Finite Group Databasebeta

← #13249671

Subgroups — #13249671

Order 1792.

432 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740657C211yesmaximal, characteristic
2#11736445C211yesmaximal, characteristic
3C2×C7×#333C211yesmaximal, characteristic, complemented
4#11729529C211yesmaximal, characteristic, complemented
5#11728179C211yesmaximal, characteristic
6#11725513C211yesmaximal, characteristic, complemented
7#11725511C211yesmaximal, characteristic, complemented
8C2×C7×C4⋊Q8C2211yescharacteristic
9C4×#1157C2211yescharacteristic
10C2×C7×C4⋊C8C2211yescharacteristic
11C2×C7×C4⋊C8C2211yescharacteristic
12#89882—21no—
13#89873—21no—
14#89866C412yes—
15#89863—21no—
16#89859C412yes—
17#89856—21no—
18#89738—21no—
19#89736—21no—
20#89697C2211yescharacteristic
21#89696C2211yescharacteristic
22#89696C2211yescharacteristic
23#89612—22no—
24#89607—21no—
25#89605—21no—
26C7×#333—21no—
27C7×#333—21no—
28#89342—22no—
29#89279—21no—
30#89278—21no—
31#9170—71nomaximal, Sylow
32C22×C7×Q8—21no—
33C2×#1157D411yescharacteristic
34C22×C7×C8—21no—
35C22×C7×C8—21no—
36C7×C4⋊Q8—21no—
37C7×C4⋊Q8—21no—
38C7×C4⋊Q8—21no—
39C7×C4⋊Q8C2×C412yes—
40C2×C7×C4⋊C4—21no—
41C2×C7×C4⋊C4—21no—
42C2×C42×C7C2311yescharacteristic
43C4×C22⋊D7—21no—
44C4×C22⋊D7—21no—
45#6489D411yescharacteristic
46C2×#1136—21no—
47C2×#1136—21no—
48C4×D28C2×C411yescharacteristic
49C4×D28D411yescharacteristic
50#6435—21no—
51C42×D7—21no—
52C4×Dic14C2×C411yescharacteristic
53C4×Dic14D411yescharacteristic
54C7×C4⋊C8—21no—
55C7×C4⋊C8—21no—
56C7×C4⋊C8—21no—
57C7×C4⋊C8D411yescharacteristic
58C7×C4⋊C8D411yescharacteristic
59C22⋊(C7⋊C8)—21no—
60(C2×D7)⋊C8—22no—
61(C2×D7)⋊C8—22no—
62#6389—22no—
63C8×Dic7—22no—
64#6384—22no—
65#6383—22no—
66#6382—22no—
67#6381—22no—
68C4⋊(C7⋊C8)—21no—
69C4⋊(C7⋊C8)—21no—
70C4⋊(C7⋊C8)—21no—
71C4⋊(C7⋊C8)C2×C412yes—
72C4⋊(C7⋊C8)D412yes—
73C4×C7⋊C8—21no—
74#3079—71no—
75#2925—71no—
76#1549—71no—
77C2×#333D711yescharacteristic, complemented
78#1477—71no—
79#1301—71no—
80#1292—71no—
81C2×C7×Q8—22no—
82C2×C7×Q8—41no—
83C2×C7×Q8—82no—
84C22×C4×C7—41no—
85C22×C4×C7C2×D411yescharacteristic
86C22×C4×C7#4111yescharacteristic
87C22×C4×C7#4111yescharacteristic
88C2×C22⋊D7—21no—
89#1157—21no—
90#1157—21no—
91#1157—21no—
92#1157—21no—
93C2×D28C22⋊C411yescharacteristic
94C2×C4×D7—21no—
95C2×C4×D7—21no—
96C2×C4×D7—21no—
97C2×Dic14C22⋊C411yescharacteristic
98C2×C7×C8—21no—
99C2×C7×C8—21no—
100C2×C7×C8—41no—
101C2×C7×C8—41no—
102C2×C7×C8—41no—
103C2×C7×C8—81no—
104C7×C4⋊C4—22no—
105C7×C4⋊C4—22no—
106C7×C4⋊C4—41no—
107C7×C4⋊C4—41no—
108C42×C7C22×C411yescharacteristic
109C42×C7C2×D411yescharacteristic
110C42×C7C2×D411yescharacteristic
111C42×C7C2×D411yescharacteristic
112C22⋊Dic7—21no—
113(C2×D7)⋊C4—21no—
114(C2×D7)⋊C4—21no—
115C4⋊Dic7C22⋊C411yescharacteristic
116C4⋊Dic7C22⋊C411yescharacteristic
117Dic7⋊C4—21no—
118Dic7⋊C4—21no—
119C4×Dic7—21no—
120C4×Dic7—21no—
121C4×Dic7—21no—
122#1136—41no—
123#1136—41no—
124#1136—41no—
125#1136—41no—
126C2×C7⋊C8—22no—
127C2×C7⋊C8—22no—
128C2×C7⋊C8—41no—
129C2×C4⋊Q8C2×D711yescharacteristic
130C4×#41—71no—
131#477—141no—
132#476—141no—
133#475—72no—
134#474—72no—
135#433—142no—
136#432—141no—
137#431—71no—
138#431—141no—
139#428—141no—
140#423—71no—
141#423—71no—
142C2×C4⋊C8C2×D711yescharacteristic
143C2×C4⋊C8C2×D711yescharacteristic
144#417—141no—
145#408—141no—
146#405—141no—
147#333—21no—
148#333—21no—
149#332—142no—
150Q8⋊C8—141no—
151D4⋊C8—141no—
152C23×C7#12311yescharacteristic
153C22×D7—21no—
154C7×Q8—82no—
155C7×Q8—82no—
156C2×C4×C7—21no—
157C2×C4×C7—21no—
158C2×C4×C7—41no—
159C2×C4×C7—42no—
160C2×C4×C7—82no—
161C2×C4×C7C2×C22⋊C411yescharacteristic
162C2×C4×C7C4×D411yescharacteristic
163C2×C4×C7C4×D411yescharacteristic
164C2×C4×C7#12011yescharacteristic
165C2×C4×C7#12111yescharacteristic
166C2×C4×C7#12111yescharacteristic
167C2×C4×C7#13511yescharacteristic
168C2×C4×C7#13511yescharacteristic
169C2×C4×C7#13711yescharacteristic
170C2×C4×C7#13711yescharacteristic
171C22⋊D7—41no—
172C22⋊D7—41no—
173C2×Dic7—21no—
174C2×Dic7—21no—
175C2×Dic7—21no—
176D28—21no—
177D28—21no—
178C4×D7—41no—
179C4×D7—41no—
180C4×D7—41no—
181C4×D7—41no—
182C4×D7—81no—
183Dic14—21no—
184Dic14—21no—
185C7×C8—41no—
186C7×C8—41no—
187C7×C8—81no—
188C7⋊C8—42no—
189C7⋊C8—42no—
190C7⋊C8—81no—
191C2×#41—71no—
192C22×Q8—21no—
193C2×M16—141no—
194C2×M16—141no—
195C22×C8—21no—
196C22×C8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8C4×D712yes—
201C4×Q8—71no—
202C4×Q8—71no—
203C4×D4—71no—
204C4×D4—71no—
205C4×D4—141no—
206C4×D4—141no—
207#117—71no—
208#117—141no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C42—141no—
212C2×C42C22×D711yescharacteristic
213#107—142no—
214#106—142no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—72no—
219C4⋊C8—72no—
220C4⋊C8—141no—
221C4⋊C8—141no—
222C4⋊C8—141no—
223C4⋊C8C22⋊D711yescharacteristic
224C4⋊C8C22⋊D711yescharacteristic
225#103—142no—
226#102—142no—
227C22⋊C8—142no—
228C22⋊C8—142no—
229C22⋊C8—141no—
230#97—142no—
231C4×C8—142no—
232C4×C8—141no—
233C22×C7—21no—
234C22×C7—21no—
235C22×C7#38611yescharacteristic
236C22×C7#48511yescharacteristic
237C22×C7#48511yescharacteristic
238C2×D7—41no—
239C2×D7—41no—
240C2×D7—41no—
241C4×C7—21no—
242C4×C7—21no—
243C4×C7—21no—
244C4×C7—82no—
245C4×C7#41611yescharacteristic
246C4×C7#41911yescharacteristic
247C4×C7#45211yescharacteristic
248C4×C7#45211yescharacteristic
249C4×C7#47111yescharacteristic
250C4×C7#47311yescharacteristic
251Dic7—41no—
252Dic7—41no—
253Dic7—41no—
254#41—141no—
255#41—141no—
256#41—141no—
257#41—141no—
258C2×Q8—22no—
259C2×Q8—41no—
260C2×Q8—71no—
261C2×Q8—82no—
262C2×D4—71no—
263C2×D4—141no—
264C22×C4—41no—
265C22×C4—141no—
266C22×C4—141no—
267C22×C4—141no—
268C22×C4#115711yescharacteristic
269C22×C4D4×D711yescharacteristic
270C22×C4#115911yescharacteristic
271M16—281no—
272M16—281no—
273M16—281no—
274M16—281no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—81no—
281C2×C8—142no—
282C2×C8—142no—
283C2×C8—281no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—71no—
289C4⋊C4—71no—
290C4⋊C4—141no—
291C4⋊C4—141no—
292C22⋊C4—141no—
293C22⋊C4—141no—
294C22⋊C4—141no—
295C42—141no—
296C42—141no—
297C42—141no—
298C42C2×C4×D711yescharacteristic
299C42D4×D711yescharacteristic
300C42D4×D711yescharacteristic
301C42C2×C22⋊D711yescharacteristic
302C2×C7—21no—
303C2×C7—21no—
304C2×C7#187311yescharacteristic
305C2×C7#190311yescharacteristic
306C2×C7#190811yescharacteristic
307D7—81no—
308C23—141no—
309C23#644611yescharacteristic
310Q8—82no—
311Q8—82no—
312Q8—141no—
313Q8—141no—
314D4—141no—
315D4—141no—
316D4—281no—
317D4—281no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—82no—
323C2×C4—141no—
324C2×C4—141no—
325C2×C4—141no—
326C2×C4—281no—
327C2×C4—281no—
328C2×C4—281no—
329C2×C4—281no—
330C2×C4—561no—
331C2×C4D7×C22⋊C411yescharacteristic
332C2×C4(C22⋊D7)⋊C411yescharacteristic
333C2×C4#644711yescharacteristic
334C2×C4#647811yescharacteristic
335C2×C4#647911yescharacteristic
336C2×C4#648111yescharacteristic
337C2×C4#648211yescharacteristic
338C2×C4C4×C22⋊D711yescharacteristic
339C2×C4#650011yescharacteristic
340C2×C4#650111yescharacteristic
341C8—41no—
342C8—41no—
343C8—81no—
344C8—282no—
345C8—282no—
346C8—561no—
347C7#917011yescharacteristic, complemented, Sylow
348C22—21no—
349C22—21no—
350C22—281no—
351C22—281no—
352C22—281no—
353C22#8958611yescharacteristic
354C22#8958711yescharacteristic
355C22#8972811yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—82no—
360C4—281no—
361C4—281no—
362C4—281no—
363C4#8957411yescharacteristic
364C4#8957611yescharacteristic
365C4#8994511yescharacteristic
366C4#8994911yescharacteristic
367C4#8995911yescharacteristic
368C4#8996411yescharacteristic
369C2—21no—
370C2—21no—
371C2—561no—
372C2#1172784111yescharacteristic
373C2#1172802311yescharacteristic
374C2#1172804011yescharacteristic
subgroupG/H
centerC22#89728
commutatorC42×C7C22×C4
FrattiniC2×C42C22×D7
FittingC2×C7×#333C2
socleC22×C7#386
prime radicalC2×#1157D4
cosocleC2×C42×C7C23
hypercenterC2×#333D7
hypocenterC7#9170
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
3. C2×C7×#333C2semidirect
4. #11729529C2semidirect
6. #11725513C2semidirect
7. #11725511C2semidirect
77. C2×#333D7semidirect
347. C7#9170semidirect

Maximal subgroups

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

subgroupindex
#117406572
#117364452
C2×C7×#3332
#117295292
#117281792
#117255132
#117255112
#91707