8951711yescharacteristic
395C22#8952311yescharacteristic
396C22D7×#10211yescharacteristic
397C22#8954411yescharacteristic
398C22#8957411yescharacteristic
399C22#8957511yescharacteristic
400C4—21no—
401C4—21no—
402C4—82no—
403C4—142no—
404C4—281no—
405C4—281no—
406C4—562no—
407C4#8954611yescharacteristic
408C4#8955611yescharacteristic
409C4#8957711yescharacteristic
410C4#8958711yescharacteristic
411C4#8963411yescharacteristic
412C4#8963811yescharacteristic
413C4#8965411yescharacteristic
414C4#8966011yescharacteristic
415C2—282no—
416C2#1172613511yescharacteristic
417C2#1172617511yescharacteristic
418C2#1172618111yescharacteristic
419C2#1172624211yescharacteristic
420C2#1172662511yescharacteristic
421C2#1172662711yescharacteristic
422C2#1172674511yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1296C2
socleC23×C7C2×C22⋊C4
prime radicalC23×D7C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1296D7
hypocenterC7#8726
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
4. C7×#1296C2semidirect
5. #11725508C2semidirect
6. #11725508C2semidirect
7. #11725440C2semidirect
69. #1296D7semidirect
385. C7#8726semidirect

Maximal subgroups

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

subgroupindex
#117317632
#117282292
C7×#12962
#117255082
#117254402
#87267