Finite Group Databasebeta

← C7×#13425 #13190641

Subgroups — C7×#13425 #13190641

Order 1792.

508 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2717C211yesmaximal, characteristic
2C2×C7×#354C211yesmaximal, characteristic
3C2×C7×#352C211yesmaximal, characteristic
4C7×#1890C211yesmaximal, characteristic
5C7×#1885C211yesmaximal, characteristic
6C7×#1867C211yesmaximal, characteristic
7C7×#1390C211yesmaximal, characteristic
8C2×C7×#124C2211yescharacteristic
9C2×C7×#123C2211yescharacteristic
10C7×#518C2211yescharacteristic
11C7×#419—21no—
12C2×C7×#100C2211yescharacteristic
13C2×C7×#99C2211yescharacteristic
14C2×C7×#99C2211yescharacteristic
15C7×#397—21no—
16C7×#397—21no—
17C7×#395—21no—
18C7×#387—21no—
19C7×#386C2211yescharacteristic
20C7×#385—21no—
21C7×#385—21no—
22C7×#381—21no—
23C7×#380—21no—
24C7×#354—22no—
25C7×#352—22no—
26C7×#342—21no—
27C7×#342—21no—
28C7×#339—21no—
29#13425C711yesmaximal, characteristic, direct product factor, Sylow
30C22×C7×Q8D411yescharacteristic
31C22×C7×D4C2311yescharacteristic
32C23×C4×C7D411yescharacteristic
33C23×C4×C7D411yescharacteristic
34C2×C7×M16—21no—
35C7×#124—21no—
36C7×#124—21no—
37C7×#124—21no—
38C7×#124—21no—
39C7×#123—21no—
40C7×#123—21no—
41C7×#123—21no—
42C7×#123—21no—
43C4×C7×D4—41no—
44C4×C7×D4—41no—
45C7×#117—21no—
46C2×C7×C4⋊C4—21no—
47C2×C7×C4⋊C4—21no—
48C2×C7×C4⋊C4—21no—
49C2×C7×C4⋊C4—21no—
50C2×C7×C4⋊C4—41no—
51C2×C7×C22⋊C4—21no—
52C2×C7×C22⋊C4—21no—
53C2×C7×C22⋊C4—21no—
54C2×C7×C22⋊C4—21no—
55C2×C7×C22⋊C4—21no—
56C2×C7×C22⋊C4—21no—
57C2×C7×C22⋊C4—21no—
58C2×C7×C22⋊C4—21no—
59C2×C7×C22⋊C4D411yescharacteristic
60C2×C7×C22⋊C4D411yescharacteristic
61C2×C42×C7D411yescharacteristic
62C7×#103—41no—
63C7×#103—41no—
64C7×#100—21no—
65C7×#100—21no—
66C7×#99—21no—
67C7×#99—21no—
68C7×#99—21no—
69C7×#99D412yes—
70C7×#95—21no—
71C7×#95—21no—
72C7×#95—21no—
73C7×#95—21no—
74C7×#95—21no—
75C7×#95—21no—
76C7×#95—41no—
77C7×#95—41no—
78C7×#95—41no—
79#2717C2×C711yescharacteristic
80C2×#354C2×C711yescharacteristic
81C2×#352C2×C711yescharacteristic
82#1890C2×C711yescharacteristic
83#1885C2×C711yescharacteristic
84#1867C2×C711yescharacteristic
85#1390C2×C711yescharacteristic
86C24×C7C2×D411yescharacteristic
87C24×C7C2×D411yescharacteristic
88C2×C7×Q8—21no—
89C2×C7×Q8—21no—
90C2×C7×Q8—41no—
91C2×C7×Q8—41no—
92C2×C7×D4—41no—
93C2×C7×D4—41no—
94C2×C7×D4C2×D411yescharacteristic
95C2×C7×D4#4111yescharacteristic
96C2×C7×D4#4111yescharacteristic
97C2×C7×D4#4111yescharacteristic
98C22×C4×C7—21no—
99C22×C4×C7—21no—
100C22×C4×C7—21no—
101C22×C4×C7—21no—
102C22×C4×C7—21no—
103C22×C4×C7—21no—
104C22×C4×C7—21no—
105C22×C4×C7—21no—
106C22×C4×C7—21no—
107C22×C4×C7—21no—
108C22×C4×C7—21no—
109C22×C4×C7—21no—
110C22×C4×C7—42no—
111C22×C4×C7—41no—
112C22×C4×C7—41no—
113C22×C4×C7—41no—
114C22×C4×C7—41no—
115C22×C4×C7—41no—
116C22×C4×C7C2×D411yescharacteristic
117C7×M16—41no—
118C7×M16—41no—
119C2×C7×C8—41no—
120C7×C4⋊C4—21no—
121C7×C4⋊C4—21no—
122C7×C4⋊C4—42no—
123C7×C4⋊C4—41no—
124C7×C4⋊C4—41no—
125C7×C4⋊C4—81no—
126C7×C4⋊C4—81no—
127C7×C4⋊C4—82no—
128C7×C22⋊C4—22no—
129C7×C22⋊C4—21no—
130C7×C22⋊C4—21no—
131C7×C22⋊C4—42no—
132C7×C22⋊C4—41no—
133C7×C22⋊C4—41no—
134C7×C22⋊C4—41no—
135C7×C22⋊C4—41no—
136C7×C22⋊C4—41no—
137C7×C22⋊C4—41no—
138C7×C22⋊C4—41no—
139C7×C22⋊C4—41no—
140C7×C22⋊C4—41no—
141C7×C22⋊C4—41no—
142C7×C22⋊C4—41no—
143C7×C22⋊C4—41no—
144C7×C22⋊C4—41no—
145C42×C7—21no—
146C42×C7—21no—
147C42×C7—41no—
148C2×#124C22×C711yescharacteristic
149C2×#123C22×C711yescharacteristic
150#518C22×C711yescharacteristic
151#419—21no—
152C2×#100C22×C711yescharacteristic
153C2×#99C22×C711yescharacteristic
154C2×#99C22×C711yescharacteristic
155#397—21no—
156#397—21no—
157#395—21no—
158#387—21no—
159#386C22×C711yescharacteristic
160#385—21no—
161#385—21no—
162#381—21no—
163#380—21no—
164#354—22no—
165#352—22no—
166#342—21no—
167#342—21no—
168#339—21no—
169C23×C7—21no—
170C23×C7—21no—
171C23×C7—21no—
172C23×C7—21no—
173C23×C7—41no—
174C23×C7—41no—
175C23×C7—41no—
176C23×C7—41no—
177C23×C7#12011yescharacteristic
178C23×C7#12111yescharacteristic
179C23×C7#12111yescharacteristic
180C23×C7#12311yescharacteristic
181C23×C7#12411yescharacteristic
182C7×Q8—42no—
183C7×Q8—81no—
184C7×D4—41no—
185C7×D4—41no—
186C7×D4—41no—
187C7×D4—41no—
188C2×C4×C7—21no—
189C2×C4×C7—21no—
190C2×C4×C7—22no—
191C2×C4×C7—41no—
192C2×C4×C7—41no—
193C2×C4×C7—42no—
194C2×C4×C7—42no—
195C2×C4×C7—41no—
196C2×C4×C7—41no—
197C2×C4×C7—41no—
198C2×C4×C7—41no—
199C2×C4×C7—41no—
200C2×C4×C7—41no—
201C2×C4×C7—42no—
202C2×C4×C7—41no—
203C2×C4×C7—41no—
204C2×C4×C7—41no—
205C2×C4×C7—41no—
206C2×C4×C7—41no—
207C2×C4×C7—41no—
208C2×C4×C7—41no—
209C2×C4×C7—41no—
210C2×C4×C7—41no—
211C2×C4×C7—41no—
212C2×C4×C7—41no—
213C2×C4×C7—81no—
214C2×C4×C7—81no—
215C2×C4×C7—81no—
216C2×C4×C7—81no—
217C2×C4×C7—81no—
218C2×C4×C7—81no—
219C2×C4×C7—81no—
220C2×C4×C7—81no—
221C2×C4×C7—81no—
222C2×C4×C7—81no—
223C2×C4×C7—81no—
224C2×C4×C7#12111yescharacteristic
225C2×C4×C7#12311yescharacteristic
226C7×C8—81no—
227C22×Q8C7×D411yescharacteristic
228C22×D4C23×C711yescharacteristic
229C23×C4C7×D411yescharacteristic
230C23×C4C7×D411yescharacteristic
231C2×M16—21no—
232#124—21no—
233#124—21no—
234#124—21no—
235#124—21no—
236#123—21no—
237#123—21no—
238#123—21no—
239#123—21no—
240C4×D4—41no—
241C4×D4—41no—
242#117—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—41no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4C7×D411yescharacteristic
257C2×C22⋊C4C7×D411yescharacteristic
258C2×C42C7×D411yescharacteristic
259#103—41no—
260#103—41no—
261#100—21no—
262#100—21no—
263#99—21no—
264#99—21no—
265#99—21no—
266#99C7×D412yes—
267#95—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—21no—
273#95—41no—
274#95—41no—
275#95—41no—
276C22×C7—21no—
277C22×C7—21no—
278C22×C7—21no—
279C22×C7—21no—
280C22×C7—21no—
281C22×C7—21no—
282C22×C7—41no—
283C22×C7—41no—
284C22×C7—41no—
285C22×C7—41no—
286C22×C7—41no—
287C22×C7—41no—
288C22×C7—41no—
289C22×C7—41no—
290C22×C7—81no—
291C22×C7—81no—
292C22×C7#39411yescharacteristic
293C22×C7B(4,𝔽2)11yescharacteristic
294C22×C7#45811yescharacteristic
295C4×C7—21no—
296C4×C7—21no—
297C4×C7—42no—
298C4×C7—81no—
299C4×C7—81no—
300C4×C7—81no—
301C4×C7—82no—
302C4×C7—81no—
303C4×C7—81no—
304C4×C7—81no—
305C4×C7—81no—
306C4×C7—161no—
307C24C2×C7×D411yescharacteristic
308C24C2×C7×D411yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4C2×C7×D411yescharacteristic
316C2×D4C7×#4111yescharacteristic
317C2×D4C7×#4111yescharacteristic
318C2×D4C7×#4111yescharacteristic
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—42no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4C2×C7×D411yescharacteristic
338M16—41no—
339M16—41no—
340C2×C8—41no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—42no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—81no—
347C4⋊C4—81no—
348C4⋊C4—82no—
349C22⋊C4—22no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—42no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C42—21no—
367C42—21no—
368C42—41no—
369C2×C7—21no—
370C2×C7—21no—
371C2×C7—41no—
372C2×C7—41no—
373C2×C7—41no—
374C2×C7—41no—
375C2×C7#204411yescharacteristic
376C2×C7#219711yescharacteristic
377C2×C7#220111yescharacteristic
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23C7×#12011yescharacteristic
387C23C7×#12111yescharacteristic
388C23C7×#12111yescharacteristic
389C23C7×#12311yescharacteristic
390C23C7×#12411yescharacteristic
391Q8—42no—
392Q8—81no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—41no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4C7×#12111yescharacteristic
434C2×C4C7×#12311yescharacteristic
435C8—81no—
436C7#1342511yescharacteristic, direct product factor, Sylow
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—81no—
452C22—81no—
453C22C7×#39411yescharacteristic
454C22C7×B(4,𝔽2)11yescharacteristic
455C22C7×#45811yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—82no—
463C4—81no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4—161no—
468C2—21no—
469C2—21no—
470C2—41no—
471C2—41no—
472C2—41no—
473C2—41no—
474C2C7×#204411yescharacteristic
475C2C7×#219711yescharacteristic
476C2C7×#220111yescharacteristic
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
29. #13425C7direct (N × H)
436. C7#13425direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#27172
C2×C7×#3542
C2×C7×#3522
C7×#18902
C7×#18852
C7×#18672
C7×#13902
#134257