Finite Group Databasebeta

← C7×#18430 #13195646

Subgroups — C7×#18430 #13195646

Order 1792.

996 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3559C211yesmaximal, characteristic, complemented
2C7×#3217C211yesmaximal, characteristic, complemented
3C7×#3205C211yesmaximal, characteristic, complemented
4C7×#2641C211yesmaximal, characteristic, complemented
5C7×#1598C214yesmaximal, complemented
6C7×#1597C214yesmaximal, complemented
7C7×#1505C211yesmaximal, characteristic, complemented
8C7×#1500C211yesmaximal, characteristic, complemented
9C7×#1470C211yesmaximal, characteristic, complemented
10C7×#563—21no—
11C7×#562—21no—
12C7×#554—21no—
13C7×#553—21no—
14C7×#553—21no—
15C7×#547—22no—
16C7×#547—21no—
17C7×#544—21no—
18C7×#540—21no—
19C7×#539—22no—
20C7×#539C2212yes—
21C7×#537C2212yes—
22C7×#532C2211yescharacteristic
23C2×C7×#127C2211yescharacteristic
24C7×#529C2211yescharacteristic
25C2×C7×#125C2211yescharacteristic
26C7×#496—21no—
27C7×#493—21no—
28C7×#490—21no—
29C7×#486—21no—
30C7×#460—21no—
31C7×#459—22no—
32C7×#459—21no—
33C7×#450C2212yes—
34C7×#447C2214yes—
35C7×#447C2212yes—
36C7×#432C2211yescharacteristic
37C7×#431C2211yescharacteristic
38C7×#394—22no—
39C7×#394C2214yes—
40C7×#390—21no—
41C7×#390—21no—
42C7×#376C2211yescharacteristic
43C7×#328C2212yes—
44C7×#327C2212yes—
45C7×#327C2214yes—
46C7×#324C2214yes—
47#18430C711yesmaximal, characteristic, direct product factor, Sylow
48C2×C7×#41—21no—
49C2×C7×#41—22no—
50C22×C7×D4—21no—
51C22×C7×D4—21no—
52C22×C7×D4C2312yes—
53C2×C7×SD16—22no—
54C2×C7×D8—24no—
55C2×C7×D8—22no—
56C7×C4⋊Q8—21no—
57C7×C4⋊Q8—22no—
58C7×C4⋊Q8D411yescharacteristic
59C7×#127—21no—
60C7×#127—21no—
61C7×#127—21no—
62C7×#127—21no—
63C7×#127D411yescharacteristic
64C7×#126—22no—
65C7×#126—22no—
66C7×#126—21no—
67C7×#125—21no—
68C7×#125—22no—
69C7×#125—21no—
70C7×#125—21no—
71C7×#125—21no—
72C7×#125—21no—
73C7×#125D411yescharacteristic
74C7×#124—21no—
75C7×#124D411yescharacteristic
76C7×#123—22no—
77C7×#123—22no—
78C7×#123—22no—
79C7×#123—22no—
80C7×#123—22no—
81C7×#123—21no—
82C7×#123—22no—
83C7×C22⋊Q8—22no—
84C7×C22⋊Q8—22no—
85C7×C22⋊Q8—22no—
86C7×C22⋊Q8—22no—
87C7×C22⋊Q8—22no—
88C7×C22⋊Q8—22no—
89C7×C22⋊Q8C2311yescharacteristic
90C7×#121—21no—
91C7×#121—22no—
92C7×#121—21no—
93C7×#121—22no—
94C7×#121—22no—
95C7×#121—21no—
96C7×#121—22no—
97C7×#121C2311yescharacteristic
98C7×#121C2312yes—
99C4×C7×Q8D411yescharacteristic
100C4×C7×D4—22no—
101C4×C7×D4—21no—
102C4×C7×D4—21no—
103C4×C7×D4—21no—
104C4×C7×D4—22no—
105C4×C7×D4—21no—
106C4×C7×D4D411yescharacteristic
107C4×C7×D4D412yes—
108C7×#117—21no—
109C7×#117—21no—
110C2×C7×C4⋊C4—22no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4D411yescharacteristic
113C2×C7×C4⋊C4D411yescharacteristic
114C2×C7×C4⋊C4D412yes—
115C2×C7×C4⋊C4C2312yes—
116C2×C7×C22⋊C4—24no—
117C2×C7×C22⋊C4—24no—
118C2×C42×C7—21no—
119C2×C42×C7C2311yescharacteristic
120C7×C4⋊C8—21no—
121C7×C4⋊C8—21no—
122C7×#102—24no—
123C7×#102—22no—
124C7×#102—22no—
125C7×C22⋊C8C2312yes—
126C7×C22⋊C8C2312yes—
127C7×#97—21no—
128C4×C7×C8—21no—
129C7×#95—21no—
130C7×#95C2312yes—
131#3559C2×C711yescharacteristic, complemented
132#3217C2×C711yescharacteristic, complemented
133#3205C2×C711yescharacteristic, complemented
134#2641C2×C711yescharacteristic, complemented
135#1598C2×C714yescomplemented
136#1597C2×C714yescomplemented
137#1505C2×C711yescharacteristic, complemented
138#1500C2×C711yescharacteristic, complemented
139#1470C2×C711yescharacteristic, complemented
140C24×C7—22no—
141C7×#41—82no—
142C7×#41—84no—
143C2×C7×Q8—22no—
144C2×C7×Q8—21no—
145C2×C7×Q8C2×D411yescharacteristic
146C2×C7×D4—21no—
147C2×C7×D4—22no—
148C2×C7×D4—22no—
149C2×C7×D4—22no—
150C2×C7×D4—21no—
151C2×C7×D4—21no—
152C2×C7×D4—22no—
153C2×C7×D4—22no—
154C2×C7×D4—44no—
155C2×C7×D4—41no—
156C2×C7×D4—41no—
157C2×C7×D4—41no—
158C2×C7×D4—41no—
159C2×C7×D4—82no—
160C2×C7×D4—82no—
161C2×C7×D4C2×D411yescharacteristic
162C2×C7×D4C2×D412yes—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—21no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7C2×D412yes—
170C22×C4×C7C2×D411yescharacteristic
171C22×C4×C7C2×D411yescharacteristic
172C22×C4×C7C2×D412yes—
173C22×C4×C7C2411yescharacteristic
174C7×SD16—82no—
175C7×D8—84no—
176C7×D8—82no—
177C2×C7×C8—22no—
178C2×C7×C8—22no—
179C7×C4⋊C4—22no—
180C7×C4⋊C4—22no—
181C7×C4⋊C4—22no—
182C7×C4⋊C4—22no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—21no—
185C7×C4⋊C4—22no—
186C7×C4⋊C4—21no—
187C7×C4⋊C4—21no—
188C7×C4⋊C4—22no—
189C7×C4⋊C4—21no—
190C7×C4⋊C4—21no—
191C7×C4⋊C4—21no—
192C7×C4⋊C4—21no—
193C7×C4⋊C4—22no—
194C7×C4⋊C4—22no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4C2×D412yes—
197C7×C4⋊C4C2×D411yescharacteristic
198C7×C4⋊C4C2×D411yescharacteristic
199C7×C22⋊C4—22no—
200C7×C22⋊C4—22no—
201C7×C22⋊C4—22no—
202C7×C22⋊C4—22no—
203C7×C22⋊C4—22no—
204C7×C22⋊C4—21no—
205C7×C22⋊C4—21no—
206C7×C22⋊C4—21no—
207C7×C22⋊C4—21no—
208C7×C22⋊C4—22no—
209C7×C22⋊C4—21no—
210C7×C22⋊C4—22no—
211C7×C22⋊C4—84no—
212C7×C22⋊C4—84no—
213C42×C7—22no—
214C42×C7—21no—
215C42×C7—42no—
216C42×C7C2×D411yescharacteristic
217C42×C7C2×D411yescharacteristic
218C42×C7C2×D411yescharacteristic
219C42×C7C2×D411yescharacteristic
220#563—21no—
221#562—21no—
222#554—21no—
223#553—21no—
224#553—21no—
225#547—22no—
226#547—21no—
227#544—21no—
228#540—21no—
229#539—22no—
230#539C22×C712yes—
231#537C22×C712yes—
232#532C22×C711yescharacteristic
233C2×#127C22×C711yescharacteristic
234#529C22×C711yescharacteristic
235C2×#125C22×C711yescharacteristic
236#496—21no—
237#493—21no—
238#490—21no—
239#486—21no—
240#460—21no—
241#459—22no—
242#459—21no—
243#450C22×C712yes—
244#447C22×C714yes—
245#447C22×C712yes—
246#432C22×C711yescharacteristic
247#431C22×C711yescharacteristic
248#394—22no—
249#394C22×C714yes—
250#390—21no—
251#390—21no—
252#376C22×C711yescharacteristic
253#328C22×C712yes—
254#327C22×C714yes—
255#327C22×C712yes—
256#324C22×C714yes—
257C23×C7—21no—
258C23×C7—22no—
259C23×C7—44no—
260C23×C7—44no—
261C23×C7—42no—
262C23×C7—44no—
263C23×C7C22×D411yescharacteristic
264C7×Q8—41no—
265C7×Q8—81no—
266C7×Q8—82no—
267C7×D4—42no—
268C7×D4—41no—
269C7×D4—44no—
270C7×D4—42no—
271C7×D4—42no—
272C7×D4—44no—
273C7×D4—42no—
274C7×D4—42no—
275C7×D4—81no—
276C7×D4—82no—
277C7×D4—82no—
278C7×D4—82no—
279C7×D4—82no—
280C7×D4—82no—
281C7×D4—82no—
282C2×C4×C7—22no—
283C2×C4×C7—22no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—22no—
287C2×C4×C7—22no—
288C2×C4×C7—21no—
289C2×C4×C7—22no—
290C2×C4×C7—24no—
291C2×C4×C7—41no—
292C2×C4×C7—42no—
293C2×C4×C7—42no—
294C2×C4×C7—42no—
295C2×C4×C7—42no—
296C2×C4×C7—42no—
297C2×C4×C7—82no—
298C2×C4×C7—82no—
299C2×C4×C7—82no—
300C2×C4×C7—82no—
301C2×C4×C7#12011yescharacteristic
302C2×C4×C7#12011yescharacteristic
303C2×C4×C7#12011yescharacteristic
304C2×C4×C7#12011yescharacteristic
305C2×C4×C7C22×D411yescharacteristic
306C2×C4×C7C22×D411yescharacteristic
307C7×C8—42no—
308C7×C8—42no—
309C2×#41—21no—
310C2×#41—22no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4C23×C712yes—
314C2×SD16—22no—
315C2×D8—24no—
316C2×D8—22no—
317C4⋊Q8—21no—
318C4⋊Q8—22no—
319C4⋊Q8C7×D411yescharacteristic
320#127—21no—
321#127—21no—
322#127—21no—
323#127—21no—
324#127C7×D411yescharacteristic
325#126—22no—
326#126—22no—
327#126—21no—
328#125—21no—
329#125—22no—
330#125—21no—
331#125—21no—
332#125—21no—
333#125—21no—
334#125C7×D411yescharacteristic
335#124—21no—
336#124C7×D411yescharacteristic
337#123—22no—
338#123—22no—
339#123—22no—
340#123—22no—
341#123—22no—
342#123—21no—
343#123—22no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8C23×C711yescharacteristic
351#121—21no—
352#121—22no—
353#121—21no—
354#121—22no—
355#121—22no—
356#121—21no—
357#121—22no—
358#121C23×C711yescharacteristic
359#121C23×C712yes—
360C4×Q8C7×D411yescharacteristic
361C4×D4—22no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—22no—
366C4×D4—21no—
367C4×D4C7×D411yescharacteristic
368C4×D4C7×D412yes—
369#117—21no—
370#117—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4C7×D411yescharacteristic
374C2×C4⋊C4C7×D412yes—
375C2×C4⋊C4C7×D411yescharacteristic
376C2×C4⋊C4C23×C712yes—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C42—21no—
380C2×C42C23×C711yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—21no—
383#102—24no—
384#102—22no—
385#102—22no—
386C22⋊C8C23×C712yes—
387C22⋊C8C23×C712yes—
388#97—21no—
389C4×C8—21no—
390#95—21no—
391#95C23×C712yes—
392C22×C7—21no—
393C22×C7—21no—
394C22×C7—42no—
395C22×C7—41no—
396C22×C7—41no—
397C22×C7—42no—
398C22×C7—42no—
399C22×C7—41no—
400C22×C7—88no—
401C22×C7—82no—
402C22×C7—82no—
403C22×C7—82no—
404C22×C7C2×#12011yescharacteristic
405C22×C7#57612yes—
406C4×C7—21no—
407C4×C7—21no—
408C4×C7—21no—
409C4×C7—21no—
410C4×C7—21no—
411C4×C7—42no—
412C4×C7—42no—
413C4×C7—41no—
414C4×C7—41no—
415C4×C7—42no—
416C4×C7—41no—
417C4×C7—82no—
418C4×C7#45412yes—
419C24—22no—
420#41—82no—
421#41—84no—
422C2×Q8—22no—
423C2×Q8—21no—
424C2×Q8C2×C7×D411yescharacteristic
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—44no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—82no—
439C2×D4—82no—
440C2×D4C2×C7×D411yescharacteristic
441C2×D4C2×C7×D412yes—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4C2×C7×D412yes—
449C22×C4C2×C7×D411yescharacteristic
450C22×C4C2×C7×D411yescharacteristic
451C22×C4C2×C7×D412yes—
452C22×C4C24×C711yescharacteristic
453SD16—82no—
454D8—84no—
455D8—82no—
456C2×C8—22no—
457C2×C8—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4C2×C7×D412yes—
476C4⋊C4C2×C7×D411yescharacteristic
477C4⋊C4C2×C7×D411yescharacteristic
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—22no—
488C22⋊C4—21no—
489C22⋊C4—22no—
490C22⋊C4—84no—
491C22⋊C4—84no—
492C42—22no—
493C42—21no—
494C42—42no—
495C42C2×C7×D411yescharacteristic
496C42C2×C7×D411yescharacteristic
497C42C2×C7×D411yescharacteristic
498C42C2×C7×D411yescharacteristic
499C2×C7—22no—
500C2×C7—81no—
501C2×C7—82no—
502C2×C7—162no—
503C2×C7#300811yescharacteristic
504C2×C7C2×#45411yescharacteristic
505C2×C7#302711yescharacteristic
506C23—21no—
507C23—22no—
508C23—44no—
509C23—44no—
510C23—42no—
511C23—44no—
512C23C22×C7×D411yescharacteristic
513Q8—41no—
514Q8—81no—
515Q8—82no—
516D4—42no—
517D4—41no—
518D4—44no—
519D4—42no—
520D4—42no—
521D4—44no—
522D4—42no—
523D4—42no—
524D4—81no—
525D4—82no—
526D4—82no—
527D4—82no—
528D4—82no—
529D4—82no—
530D4—82no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—82no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4C7×#12011yescharacteristic
551C2×C4C7×#12011yescharacteristic
552C2×C4C7×#12011yescharacteristic
553C2×C4C7×#12011yescharacteristic
554C2×C4C22×C7×D411yescharacteristic
555C2×C4C22×C7×D411yescharacteristic
556C8—42no—
557C8—42no—
558C7#1843011yescharacteristic, direct product factor, Sylow
559C22—21no—
560C22—21no—
561C22—42no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22—42no—
566C22—41no—
567C22—88no—
568C22—82no—
569C22—82no—
570C22—82no—
571C22C2×C7×#12011yescharacteristic
572C22C7×#57612yes—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—21no—
577C4—21no—
578C4—42no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—41no—
584C4—82no—
585C4C7×#45412yes—
586C2—22no—
587C2—81no—
588C2—82no—
589C2—162no—
590C2C7×#300811yescharacteristic
591C2C2×C7×#45411yescharacteristic
592C2C7×#302711yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3559C2semidirect
2. C7×#3217C2semidirect
3. C7×#3205C2semidirect
4. C7×#2641C2semidirect
5. C7×#1598C2semidirect
6. C7×#1597C2semidirect
7. C7×#1505C2semidirect
8. C7×#1500C2semidirect
9. C7×#1470C2semidirect
47. #18430C7direct (N × H)
131. #3559C2×C7semidirect
132. #3217C2×C7semidirect
133. #3205C2×C7semidirect
134. #2641C2×C7semidirect
135. #1598C2×C7semidirect
136. #1597C2×C7semidirect
137. #1505C2×C7semidirect
138. #1500C2×C7semidirect
139. #1470C2×C7semidirect
558. C7#18430direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35592
C7×#32172
C7×#32052
C7×#26412
C7×#15982
C7×#15972
C7×#15052
C7×#15002
C7×#14702
#184307