Finite Group Databasebeta

← C7×#19044 #13196260

Subgroups — C7×#19044 #13196260

Order 1792.

956 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3559C211yesmaximal, characteristic, complemented
2C7×#3234C211yesmaximal, characteristic, complemented
3C7×#3180C211yesmaximal, characteristic, complemented
4C7×#3150C211yesmaximal, characteristic, complemented
5C7×#1661C212yesmaximal, complemented
6C7×#1660C212yesmaximal, complemented
7C7×#1657C212yesmaximal, complemented
8C7×#1656C212yesmaximal, complemented
9C7×#1532C211yesmaximal, characteristic, complemented
10C7×#1530C211yesmaximal, characteristic, complemented
11C2×C7×#330C211yesmaximal, characteristic, complemented
12C2×C7×#135—22no—
13C7×#563C2212yes—
14C7×#562C2212yes—
15C7×#554—21no—
16C7×#553—21no—
17C7×#553—21no—
18C7×#547—22no—
19C7×#547—21no—
20C7×#544—21no—
21C7×#540—21no—
22C7×#539—22no—
23C7×#539—21no—
24C7×#537—21no—
25C7×#532C2211yescharacteristic
26C7×#532C2211yescharacteristic
27C7×#529C2211yescharacteristic
28C2×C7×#125C2211yescharacteristic
29C7×#501C2211yescharacteristic
30C7×#501C2212yes—
31C7×#497—21no—
32C7×#497C2212yes—
33C7×#496—21no—
34C7×#496C2211yescharacteristic
35C7×#496C2212yes—
36C7×#490C2211yescharacteristic
37C7×#490C2212yes—
38C7×#489C2211yescharacteristic
39C7×#481—21no—
40C7×#480—21no—
41C7×#478—22no—
42C7×#466—21no—
43C7×#465—21no—
44C7×#442—21no—
45C7×#440—21no—
46C7×#432C2211yescharacteristic
47C2×C7×#97C2211yescharacteristic
48C2×C7×#97C2211yescharacteristic
49C7×#330C2212yes—
50C7×#330C2212yes—
51C7×#330C2212yes—
52C7×#329C2212yes—
53C7×#329C2212yes—
54C7×#329C2212yes—
55#19044C711yesmaximal, characteristic, direct product factor, Sylow
56C2×C7×#41—22no—
57C2×C7×#41—21no—
58C2×C7×#41D412yes—
59C7×#135—48no—
60C2×C7×Q16—22no—
61C2×C7×SD16—22no—
62C2×C7×SD16—21no—
63C2×C7×SD16—22no—
64C2×C7×D8—21no—
65C2×C7×D8—22no—
66C22×C7×C8—21no—
67C22×C7×C8—21no—
68C7×C4⋊Q8—21no—
69C7×C4⋊Q8—22no—
70C7×C4⋊Q8D411yescharacteristic
71C7×C4⋊Q8C2311yescharacteristic
72C7×#127D411yescharacteristic
73C7×#127C2311yescharacteristic
74C7×#126—22no—
75C7×#126—22no—
76C7×#126—21no—
77C7×#125—22no—
78C7×#125—21no—
79C7×#125—21no—
80C7×#125—21no—
81C7×#125D412yes—
82C7×#125C2312yes—
83C7×#125C2311yescharacteristic
84C7×#124—21no—
85C7×#124C2311yescharacteristic
86C7×#124C2312yes—
87C7×#123—22no—
88C7×#123—22no—
89C7×#123—22no—
90C7×#123—22no—
91C7×#123—21no—
92C7×#123—22no—
93C7×#123—22no—
94C7×C22⋊Q8—22no—
95C7×C22⋊Q8—22no—
96C7×C22⋊Q8—22no—
97C7×C22⋊Q8—22no—
98C7×C22⋊Q8—22no—
99C7×C22⋊Q8—22no—
100C7×C22⋊Q8D411yescharacteristic
101C7×#121—22no—
102C7×#121—22no—
103C7×#121—21no—
104C7×#121—21no—
105C7×#121—22no—
106C7×#121—22no—
107C7×#121—21no—
108C7×#121—21no—
109C7×#121—21no—
110C7×#121—21no—
111C7×#121D411yescharacteristic
112C4×C7×Q8D411yescharacteristic
113C4×C7×D4—22no—
114C4×C7×D4—22no—
115C4×C7×D4—21no—
116C4×C7×D4—21no—
117C4×C7×D4—21no—
118C4×C7×D4—21no—
119C4×C7×D4—21no—
120C4×C7×D4—21no—
121C4×C7×D4—21no—
122C4×C7×D4D411yescharacteristic
123C7×#117—21no—
124C7×#117—21no—
125C2×C7×C4⋊C4—22no—
126C2×C7×C4⋊C4—21no—
127C2×C7×C4⋊C4—21no—
128C2×C7×C4⋊C4—21no—
129C2×C7×C4⋊C4D411yescharacteristic
130C2×C7×C4⋊C4D411yescharacteristic
131C2×C42×C7C2311yescharacteristic
132C7×#107—21no—
133C7×#107—22no—
134C7×#106—22no—
135C7×#106—21no—
136C7×C4⋊C8—21no—
137C7×#103—21no—
138C7×#102—21no—
139C7×#102—21no—
140C7×#102—22no—
141C7×#102—22no—
142C7×#102—21no—
143C7×C22⋊C8—21no—
144C7×#97—21no—
145C7×#97—21no—
146C7×#97C2311yescharacteristic
147C7×#97C2312yes—
148C7×#97C2311yescharacteristic
149C7×#97C2312yes—
150#3559C2×C711yescharacteristic, complemented
151#3234C2×C711yescharacteristic, complemented
152#3180C2×C711yescharacteristic, complemented
153#3150C2×C711yescharacteristic, complemented
154#1661C2×C712yescomplemented
155#1660C2×C712yescomplemented
156#1657C2×C712yescomplemented
157#1656C2×C712yescomplemented
158#1532C2×C711yescharacteristic, complemented
159#1530C2×C711yescharacteristic, complemented
160C2×#330C2×C711yescharacteristic, complemented
161C7×#41—44no—
162C7×#41—44no—
163C7×#41—84no—
164C2×C7×Q8—22no—
165C2×C7×Q8—21no—
166C2×C7×Q8C2×D411yescharacteristic
167C2×C7×Q8C2×D412yes—
168C2×C7×D4—22no—
169C2×C7×D4—21no—
170C2×C7×D4—22no—
171C2×C7×D4—22no—
172C2×C7×D4—21no—
173C2×C7×D4—21no—
174C2×C7×D4—21no—
175C2×C7×D4—21no—
176C2×C7×D4—21no—
177C2×C7×D4—41no—
178C2×C7×D4C2×D411yescharacteristic
179C2×C7×D4C2×D412yes—
180C22×C4×C7—21no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—22no—
187C22×C4×C7—41no—
188C22×C4×C7C2×D411yescharacteristic
189C22×C4×C7C2×D411yescharacteristic
190C22×C4×C7C2×D411yescharacteristic
191C7×Q16—44no—
192C7×SD16—42no—
193C7×SD16—44no—
194C7×SD16—44no—
195C7×D8—42no—
196C7×D8—44no—
197C2×C7×C8—24no—
198C2×C7×C8—21no—
199C2×C7×C8—22no—
200C2×C7×C8—21no—
201C2×C7×C8—22no—
202C2×C7×C8—42no—
203C7×C4⋊C4—22no—
204C7×C4⋊C4—22no—
205C7×C4⋊C4—22no—
206C7×C4⋊C4—22no—
207C7×C4⋊C4—22no—
208C7×C4⋊C4—21no—
209C7×C4⋊C4—21no—
210C7×C4⋊C4—21no—
211C7×C4⋊C4—22no—
212C7×C4⋊C4—21no—
213C7×C4⋊C4—21no—
214C7×C4⋊C4—21no—
215C7×C4⋊C4—22no—
216C7×C4⋊C4—22no—
217C7×C4⋊C4—21no—
218C7×C4⋊C4—21no—
219C7×C4⋊C4—21no—
220C7×C4⋊C4—21no—
221C7×C4⋊C4C2×D412yes—
222C7×C4⋊C4C2×D411yescharacteristic
223C7×C4⋊C4C2×D412yes—
224C7×C4⋊C4C2×D411yescharacteristic
225C7×C22⋊C4—22no—
226C7×C22⋊C4—22no—
227C7×C22⋊C4—22no—
228C7×C22⋊C4—22no—
229C7×C22⋊C4—22no—
230C7×C22⋊C4—21no—
231C7×C22⋊C4—21no—
232C7×C22⋊C4—21no—
233C7×C22⋊C4—21no—
234C7×C22⋊C4—22no—
235C7×C22⋊C4—22no—
236C7×C22⋊C4—21no—
237C7×C22⋊C4—41no—
238C7×C22⋊C4—41no—
239C42×C7—22no—
240C42×C7—21no—
241C42×C7C2×D411yescharacteristic
242C42×C7C2×D411yescharacteristic
243C42×C7C2×D411yescharacteristic
244C42×C7C2411yescharacteristic
245C2×#135—22no—
246#563C22×C712yes—
247#562C22×C712yes—
248#554—21no—
249#553—21no—
250#553—21no—
251#547—22no—
252#547—21no—
253#544—21no—
254#540—21no—
255#539—22no—
256#539—21no—
257#537—21no—
258#532C22×C711yescharacteristic
259#532C22×C711yescharacteristic
260#529C22×C711yescharacteristic
261C2×#125C22×C711yescharacteristic
262#501C22×C711yescharacteristic
263#501C22×C712yes—
264#497—21no—
265#497C22×C712yes—
266#496—21no—
267#496C22×C712yes—
268#496C22×C711yescharacteristic
269#490C22×C711yescharacteristic
270#490C22×C712yes—
271#489C22×C711yescharacteristic
272#481—21no—
273#480—21no—
274#478—22no—
275#466—21no—
276#465—21no—
277#442—21no—
278#440—21no—
279#432C22×C711yescharacteristic
280C2×#97C22×C711yescharacteristic
281C2×#97C22×C711yescharacteristic
282#330C22×C712yes—
283#330C22×C712yes—
284#330C22×C712yes—
285#329C22×C712yes—
286#329C22×C712yes—
287#329C22×C712yes—
288C23×C7—22no—
289C23×C7—21no—
290C23×C7—41no—
291C23×C7#12011yescharacteristic
292C7×Q8—42no—
293C7×Q8—41no—
294C7×Q8—42no—
295C7×Q8—82no—
296C7×D4—42no—
297C7×D4—41no—
298C7×D4—42no—
299C7×D4—42no—
300C7×D4—41no—
301C7×D4—41no—
302C7×D4—42no—
303C7×D4—44no—
304C7×D4—42no—
305C7×D4—81no—
306C7×D4—82no—
307C7×D4—82no—
308C7×D4—82no—
309C2×C4×C7—22no—
310C2×C4×C7—21no—
311C2×C4×C7—21no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—21no—
315C2×C4×C7—22no—
316C2×C4×C7—41no—
317C2×C4×C7—41no—
318C2×C4×C7—42no—
319C2×C4×C7—42no—
320C2×C4×C7—41no—
321C2×C4×C7—82no—
322C2×C4×C7—82no—
323C2×C4×C7—81no—
324C2×C4×C7—82no—
325C2×C4×C7—82no—
326C2×C4×C7—82no—
327C2×C4×C7#12011yescharacteristic
328C2×C4×C7#12011yescharacteristic
329C2×C4×C7#12011yescharacteristic
330C2×C4×C7C22×D411yescharacteristic
331C2×C4×C7C22×D411yescharacteristic
332C2×C4×C7C22×D411yescharacteristic
333C7×C8—24no—
334C7×C8—22no—
335C7×C8—42no—
336C7×C8—41no—
337C2×#41—22no—
338C2×#41—21no—
339C2×#41C7×D412yes—
340#135—48no—
341C2×Q16—22no—
342C2×SD16—22no—
343C2×SD16—21no—
344C2×SD16—22no—
345C2×D8—22no—
346C2×D8—21no—
347C22×C8—21no—
348C22×C8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—22no—
351C4⋊Q8C7×D411yescharacteristic
352C4⋊Q8C23×C711yescharacteristic
353#127C7×D411yescharacteristic
354#127C23×C711yescharacteristic
355#126—22no—
356#126—22no—
357#126—21no—
358#125—22no—
359#125—21no—
360#125—21no—
361#125—21no—
362#125C7×D412yes—
363#125C23×C712yes—
364#125C23×C711yescharacteristic
365#124—21no—
366#124C23×C711yescharacteristic
367#124C23×C712yes—
368#123—22no—
369#123—22no—
370#123—22no—
371#123—22no—
372#123—21no—
373#123—22no—
374#123—22no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8C7×D411yescharacteristic
382#121—22no—
383#121—22no—
384#121—21no—
385#121—21no—
386#121—22no—
387#121—22no—
388#121—21no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121C7×D411yescharacteristic
393C4×Q8C7×D411yescharacteristic
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4C7×D411yescharacteristic
404#117—21no—
405#117—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4C7×D411yescharacteristic
411C2×C4⋊C4C7×D411yescharacteristic
412C2×C42C23×C711yescharacteristic
413#107—21no—
414#107—22no—
415#106—21no—
416#106—22no—
417C4⋊C8—21no—
418#103—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—22no—
423#102—22no—
424C22⋊C8—21no—
425#97—21no—
426#97—21no—
427#97C23×C712yes—
428#97C23×C711yescharacteristic
429#97C23×C711yescharacteristic
430#97C23×C712yes—
431C22×C7—21no—
432C22×C7—21no—
433C22×C7—42no—
434C22×C7—41no—
435C22×C7—42no—
436C22×C7—41no—
437C22×C7—41no—
438C22×C7—42no—
439C22×C7—81no—
440C22×C7—81no—
441C22×C7—81no—
442C22×C7#45312yes—
443C22×C7C2×#12011yescharacteristic
444C4×C7—21no—
445C4×C7—21no—
446C4×C7—21no—
447C4×C7—21no—
448C4×C7—21no—
449C4×C7—21no—
450C4×C7—42no—
451C4×C7—42no—
452C4×C7—41no—
453C4×C7—42no—
454C4×C7—41no—
455C4×C7—41no—
456C4×C7—81no—
457#41—44no—
458#41—44no—
459#41—84no—
460C2×Q8—22no—
461C2×Q8—21no—
462C2×Q8C2×C7×D411yescharacteristic
463C2×Q8C2×C7×D412yes—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4C2×C7×D411yescharacteristic
475C2×D4C2×C7×D412yes—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—41no—
484C22×C4C2×C7×D411yescharacteristic
485C22×C4C2×C7×D411yescharacteristic
486C22×C4C2×C7×D411yescharacteristic
487Q16—44no—
488SD16—42no—
489SD16—44no—
490SD16—44no—
491D8—42no—
492D8—44no—
493C2×C8—24no—
494C2×C8—21no—
495C2×C8—22no—
496C2×C8—21no—
497C2×C8—22no—
498C2×C8—42no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4C2×C7×D412yes—
518C4⋊C4C2×C7×D411yescharacteristic
519C4⋊C4C2×C7×D412yes—
520C4⋊C4C2×C7×D411yescharacteristic
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—21no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C42—22no—
536C42—21no—
537C42C2×C7×D411yescharacteristic
538C42C2×C7×D411yescharacteristic
539C42C2×C7×D411yescharacteristic
540C42C24×C711yescharacteristic
541C2×C7—22no—
542C2×C7—82no—
543C2×C7—81no—
544C2×C7—161no—
545C2×C7C2×#45311yescharacteristic
546C2×C7#301811yescharacteristic
547C2×C7#302011yescharacteristic
548C23—22no—
549C23—21no—
550C23—41no—
551C23C7×#12011yescharacteristic
552Q8—42no—
553Q8—41no—
554Q8—42no—
555Q8—82no—
556D4—42no—
557D4—41no—
558D4—42no—
559D4—42no—
560D4—41no—
561D4—41no—
562D4—42no—
563D4—44no—
564D4—42no—
565D4—81no—
566D4—82no—
567D4—82no—
568D4—82no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—81no—
584C2×C4—82no—
585C2×C4—82no—
586C2×C4—82no—
587C2×C4C7×#12011yescharacteristic
588C2×C4C7×#12011yescharacteristic
589C2×C4C7×#12011yescharacteristic
590C2×C4C22×C7×D411yescharacteristic
591C2×C4C22×C7×D411yescharacteristic
592C2×C4C22×C7×D411yescharacteristic
593C8—24no—
594C8—22no—
595C8—42no—
596C8—41no—
597C7#1904411yescharacteristic, direct product factor, Sylow
598C22—21no—
599C22—21no—
600C22—42no—
601C22—41no—
602C22—42no—
603C22—41no—
604C22—41no—
605C22—42no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22C7×#45312yes—
610C22C2×C7×#12011yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—42no—
618C4—42no—
619C4—41no—
620C4—42no—
621C4—41no—
622C4—41no—
623C4—81no—
624C2—22no—
625C2—82no—
626C2—81no—
627C2—161no—
628C2C2×C7×#45311yescharacteristic
629C2C7×#301811yescharacteristic
630C2C7×#302011yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC42C24×C7
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
1. C7×#3559C2semidirect
2. C7×#3234C2semidirect
3. C7×#3180C2semidirect
4. C7×#3150C2semidirect
5. C7×#1661C2semidirect
6. C7×#1660C2semidirect
7. C7×#1657C2semidirect
8. C7×#1656C2semidirect
9. C7×#1532C2semidirect
10. C7×#1530C2semidirect
11. C2×C7×#330C2semidirect
55. #19044C7direct (N × H)
150. #3559C2×C7semidirect
151. #3234C2×C7semidirect
152. #3180C2×C7semidirect
153. #3150C2×C7semidirect
154. #1661C2×C7semidirect
155. #1660C2×C7semidirect
156. #1657C2×C7semidirect
157. #1656C2×C7semidirect
158. #1532C2×C7semidirect
159. #1530C2×C7semidirect
160. C2×#330C2×C7semidirect
597. C7#19044direct (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×#32342
C7×#31802
C7×#31502
C7×#16612
C7×#16602
C7×#16572
C7×#16562
C7×#15322
C7×#15302
C2×C7×#3302
#190447