Finite Group Databasebeta

← C7×#13462 #13190678

Subgroups — C7×#13462 #13190678

Order 1792.

476 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2748C211yesmaximal, characteristic
2C7×#1867C211yesmaximal, characteristic
3C7×#1867C211yesmaximal, characteristic
4C7×#1856C211yesmaximal, characteristic
5C7×#1393C211yesmaximal, characteristic
6C7×#1390C211yesmaximal, characteristic
7C7×#1390C211yesmaximal, characteristic
8C7×#518C2211yescharacteristic
9C7×#428—21no—
10C2×C7×#100C2211yescharacteristic
11C2×C7×#99C2211yescharacteristic
12C2×C7×#99C2211yescharacteristic
13C7×#399—21no—
14C7×#398—21no—
15C7×#396—21no—
16C7×#390C2211yescharacteristic
17C7×#387—21no—
18C7×#386C2211yescharacteristic
19C7×#386C2211yescharacteristic
20C7×#385—21no—
21C7×#385—21no—
22C7×#385—21no—
23C7×#380—21no—
24C7×#342—21no—
25C7×#342—21no—
26C7×#339—21no—
27#13462C711yesmaximal, characteristic, direct product factor, Sylow
28C22×C7×D4C2311yescharacteristic
29C23×C4×C7D411yescharacteristic
30C23×C4×C7D411yescharacteristic
31C2×C7×M16—21no—
32C4×C7×D4—41no—
33C4×C7×D4—41no—
34C7×#117—21no—
35C2×C7×C4⋊C4—21no—
36C2×C7×C4⋊C4—21no—
37C2×C7×C4⋊C4—21no—
38C2×C7×C4⋊C4—21no—
39C2×C7×C4⋊C4—21no—
40C2×C7×C4⋊C4—41no—
41C2×C7×C4⋊C4—41no—
42C2×C7×C4⋊C4D411yescharacteristic
43C2×C7×C22⋊C4—21no—
44C2×C7×C22⋊C4—21no—
45C2×C7×C22⋊C4—21no—
46C2×C7×C22⋊C4—21no—
47C2×C7×C22⋊C4—21no—
48C2×C7×C22⋊C4—21no—
49C2×C7×C22⋊C4—21no—
50C2×C7×C22⋊C4—21no—
51C2×C7×C22⋊C4D411yescharacteristic
52C2×C7×C22⋊C4D411yescharacteristic
53C2×C42×C7D411yescharacteristic
54C7×#107—41no—
55C7×#106—41no—
56C7×#100—21no—
57C7×#100Q812yes—
58C7×#99—21no—
59C7×#99—21no—
60C7×#99Q812yes—
61C7×#99Q812yes—
62C7×#95—21no—
63C7×#95—21no—
64C7×#95—21no—
65C7×#95—21no—
66C7×#95—21no—
67C7×#95—41no—
68C7×#95—41no—
69#2748C2×C711yescharacteristic
70#1867C2×C711yescharacteristic
71#1867C2×C711yescharacteristic
72#1856C2×C711yescharacteristic
73#1393C2×C711yescharacteristic
74#1390C2×C711yescharacteristic
75#1390C2×C711yescharacteristic
76C24×C7C2×D411yescharacteristic
77C24×C7C2×D411yescharacteristic
78C2×C7×D4—41no—
79C2×C7×D4—41no—
80C2×C7×D4C2×Q811yescharacteristic
81C2×C7×D4C2×Q811yescharacteristic
82C2×C7×D4C2×Q811yescharacteristic
83C2×C7×D4#4111yescharacteristic
84C22×C4×C7—21no—
85C22×C4×C7—21no—
86C22×C4×C7—21no—
87C22×C4×C7—21no—
88C22×C4×C7—21no—
89C22×C4×C7—21no—
90C22×C4×C7—21no—
91C22×C4×C7—21no—
92C22×C4×C7—21no—
93C22×C4×C7—21no—
94C22×C4×C7—42no—
95C22×C4×C7—41no—
96C22×C4×C7—41no—
97C22×C4×C7—41no—
98C22×C4×C7—41no—
99C22×C4×C7—81no—
100C22×C4×C7C2×D411yescharacteristic
101C7×M16—22no—
102C7×M16—41no—
103C2×C7×C8—41no—
104C7×C4⋊C4—21no—
105C7×C4⋊C4—21no—
106C7×C4⋊C4—41no—
107C7×C4⋊C4—42no—
108C7×C4⋊C4—81no—
109C7×C4⋊C4—81no—
110C7×C4⋊C4—81no—
111C7×C4⋊C4—81no—
112C7×C4⋊C4—82no—
113C7×C4⋊C4—82no—
114C7×C22⋊C4—22no—
115C7×C22⋊C4—22no—
116C7×C22⋊C4—42no—
117C7×C22⋊C4—41no—
118C7×C22⋊C4—41no—
119C7×C22⋊C4—41no—
120C7×C22⋊C4—41no—
121C7×C22⋊C4—41no—
122C7×C22⋊C4—41no—
123C7×C22⋊C4—41no—
124C7×C22⋊C4—81no—
125C7×C22⋊C4—81no—
126C7×C22⋊C4—81no—
127C42×C7—41no—
128C42×C7—41no—
129#518C22×C711yescharacteristic
130#428—21no—
131C2×#100C22×C711yescharacteristic
132C2×#99C22×C711yescharacteristic
133C2×#99C22×C711yescharacteristic
134#399—21no—
135#398—21no—
136#396—21no—
137#390C22×C711yescharacteristic
138#387—21no—
139#386C22×C711yescharacteristic
140#386C22×C711yescharacteristic
141#385—21no—
142#385—21no—
143#385—21no—
144#380—21no—
145#342—21no—
146#342—21no—
147#339—21no—
148C23×C7—21no—
149C23×C7—21no—
150C23×C7—21no—
151C23×C7—21no—
152C23×C7—41no—
153C23×C7—41no—
154C23×C7—41no—
155C23×C7—41no—
156C23×C7#12011yescharacteristic
157C23×C7C22⋊Q811yescharacteristic
158C23×C7C22⋊Q811yescharacteristic
159C23×C7C4⋊Q811yescharacteristic
160C23×C7C4⋊Q811yescharacteristic
161C7×D4—41no—
162C7×D4—41no—
163C7×D4—41no—
164C7×D4—41no—
165C2×C4×C7—21no—
166C2×C4×C7—21no—
167C2×C4×C7—22no—
168C2×C4×C7—41no—
169C2×C4×C7—41no—
170C2×C4×C7—42no—
171C2×C4×C7—42no—
172C2×C4×C7—42no—
173C2×C4×C7—41no—
174C2×C4×C7—41no—
175C2×C4×C7—41no—
176C2×C4×C7—41no—
177C2×C4×C7—41no—
178C2×C4×C7—41no—
179C2×C4×C7—41no—
180C2×C4×C7—41no—
181C2×C4×C7—41no—
182C2×C4×C7—41no—
183C2×C4×C7—42no—
184C2×C4×C7—41no—
185C2×C4×C7—41no—
186C2×C4×C7—41no—
187C2×C4×C7—41no—
188C2×C4×C7—41no—
189C2×C4×C7—41no—
190C2×C4×C7—41no—
191C2×C4×C7—81no—
192C2×C4×C7—81no—
193C2×C4×C7—81no—
194C2×C4×C7—81no—
195C2×C4×C7—81no—
196C2×C4×C7—81no—
197C2×C4×C7—81no—
198C2×C4×C7—81no—
199C2×C4×C7—81no—
200C2×C4×C7—81no—
201C2×C4×C7C22⋊Q811yescharacteristic
202C2×C4×C7C4⋊Q811yescharacteristic
203C7×C8—42no—
204C22×D4C23×C711yescharacteristic
205C23×C4C7×D411yescharacteristic
206C23×C4C7×D411yescharacteristic
207C2×M16—21no—
208C4×D4—41no—
209C4×D4—41no—
210#117—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—41no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4C7×D411yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4C7×D411yescharacteristic
228C2×C22⋊C4C7×D411yescharacteristic
229C2×C42C7×D411yescharacteristic
230#107—41no—
231#106—41no—
232#100—21no—
233#100C7×Q812yes—
234#99—21no—
235#99—21no—
236#99C7×Q812yes—
237#99C7×Q812yes—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—41no—
244#95—41no—
245C22×C7—21no—
246C22×C7—21no—
247C22×C7—21no—
248C22×C7—21no—
249C22×C7—21no—
250C22×C7—21no—
251C22×C7—41no—
252C22×C7—41no—
253C22×C7—41no—
254C22×C7—41no—
255C22×C7—41no—
256C22×C7—41no—
257C22×C7—41no—
258C22×C7—41no—
259C22×C7—81no—
260C22×C7—81no—
261C22×C7#39511yescharacteristic
262C22×C7B(4,𝔽2)11yescharacteristic
263C22×C7#45811yescharacteristic
264C4×C7—21no—
265C4×C7—21no—
266C4×C7—42no—
267C4×C7—81no—
268C4×C7—81no—
269C4×C7—81no—
270C4×C7—82no—
271C4×C7—82no—
272C4×C7—81no—
273C4×C7—81no—
274C4×C7—81no—
275C4×C7—81no—
276C24C2×C7×D411yescharacteristic
277C24C2×C7×D411yescharacteristic
278C2×D4—41no—
279C2×D4—41no—
280C2×D4C2×C7×Q811yescharacteristic
281C2×D4C2×C7×Q811yescharacteristic
282C2×D4C2×C7×Q811yescharacteristic
283C2×D4C7×#4111yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—42no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—81no—
300C22×C4C2×C7×D411yescharacteristic
301M16—22no—
302M16—41no—
303C2×C8—41no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—42no—
308C4⋊C4—81no—
309C4⋊C4—81no—
310C4⋊C4—81no—
311C4⋊C4—81no—
312C4⋊C4—82no—
313C4⋊C4—82no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—42no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—81no—
325C22⋊C4—81no—
326C22⋊C4—81no—
327C42—41no—
328C42—41no—
329C2×C7—21no—
330C2×C7—21no—
331C2×C7—41no—
332C2×C7—41no—
333C2×C7—41no—
334C2×C7—41no—
335C2×C7#206211yescharacteristic
336C2×C7#219711yescharacteristic
337C2×C7#220011yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23C7×#12011yescharacteristic
347C23C7×C22⋊Q811yescharacteristic
348C23C7×C22⋊Q811yescharacteristic
349C23C7×C4⋊Q811yescharacteristic
350C23C7×C4⋊Q811yescharacteristic
351D4—41no—
352D4—41no—
353D4—41no—
354D4—41no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4C7×C22⋊Q811yescharacteristic
392C2×C4C7×C4⋊Q811yescharacteristic
393C8—42no—
394C7#1346211yescharacteristic, direct product factor, Sylow
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22C7×#39511yescharacteristic
412C22C7×B(4,𝔽2)11yescharacteristic
413C22C7×#45811yescharacteristic
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—81no—
419C4—81no—
420C4—82no—
421C4—82no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4—81no—
426C2—21no—
427C2—21no—
428C2—41no—
429C2—41no—
430C2—41no—
431C2—41no—
432C2C7×#206211yescharacteristic
433C2C7×#219711yescharacteristic
434C2C7×#220011yescharacteristic
subgroupG/H
center, socleC22×C7B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C7
prime radicalC22×C7×D4C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C7 ◁ C22×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
27. #13462C7direct (N × H)
394. C7#13462direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#27482
C7×#18672
C7×#18562
C7×#13932
C7×#13902
#134627