Finite Group Databasebeta

← #13258172

Subgroups — #13258172

Order 1792.

438 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3195C211yesmaximal, characteristic
2#11729452C211yesmaximal, characteristic
3#11729451C211yesmaximal, characteristic
4#11729445C211yesmaximal, characteristic
5#11729444C211yesmaximal, characteristic
6#11727738C211yesmaximal, characteristic
7#11725490C211yesmaximal, characteristic
8C2×C7×C22⋊Q8C2211yescharacteristic
9C2×C7×C22⋊Q8C2211yescharacteristic
10C22×#1136C2211yescharacteristic
11C7×#483—21no—
12C7×#483—21no—
13C7×#470—21no—
14C7×#470—21no—
15C7×#451—21no—
16C7×#451—21no—
17C7×#407C2211yescharacteristic
18C2×#6410—21no—
19C2×#6409—21no—
20#89984C2211yescharacteristic
21#89979C2211yescharacteristic
22C2×C22⋊(C7⋊C8)C2211yescharacteristic
23C2×#6396—21no—
24#89353—21no—
25#89333—22no—
26#89325—21no—
27#89324—21no—
28#89323—22no—
29#10563—71nomaximal, Sylow
30C22×C7×Q8D411yescharacteristic
31C22×C7×Q8D411yescharacteristic
32C23×C4×C7C2311yescharacteristic
33C2×C7×Q16—21no—
34C2×C7×Q16—21no—
35C2×C7×M16D411yescharacteristic
36C2×C7×M16D411yescharacteristic
37C7×C22⋊Q8—21no—
38C7×C22⋊Q8—21no—
39C7×C22⋊Q8—21no—
40C7×C22⋊Q8—21no—
41C7×C22⋊Q8—21no—
42C7×C22⋊Q8—21no—
43C7×C22⋊Q8—21no—
44C7×C22⋊Q8—21no—
45C2×C7×C4⋊C4—21no—
46C2×C7×C4⋊C4—21no—
47C2×C7×C4⋊C4D411yescharacteristic
48C2×C7×C4⋊C4D411yescharacteristic
49C2×C7×C22⋊C4—21no—
50C2×C7×C22⋊C4—21no—
51C2×C22⋊Dic7—21no—
52C2×C4⋊Dic7—21no—
53C2×#1136—21no—
54C2×#1136—21no—
55C2×#1136—21no—
56C2×#1136—42no—
57C22×C7⋊C8—21no—
58C22×C7⋊C8—21no—
59C7×#106—21no—
60C7×#106—21no—
61C7×#103—21no—
62C7×#103—21no—
63C7×#103—21no—
64C7×#103—21no—
65C7×C22⋊C8—21no—
66C7×C22⋊C8—21no—
67#6410—42no—
68#6409—42no—
69C7⋊#95—21no—
70C22⋊(C7⋊C8)—21no—
71C22⋊(C7⋊C8)—21no—
72C22⋊(C7⋊C8)—21no—
73C22⋊(C7⋊C8)D412yes—
74#6396—42no—
75#3195D711yescharacteristic
76#1901—71no—
77#1894—71no—
78#1855—71no—
79#1520—71no—
80#1472—71no—
81#1305—71no—
82C24×C7#4111yescharacteristic
83C2×C7×Q8—21no—
84C2×C7×Q8—21no—
85C2×C7×Q8—21no—
86C2×C7×Q8—21no—
87C2×C7×Q8—41no—
88C2×C7×Q8—41no—
89C2×C7×Q8—41no—
90C2×C7×Q8—41no—
91C22×C4×C7—21no—
92C22×C4×C7—21no—
93C22×C4×C7—21no—
94C22×C4×C7—21no—
95C22×C4×C7—41no—
96C22×C4×C7—41no—
97C22×C4×C7C2×D411yescharacteristic
98C22×C4×C7C2×D411yescharacteristic
99C22×C4×C7C2×D411yescharacteristic
100C22×C4×C7C2×D411yescharacteristic
101C22×C4×C7#4111yescharacteristic
102C22×C4×C7#4111yescharacteristic
103C22×Dic7—41no—
104C7×Q16—81no—
105C7×Q16—81no—
106C7×M16—41no—
107C7×M16—41no—
108C2×C7×C8—21no—
109C2×C7×C8—21no—
110C7×C4⋊C4—21no—
111C7×C4⋊C4—21no—
112C7×C4⋊C4—21no—
113C7×C4⋊C4—21no—
114C7×C4⋊C4—41no—
115C7×C4⋊C4—41no—
116C7×C4⋊C4—41no—
117C7×C4⋊C4—41no—
118C7×C22⋊C4—41no—
119C7×C22⋊C4—41no—
120C7×C22⋊C4—41no—
121C7×C22⋊C4—41no—
122C22⋊Dic7—81no—
123C4⋊Dic7—41no—
124C4⋊Dic7—41no—
125#1136—22no—
126#1136—22no—
127#1136—41no—
128#1136—41no—
129#1136—41no—
130#1136—41no—
131C2×C7⋊C8—22no—
132C2×C7⋊C8—22no—
133C2×C7⋊C8—41no—
134C2×C7⋊C8—41no—
135C2×C7⋊C8—41no—
136C2×C7⋊C8—41no—
137C2×C7⋊C8—41no—
138C22×M16—71no—
139C2×C22⋊Q8C2×D711yescharacteristic
140C2×C22⋊Q8C2×D711yescharacteristic
141#483—21no—
142#483—21no—
143#470—21no—
144#470—21no—
145#451—21no—
146#451—21no—
147C2×#108—141no—
148C2×#103—141no—
149C2×#101—141no—
150#407—71no—
151#407C2×D711yescharacteristic
152C2×C22⋊C8—71no—
153#380—71no—
154#343—141no—
155#341—141no—
156#340—141no—
157#328—142no—
158#324—142no—
159C23×C7—21no—
160C23×C7—21no—
161C23×C7—41no—
162C23×C7—41no—
163C23×C7#12111yescharacteristic
164C23×C7#12311yescharacteristic
165C23×C7#12411yescharacteristic
166C7×Q8—42no—
167C7×Q8—41no—
168C7×Q8—41no—
169C7×Q8—41no—
170C7×Q8—41no—
171C7×Q8—81no—
172C2×C4×C7—21no—
173C2×C4×C7—21no—
174C2×C4×C7—21no—
175C2×C4×C7—21no—
176C2×C4×C7—21no—
177C2×C4×C7—21no—
178C2×C4×C7—41no—
179C2×C4×C7—41no—
180C2×C4×C7—41no—
181C2×C4×C7—42no—
182C2×C4×C7—41no—
183C2×C4×C7—41no—
184C2×C4×C7—41no—
185C2×C4×C7—41no—
186C2×C4×C7—41no—
187C2×C4×C7—41no—
188C2×C4×C7—81no—
189C2×C4×C7—81no—
190C2×C4×C7#12011yescharacteristic
191C2×C4×C7#12111yescharacteristic
192C2×C4×C7#12111yescharacteristic
193C2×C4×C7#12311yescharacteristic
194C2×Dic7—81no—
195C2×Dic7—81no—
196C2×Dic7—81no—
197C7×C8—41no—
198C7×C8—41no—
199C7⋊C8—42no—
200C7⋊C8—42no—
201C7⋊C8—81no—
202C22×Q8C22⋊D711yescharacteristic
203C22×Q8C22⋊D711yescharacteristic
204C23×C4C22×D711yescharacteristic
205C2×Q16—21no—
206C2×Q16—21no—
207C2×M16—141no—
208C2×M16—141no—
209C2×M16—141no—
210C2×M16—282no—
211C2×M16C22⋊D711yescharacteristic
212C2×M16C22⋊D711yescharacteristic
213C22×C8—141no—
214C22×C8—141no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—141no—
226C2×C4⋊C4C22⋊D711yescharacteristic
227C2×C4⋊C4C22⋊D711yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—141no—
231#108—282no—
232#106—21no—
233#106—21no—
234#103—21no—
235#103—21no—
236#103—21no—
237#103—21no—
238#103—282no—
239#101—282no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—72no—
243C22⋊C8—141no—
244C22⋊C8—141no—
245C22⋊C8—141no—
246#95—141no—
247C22×C7—21no—
248C22×C7—21no—
249C22×C7—21no—
250C22×C7—21no—
251C22×C7—21no—
252C22×C7—21no—
253C22×C7—21no—
254C22×C7—21no—
255C22×C7—81no—
256C22×C7—81no—
257C22×C7#39411yescharacteristic
258C22×C7#47111yescharacteristic
259C22×C7#47311yescharacteristic
260C4×C7—21no—
261C4×C7—21no—
262C4×C7—21no—
263C4×C7—81no—
264C4×C7—81no—
265C4×C7—81no—
266C4×C7—81no—
267C4×C7B(4,𝔽2)11yescharacteristic
268C4×C7#45811yescharacteristic
269Dic7—161no—
270C24#115911yescharacteristic
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—281no—
286C22×C4D4×D711yescharacteristic
287C22×C4#115911yescharacteristic
288C22×C4#115911yescharacteristic
289C22×C4C2×C22⋊D711yescharacteristic
290C22×C4C2×C22⋊D711yescharacteristic
291C22×C4C2×C22⋊D711yescharacteristic
292Q16—81no—
293Q16—81no—
294M16—41no—
295M16—41no—
296M16—142no—
297M16—142no—
298M16—281no—
299M16—281no—
300M16—281no—
301M16—281no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—142no—
305C2×C8—142no—
306C2×C8—281no—
307C2×C8—281no—
308C2×C8—281no—
309C2×C8—281no—
310C2×C8—281no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—281no—
320C4⋊C4—281no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—561no—
326C2×C7—21no—
327C2×C7—21no—
328C2×C7—41no—
329C2×C7—41no—
330C2×C7#204411yescharacteristic
331C2×C7#204911yescharacteristic
332C2×C7#205211yescharacteristic
333C23—21no—
334C23—21no—
335C23—41no—
336C23—41no—
337C23#649811yescharacteristic
338C23#649911yescharacteristic
339C23#650211yescharacteristic
340Q8—42no—
341Q8—41no—
342Q8—41no—
343Q8—41no—
344Q8—41no—
345Q8—81no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—561no—
365C2×C4—561no—
366C2×C4—561no—
367C2×C4#649811yescharacteristic
368C2×C4#650111yescharacteristic
369C2×C4#650211yescharacteristic
370C2×C4#651611yescharacteristic
371C8—41no—
372C8—41no—
373C8—282no—
374C8—282no—
375C8—561no—
376C7#1056311yescharacteristic, complemented, Sylow
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—81no—
386C22—81no—
387C22#8997511yescharacteristic
388C22#8997611yescharacteristic
389C22#8999411yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—81no—
394C4—81no—
395C4—81no—
396C4—81no—
397C4—1121no—
398C4#9001511yescharacteristic
399C4#9001611yescharacteristic
400C2—21no—
401C2—21no—
402C2—41no—
403C2—41no—
404C2#1172960411yescharacteristic
405C2#1172985811yescharacteristic
406C2#1172985911yescharacteristic
subgroupG/H
centerC22#89994
commutator, cosocleC23×C4×C7C23
FrattiniC23×C4C22×D7
FittingC7×#3195C2
socleC22×C7#394
prime radicalC24×C7#41
hypercenter#3195D7
hypocenterC7#10563
LCSG ▷ C23×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
376. C7#10563semidirect

Maximal subgroups

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

subgroupindex
C7×#31952
#117294522
#117294512
#117294452
#117294442
#117277382
#117254902
#105637