Finite Group Databasebeta

← C7×#19032 #13196248

Subgroups — C7×#19032 #13196248

Order 1792.

896 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3561C211yesmaximal, characteristic
2C7×#3218C211yesmaximal, characteristic, complemented
3C7×#3165C211yesmaximal, characteristic, complemented
4C2×C7×#489C211yesmaximal, characteristic, complemented
5C7×#1664C214yesmaximal, complemented
6C7×#1661C214yesmaximal, complemented
7C7×#1531C211yesmaximal, characteristic, complemented
8C7×#1527C211yesmaximal, characteristic, complemented
9C7×#1524C211yesmaximal, characteristic, complemented
10C7×#563C2212yes—
11C7×#562C2212yes—
12C7×#556—21no—
13C7×#551—22no—
14C7×D4×Q8—21no—
15C7×#548—21no—
16C7×#546—21no—
17C7×#543—21no—
18C7×#542—21no—
19C7×#542—22no—
20C7×#538—21no—
21C7×#536—21no—
22C7×#533C2211yescharacteristic
23C2×C7×C4⋊Q8C2211yescharacteristic
24C7×#529C2211yescharacteristic
25C2×C7×#124C2211yescharacteristic
26C7×#501C2214yescomplemented
27C7×#500—21no—
28C7×#498—21no—
29C7×#497C2212yescomplemented
30C7×#491C2212yescomplemented
31C7×#489—22no—
32C7×#489C2214yes—
33C7×#462—21no—
34C7×#461—21no—
35C7×#451—21no—
36C7×#448—21no—
37C7×#432C2211yescharacteristic
38C7×#428—22no—
39C2×C7×#103—21no—
40C2×C7×#102—21no—
41C4×C7×M16C2211yescharacteristic
42C2×C7×#97C2211yescharacteristic
43C7×#330C2212yescomplemented
44C7×#330C2214yescomplemented
45C7×#329C2214yes—
46C7×#329C2212yescomplemented
47#19032C711yesmaximal, characteristic, direct product factor, Sylow
48C2×C7×#41—21no—
49C22×C7×Q8—21no—
50C22×C7×Q8—21no—
51C22×C7×Q8D411yescharacteristic
52C22×C7×D4D411yescharacteristic
53C2×C7×Q16—22no—
54C2×C7×SD16—22no—
55C2×C7×M16—21no—
56C22×C7×C8—21no—
57C7×C4⋊Q8—21no—
58C7×C4⋊Q8—22no—
59C7×C4⋊Q8—21no—
60C7×C4⋊Q8—21no—
61C7×C4⋊Q8—21no—
62C7×C4⋊Q8D411yescharacteristic
63C7×C4⋊Q8D411yescharacteristic
64C7×C4⋊Q8C2312yes—
65C7×#126—22no—
66C7×#126—22no—
67C7×#126—22no—
68C7×#126—21no—
69C7×#125C2311yescharacteristic
70C7×#125C2312yes—
71C7×#124—21no—
72C7×#124—22no—
73C7×#124—22no—
74C7×#124—21no—
75C7×#124—21no—
76C7×#124D412yes—
77C7×#124C2312yes—
78C7×#124C2311yescharacteristic
79C7×#123—22no—
80C7×#123—22no—
81C7×#123—21no—
82C7×#123—22no—
83C7×#123—22no—
84C7×C22⋊Q8—22no—
85C7×C22⋊Q8—22no—
86C7×C22⋊Q8—21no—
87C7×C22⋊Q8—22no—
88C7×C22⋊Q8—22no—
89C7×C22⋊Q8—22no—
90C7×C22⋊Q8—21no—
91C7×C22⋊Q8—21no—
92C7×C22⋊Q8—22no—
93C7×C22⋊Q8—22no—
94C7×C22⋊Q8D411yescharacteristic
95C7×#121—21no—
96C7×#121—22no—
97C7×#121—22no—
98C7×#121D411yescharacteristic
99C7×#120—22no—
100C4×C7×Q8—21no—
101C4×C7×Q8—21no—
102C4×C7×Q8—21no—
103C4×C7×Q8D411yescharacteristic
104C4×C7×D4—22no—
105C4×C7×D4—21no—
106C4×C7×D4—22no—
107C4×C7×D4—21no—
108C4×C7×D4D411yescharacteristic
109C7×#117—22no—
110C7×#117—21no—
111C7×#117D412yes—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4—21no—
114C2×C7×C22⋊C4—22no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C42×C7C2311yescharacteristic
118C7×#107—24no—
119C7×#106—24no—
120C7×C4⋊C8—21no—
121C7×#103—24no—
122C7×#103—22no—
123C7×#103—22no—
124C7×#102—24no—
125C7×C22⋊C8—21no—
126C7×#97—21no—
127C7×#97C2312yes—
128C7×#97C2312yes—
129C7×#97C2312yes—
130C4×C7×C8—21no—
131#3561C2×C711yescharacteristic
132#3218C2×C711yescharacteristic, complemented
133#3165C2×C711yescharacteristic, complemented
134C2×#489C2×C711yescharacteristic, complemented
135#1664C2×C714yescomplemented
136#1661C2×C714yescomplemented
137#1531C2×C711yescharacteristic, complemented
138#1527C2×C711yescharacteristic, complemented
139#1524C2×C711yescharacteristic, complemented
140C24×C7—21no—
141C7×#41—82no—
142C2×C7×Q8—22no—
143C2×C7×Q8—21no—
144C2×C7×Q8—21no—
145C2×C7×Q8—21no—
146C2×C7×Q8—22no—
147C2×C7×Q8—42no—
148C2×C7×Q8—41no—
149C2×C7×Q8—82no—
150C2×C7×Q8—82no—
151C2×C7×Q8C2×D412yes—
152C2×C7×Q8C2×D411yescharacteristic
153C2×C7×D4—21no—
154C2×C7×D4—22no—
155C2×C7×D4—22no—
156C2×C7×D4—21no—
157C2×C7×D4—42no—
158C2×C7×D4C2×D412yes—
159C2×C7×D4C2×D411yescharacteristic
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—41no—
166C22×C4×C7C2×D411yescharacteristic
167C22×C4×C7C2×D411yescharacteristic
168C22×C4×C7C2×D411yescharacteristic
169C7×Q16—82no—
170C7×SD16—82no—
171C7×M16—24no—
172C2×C7×C8—22no—
173C2×C7×C8—22no—
174C2×C7×C8—22no—
175C2×C7×C8—42no—
176C7×C4⋊C4—22no—
177C7×C4⋊C4—22no—
178C7×C4⋊C4—22no—
179C7×C4⋊C4—22no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—21no—
185C7×C4⋊C4—21no—
186C7×C4⋊C4—22no—
187C7×C4⋊C4—22no—
188C7×C4⋊C4—22no—
189C7×C4⋊C4—22no—
190C7×C4⋊C4—41no—
191C7×C4⋊C4—41no—
192C7×C4⋊C4C2×D411yescharacteristic
193C7×C4⋊C4C2×D411yescharacteristic
194C7×C4⋊C4C2×D412yes—
195C7×C4⋊C4C2×D412yes—
196C7×C22⋊C4—22no—
197C7×C22⋊C4—22no—
198C7×C22⋊C4—22no—
199C7×C22⋊C4—22no—
200C7×C22⋊C4—22no—
201C7×C22⋊C4—21no—
202C7×C22⋊C4—22no—
203C7×C22⋊C4—22no—
204C7×C22⋊C4—22no—
205C7×C22⋊C4—21no—
206C7×C22⋊C4—21no—
207C7×C22⋊C4—22no—
208C7×C22⋊C4—22no—
209C7×C22⋊C4—21no—
210C7×C22⋊C4—21no—
211C42×C7—22no—
212C42×C7—22no—
213C42×C7—21no—
214C42×C7C2×D411yescharacteristic
215C42×C7C2×D411yescharacteristic
216C42×C7C2×D411yescharacteristic
217C42×C7C2411yescharacteristic
218#563C22×C712yes—
219#562C22×C712yes—
220#556—21no—
221#551—22no—
222D4×Q8—21no—
223#548—21no—
224#546—21no—
225#543—21no—
226#542—21no—
227#542—22no—
228#538—21no—
229#536—21no—
230#533C22×C711yescharacteristic
231C2×C4⋊Q8C22×C711yescharacteristic
232#529C22×C711yescharacteristic
233C2×#124C22×C711yescharacteristic
234#501C22×C714yescomplemented
235#500—21no—
236#498—21no—
237#497C22×C712yescomplemented
238#491C22×C712yescomplemented
239#489—22no—
240#489C22×C714yes—
241#462—21no—
242#461—21no—
243#451—21no—
244#448—21no—
245#432C22×C711yescharacteristic
246#428—22no—
247C2×#103—21no—
248C2×#102—21no—
249C4×M16C22×C711yescharacteristic
250C2×#97C22×C711yescharacteristic
251#330C22×C714yescomplemented
252#330C22×C712yescomplemented
253#329C22×C714yes—
254#329C22×C712yescomplemented
255C23×C7—22no—
256C23×C7—21no—
257C23×C7—42no—
258C23×C7—81no—
259C23×C7—81no—
260C23×C7#12011yescharacteristic
261C7×Q8—41no—
262C7×Q8—42no—
263C7×Q8—42no—
264C7×Q8—42no—
265C7×Q8—42no—
266C7×Q8—42no—
267C7×Q8—81no—
268C7×Q8—82no—
269C7×Q8—82no—
270C7×D4—41no—
271C7×D4—42no—
272C7×D4—42no—
273C7×D4—42no—
274C7×D4—82no—
275C7×D4—82no—
276C2×C4×C7—22no—
277C2×C4×C7—22no—
278C2×C4×C7—21no—
279C2×C4×C7—22no—
280C2×C4×C7—21no—
281C2×C4×C7—22no—
282C2×C4×C7—22no—
283C2×C4×C7—21no—
284C2×C4×C7—41no—
285C2×C4×C7—42no—
286C2×C4×C7—42no—
287C2×C4×C7—81no—
288C2×C4×C7—82no—
289C2×C4×C7—82no—
290C2×C4×C7—82no—
291C2×C4×C7—82no—
292C2×C4×C7#12011yescharacteristic
293C2×C4×C7#12011yescharacteristic
294C2×C4×C7#12011yescharacteristic
295C2×C4×C7C22×D411yescharacteristic
296C2×C4×C7C22×D411yescharacteristic
297C2×C4×C7C22×D411yescharacteristic
298C7×C8—24no—
299C7×C8—42no—
300C7×C8—42no—
301C2×#41—21no—
302C22×Q8—21no—
303C22×Q8—21no—
304C22×Q8C7×D411yescharacteristic
305C22×D4C7×D411yescharacteristic
306C2×Q16—22no—
307C2×SD16—22no—
308C2×M16—21no—
309C22×C8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—22no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8C7×D411yescharacteristic
316C4⋊Q8C7×D411yescharacteristic
317C4⋊Q8C23×C712yes—
318#126—22no—
319#126—22no—
320#126—22no—
321#126—21no—
322#125C23×C711yescharacteristic
323#125C23×C712yes—
324#124—21no—
325#124—22no—
326#124—22no—
327#124—21no—
328#124—21no—
329#124C7×D412yes—
330#124C23×C712yes—
331#124C23×C711yescharacteristic
332#123—22no—
333#123—22no—
334#123—21no—
335#123—22no—
336#123—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—21no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—21no—
344C22⋊Q8—21no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8C7×D411yescharacteristic
348#121—21no—
349#121—22no—
350#121—22no—
351#121C7×D411yescharacteristic
352#120—22no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8C7×D411yescharacteristic
357C4×D4—22no—
358C4×D4—21no—
359C4×D4—22no—
360C4×D4—21no—
361C4×D4C7×D411yescharacteristic
362#117—22no—
363#117—21no—
364#117C7×D412yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C42C23×C711yescharacteristic
371#107—24no—
372#106—24no—
373C4⋊C8—21no—
374#103—24no—
375#103—22no—
376#103—22no—
377#102—24no—
378C22⋊C8—21no—
379#97—21no—
380#97C23×C712yes—
381#97C23×C712yes—
382#97C23×C712yes—
383C4×C8—21no—
384C22×C7—21no—
385C22×C7—21no—
386C22×C7—41no—
387C22×C7—42no—
388C22×C7—41no—
389C22×C7—42no—
390C22×C7—42no—
391C22×C7—41no—
392C22×C7—162no—
393C22×C7#45612yes—
394C22×C7C2×#12011yescharacteristic
395C4×C7—21no—
396C4×C7—21no—
397C4×C7—21no—
398C4×C7—21no—
399C4×C7—21no—
400C4×C7—41no—
401C4×C7—42no—
402C4×C7—42no—
403C4×C7—41no—
404C4×C7—41no—
405C4×C7—42no—
406C4×C7—82no—
407C4×C7#45512yes—
408C24—21no—
409#41—82no—
410C2×Q8—22no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—22no—
415C2×Q8—42no—
416C2×Q8—41no—
417C2×Q8—82no—
418C2×Q8—82no—
419C2×Q8C2×C7×D412yes—
420C2×Q8C2×C7×D411yescharacteristic
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—42no—
426C2×D4C2×C7×D412yes—
427C2×D4C2×C7×D411yescharacteristic
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—41no—
434C22×C4C2×C7×D411yescharacteristic
435C22×C4C2×C7×D411yescharacteristic
436C22×C4C2×C7×D411yescharacteristic
437Q16—82no—
438SD16—82no—
439M16—24no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—42no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4C2×C7×D411yescharacteristic
461C4⋊C4C2×C7×D411yescharacteristic
462C4⋊C4C2×C7×D412yes—
463C4⋊C4C2×C7×D412yes—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—21no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C42—22no—
480C42—22no—
481C42—21no—
482C42C2×C7×D411yescharacteristic
483C42C2×C7×D411yescharacteristic
484C42C2×C7×D411yescharacteristic
485C42C24×C711yescharacteristic
486C2×C7—22no—
487C2×C7—81no—
488C2×C7—82no—
489C2×C7C2×#45511yescharacteristic
490C2×C7C2×#45611yescharacteristic
491C2×C7#302111yescharacteristic
492C23—22no—
493C23—21no—
494C23—42no—
495C23—81no—
496C23—81no—
497C23C7×#12011yescharacteristic
498Q8—41no—
499Q8—42no—
500Q8—42no—
501Q8—42no—
502Q8—42no—
503Q8—42no—
504Q8—81no—
505Q8—82no—
506Q8—82no—
507D4—41no—
508D4—42no—
509D4—42no—
510D4—42no—
511D4—82no—
512D4—82no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—81no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4C7×#12011yescharacteristic
530C2×C4C7×#12011yescharacteristic
531C2×C4C7×#12011yescharacteristic
532C2×C4C22×C7×D411yescharacteristic
533C2×C4C22×C7×D411yescharacteristic
534C2×C4C22×C7×D411yescharacteristic
535C8—24no—
536C8—42no—
537C8—42no—
538C7#1903211yescharacteristic, direct product factor, Sylow
539C22—21no—
540C22—21no—
541C22—41no—
542C22—42no—
543C22—41no—
544C22—42no—
545C22—42no—
546C22—41no—
547C22—162no—
548C22C7×#45612yes—
549C22C2×C7×#12011yescharacteristic
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—41no—
559C4—41no—
560C4—42no—
561C4—82no—
562C4C7×#45512yes—
563C2—22no—
564C2—82no—
565C2—81no—
566C2C2×C7×#45511yescharacteristic
567C2C2×C7×#45611yescharacteristic
568C2C7×#302111yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC42C24×C7
prime radicalC7×#3561C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#3218C2semidirect
3. C7×#3165C2semidirect
4. C2×C7×#489C2semidirect
5. C7×#1664C2semidirect
6. C7×#1661C2semidirect
7. C7×#1531C2semidirect
8. C7×#1527C2semidirect
9. C7×#1524C2semidirect
26. C7×#501C22semidirect
29. C7×#497C22semidirect
30. C7×#491C22semidirect
43. C7×#330C22semidirect
44. C7×#330C22semidirect
46. C7×#329C22semidirect
47. #19032C7direct (N × H)
132. #3218C2×C7semidirect
133. #3165C2×C7semidirect
134. C2×#489C2×C7semidirect
135. #1664C2×C7semidirect
136. #1661C2×C7semidirect
137. #1531C2×C7semidirect
138. #1527C2×C7semidirect
139. #1524C2×C7semidirect
234. #501C22×C7semidirect
237. #497C22×C7semidirect
238. #491C22×C7semidirect
251. #330C22×C7semidirect
252. #330C22×C7semidirect
254. #329C22×C7semidirect
538. C7#19032direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35612
C7×#32182
C7×#31652
C2×C7×#4892
C7×#16642
C7×#16612
C7×#15312
C7×#15272
C7×#15242
#190327