Finite Group Databasebeta

← C7×#14449 #13191665

Subgroups — C7×#14449 #13191665

Order 1792.

1810 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C22⋊Q8C211yesmaximal, characteristic
2C2×C7×#391C212yesmaximal, complemented
3C7×#1445C212yesmaximal, complemented
4C7×#1441C212yesmaximal, complemented
5C7×#1439C212yesmaximal
6C7×#1437C212yesmaximal
7C7×#1436C212yesmaximal, complemented
8C7×C22⋊#95C211yesmaximal, characteristic
9C7×C22⋊#95C211yesmaximal, characteristic
10C23×C7×Q8C2211yescharacteristic
11C24×C4×C7C2211yescharacteristic
12C2×C7×C22⋊Q8—28no—
13C2×C7×C22⋊Q8C418yescomplemented
14C22×C7×C4⋊C4C2212yes—
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2212yes—
17C22×C7×C22⋊C4C2212yes—
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C42×C7C2212yes—
22C7×#391—28no—
23C2×C7×#95C2212yes—
24C2×C7×#95C2212yes—
25C2×C7×#95C2212yes—
26C2×C7×#95C2212yes—
27C2×C7×#95C2212yes—
28C2×C7×#95C2212yes—
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2212yes—
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34#14449C711yesmaximal, characteristic, direct product factor, Sylow
35C25×C7C2311yescharacteristic
36C22×C7×Q8—41no—
37C22×C7×Q8—42no—
38C22×C7×Q8—41no—
39C22×C7×Q8C2×C414yes—
40C22×C7×Q8D418yes—
41C23×C4×C7—24no—
42C23×C4×C7—41no—
43C23×C4×C7—41no—
44C23×C4×C7—42no—
45C23×C4×C7C2×C414yes—
46C23×C4×C7C2312yes—
47C23×C4×C7C2312yes—
48C23×C4×C7C2312yes—
49C23×C4×C7C2311yescharacteristic
50C23×C4×C7C2312yes—
51C23×C4×C7C2312yes—
52C23×C4×C7C2312yes—
53C23×C4×C7C2311yescharacteristic
54C7×C22⋊Q8—232no—
55C2×C7×C4⋊C4—24no—
56C2×C7×C4⋊C4—24no—
57C2×C7×C4⋊C4—24no—
58C2×C7×C4⋊C4—24no—
59C2×C7×C4⋊C4—42no—
60C2×C7×C4⋊C4—42no—
61C2×C7×C4⋊C4C2×C414yes—
62C2×C7×C4⋊C4C2×C418yes—
63C2×C7×C22⋊C4—24no—
64C2×C7×C22⋊C4—24no—
65C2×C7×C22⋊C4—24no—
66C2×C7×C22⋊C4—22no—
67C2×C7×C22⋊C4—24no—
68C2×C7×C22⋊C4—41no—
69C2×C7×C22⋊C4—41no—
70C2×C7×C22⋊C4—42no—
71C2×C7×C22⋊C4—41no—
72C2×C7×C22⋊C4—41no—
73C2×C7×C22⋊C4C2×C418yes—
74C2×C7×C22⋊C4Q814yescomplemented
75C2×C42×C7—24no—
76C2×C42×C7—42no—
77C2×C42×C7—42no—
78C7×#95—24no—
79C7×#95—24no—
80C7×#95—24no—
81C7×#95—24no—
82C7×#95—24no—
83C7×#95—24no—
84C7×#95—42no—
85C7×#95—42no—
86C7×#95—41no—
87C7×#95—42no—
88C7×#95—41no—
89C22×C22⋊Q8C2×C711yescharacteristic
90C2×#391C2×C712yescomplemented
91#1445C2×C712yescomplemented
92#1441C2×C712yescomplemented
93#1439C2×C712yes—
94#1437C2×C712yes—
95#1436C2×C712yescomplemented
96C22⋊#95C2×C711yescharacteristic
97C22⋊#95C2×C711yescharacteristic
98C24×C7—22no—
99C24×C7—22no—
100C24×C7—21no—
101C24×C7—21no—
102C24×C7—21no—
103C24×C7—22no—
104C24×C7—22no—
105C24×C7—21no—
106C24×C7C22×C412yes—
107C24×C7C2×Q812yes—
108C24×C7#4112yes—
109C24×C7C2411yescharacteristic
110C2×C7×Q8—44no—
111C2×C7×Q8—44no—
112C2×C7×Q8—48no—
113C2×C7×Q8—48no—
114C2×C7×Q8C22⋊C4116yescomplemented
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—28no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—44no—
160C22×C4×C7—44no—
161C22×C4×C7—48no—
162C22×C4×C7—48no—
163C22×C4×C7C22×C414yes—
164C22×C4×C7C22×C412yes—
165C22×C4×C7C22×C414yes—
166C22×C4×C7C22×C412yes—
167C22×C4×C7C2×D414yes—
168C22×C4×C7C2×D414yes—
169C22×C4×C7C2×D414yes—
170C22×C4×C7C2×Q814yes—
171C22×C4×C7#4114yes—
172C7×C4⋊C4—28no—
173C7×C4⋊C4—216no—
174C7×C4⋊C4—48no—
175C7×C22⋊C4—216no—
176C7×C22⋊C4—44no—
177C7×C22⋊C4—48no—
178C7×C22⋊C4—44no—
179C42×C7—48no—
180C23×Q8C22×C711yescharacteristic
181C24×C4C22×C711yescharacteristic
182C2×C22⋊Q8—28no—
183C2×C22⋊Q8C4×C718yescomplemented
184C22×C4⋊C4C22×C712yes—
185C22×C4⋊C4C22×C711yescharacteristic
186C22×C4⋊C4C22×C712yes—
187C22×C22⋊C4C22×C712yes—
188C22×C22⋊C4C22×C712yes—
189C22×C22⋊C4C22×C711yescharacteristic
190C22×C22⋊C4C22×C711yescharacteristic
191C22×C42C22×C712yes—
192#391—28no—
193C2×#95C22×C712yes—
194C2×#95C22×C712yes—
195C2×#95C22×C712yes—
196C2×#95C22×C712yes—
197C2×#95C22×C712yes—
198C2×#95C22×C712yes—
199C2×#95C22×C711yescharacteristic
200C2×#95C22×C712yes—
201C2×#95C22×C711yescharacteristic
202C2×#95C22×C712yes—
203C2×#95C22×C712yes—
204C23×C7—22no—
205C23×C7—22no—
206C23×C7—22no—
207C23×C7—22no—
208C23×C7—22no—
209C23×C7—22no—
210C23×C7—22no—
211C23×C7—22no—
212C23×C7—22no—
213C23×C7—22no—
214C23×C7—24no—
215C23×C7—24no—
216C23×C7—24no—
217C23×C7—24no—
218C23×C7—42no—
219C23×C7—42no—
220C23×C7—42no—
221C23×C7—42no—
222C23×C7—42no—
223C23×C7—42no—
224C23×C7—42no—
225C23×C7—42no—
226C23×C7C4×Q814yes—
227C23×C7C23×C411yescharacteristic
228C23×C7C22×D412yes—
229C23×C7C22×Q811yescharacteristic
230C23×C7C2×#4111yescharacteristic
231C23×C7C2×#4112yes—
232C23×C7H(5,𝔽2)11yescharacteristic
233C23×C7H(5,𝔽2)11yescharacteristic
234C23×C7H(5,𝔽2)12yes—
235C23×C7H(5,𝔽2)11yescharacteristic
236C23×C72−1+412yes—
237C23×C72−1+411yescharacteristic
238C7×Q8—416no—
239C2×C4×C7—22no—
240C2×C4×C7—22no—
241C2×C4×C7—24no—
242C2×C4×C7—24no—
243C2×C4×C7—24no—
244C2×C4×C7—24no—
245C2×C4×C7—24no—
246C2×C4×C7—24no—
247C2×C4×C7—24no—
248C2×C4×C7—24no—
249C2×C4×C7—24no—
250C2×C4×C7—22no—
251C2×C4×C7—24no—
252C2×C4×C7—22no—
253C2×C4×C7—22no—
254C2×C4×C7—24no—
255C2×C4×C7—24no—
256C2×C4×C7—24no—
257C2×C4×C7—24no—
258C2×C4×C7—24no—
259C2×C4×C7—24no—
260C2×C4×C7—24no—
261C2×C4×C7—416no—
262C2×C4×C7—42no—
263C2×C4×C7—42no—
264C2×C4×C7—42no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7—42no—
268C2×C4×C7—42no—
269C2×C4×C7—42no—
270C2×C4×C7—42no—
271C2×C4×C7—42no—
272C2×C4×C7—42no—
273C2×C4×C7—42no—
274C2×C4×C7—42no—
275C2×C4×C7—42no—
276C2×C4×C7—42no—
277C2×C4×C7—42no—
278C2×C4×C7—42no—
279C2×C4×C7—42no—
280C2×C4×C7—42no—
281C2×C4×C7—42no—
282C2×C4×C7—42no—
283C2×C4×C7—42no—
284C2×C4×C7—42no—
285C2×C4×C7—42no—
286C2×C4×C7—42no—
287C2×C4×C7—42no—
288C2×C4×C7—42no—
289C2×C4×C7—42no—
290C2×C4×C7C2×C22⋊C418yes—
291C2×C4×C7C2×C22⋊C414yes—
292C25C23×C711yescharacteristic
293C22×Q8—41no—
294C22×Q8—42no—
295C22×Q8—41no—
296C22×Q8C2×C4×C714yes—
297C22×Q8C7×D418yes—
298C23×C4—24no—
299C23×C4—41no—
300C23×C4—41no—
301C23×C4—42no—
302C23×C4C2×C4×C714yes—
303C23×C4C23×C712yes—
304C23×C4C23×C712yes—
305C23×C4C23×C712yes—
306C23×C4C23×C711yescharacteristic
307C23×C4C23×C712yes—
308C23×C4C23×C712yes—
309C23×C4C23×C712yes—
310C23×C4C23×C711yescharacteristic
311C22⋊Q8—232no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4C2×C4×C714yes—
319C2×C4⋊C4C2×C4×C718yes—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—41no—
326C2×C22⋊C4—41no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—41no—
329C2×C22⋊C4—41no—
330C2×C22⋊C4C2×C4×C718yes—
331C2×C22⋊C4C7×Q814yescomplemented
332C2×C42—24no—
333C2×C42—42no—
334C2×C42—42no—
335#95—24no—
336#95—24no—
337#95—24no—
338#95—24no—
339#95—24no—
340#95—24no—
341#95—42no—
342#95—42no—
343#95—41no—
344#95—42no—
345#95—41no—
346C22×C7—24no—
347C22×C7—24no—
348C22×C7—24no—
349C22×C7—42no—
350C22×C7—42no—
351C22×C7—42no—
352C22×C7—42no—
353C22×C7—44no—
354C22×C7—44no—
355C22×C7—44no—
356C22×C7—44no—
357C22×C7C22×C22⋊C411yescharacteristic
358C22×C7C2×C4×Q811yescharacteristic
359C22×C7C4×#4111yescharacteristic
360C22×C7#51811yescharacteristic
361C22×C7#51811yescharacteristic
362C22×C7#51911yescharacteristic
363C22×C7#52011yescharacteristic
364C22×C7#53412yes—
365C22×C7#53412yes—
366C22×C7#53811yescharacteristic
367C22×C7#53911yescharacteristic
368C22×C7#53912yes—
369C22×C7#54212yes—
370C22×C7#54311yescharacteristic
371C22×C7#54411yescharacteristic
372C22×C7#54812yes—
373C22×C7#54812yes—
374C22×C7D4×Q812yes—
375C22×C7#55012yes—
376C22×C7#55112yes—
377C22×C7#55412yes—
378C22×C7#56212yes—
379C22×C7#56312yes—
380C4×C7—24no—
381C4×C7—28no—
382C4×C7—42no—
383C4×C7—44no—
384C4×C7—44no—
385C4×C7—44no—
386C4×C7—82no—
387C4×C7—82no—
388C24—22no—
389C24—22no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—22no—
394C24—22no—
395C24—21no—
396C24C22×C4×C712yes—
397C24C2×C7×Q812yes—
398C24C7×#4112yes—
399C24C24×C711yescharacteristic
400C2×Q8—44no—
401C2×Q8—44no—
402C2×Q8—48no—
403C2×Q8—48no—
404C2×Q8C7×C22⋊C4116yescomplemented
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—28no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—48no—
452C22×C4—48no—
453C22×C4C22×C4×C714yes—
454C22×C4C22×C4×C712yes—
455C22×C4C22×C4×C714yes—
456C22×C4C22×C4×C712yes—
457C22×C4C2×C7×D414yes—
458C22×C4C2×C7×D414yes—
459C22×C4C2×C7×D414yes—
460C22×C4C2×C7×Q814yes—
461C22×C4C7×#4114yes—
462C4⋊C4—28no—
463C4⋊C4—216no—
464C4⋊C4—48no—
465C22⋊C4—216no—
466C22⋊C4—44no—
467C22⋊C4—48no—
468C22⋊C4—44no—
469C42—48no—
470C2×C7—44no—
471C2×C7#230811yescharacteristic
472C2×C7#232911yescharacteristic
473C2×C7#233211yescharacteristic
474C2×C7Q8×C22⋊C411yescharacteristic
475C2×C7#234111yescharacteristic
476C2×C7#236811yescharacteristic
477C2×C7#237811yescharacteristic
478C2×C7#272812yes—
479C2×C7#272912yes—
480C2×C7#273012yes—
481C2×C7#273212yes—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—24no—
494C23—24no—
495C23—24no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23C4×C7×Q814yes—
505C23C23×C4×C711yescharacteristic
506C23C22×C7×D412yes—
507C23C22×C7×Q811yescharacteristic
508C23C2×C7×#4111yescharacteristic
509C23C2×C7×#4112yes—
510C23C7×H(5,𝔽2)11yescharacteristic
511C23C7×H(5,𝔽2)11yescharacteristic
512C23C7×H(5,𝔽2)12yes—
513C23C7×H(5,𝔽2)11yescharacteristic
514C23C7×2−1+412yes—
515C23C7×2−1+411yescharacteristic
516Q8—416no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—416no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4C2×C7×C22⋊C418yes—
569C2×C4C2×C7×C22⋊C414yes—
570C7#1444911yescharacteristic, direct product factor, Sylow
571C22—24no—
572C22—24no—
573C22—24no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—44no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22C22×C7×C22⋊C411yescharacteristic
583C22C2×C4×C7×Q811yescharacteristic
584C22C4×C7×#4111yescharacteristic
585C22C7×#51811yescharacteristic
586C22C7×#51811yescharacteristic
587C22C7×#51911yescharacteristic
588C22C7×#52011yescharacteristic
589C22C7×#53412yes—
590C22C7×#53412yes—
591C22C7×#53811yescharacteristic
592C22C7×#53911yescharacteristic
593C22C7×#53912yes—
594C22C7×#54212yes—
595C22C7×#54311yescharacteristic
596C22C7×#54411yescharacteristic
597C22C7×#54812yes—
598C22C7×#54812yes—
599C22C7×D4×Q812yes—
600C22C7×#55012yes—
601C22C7×#55112yes—
602C22C7×#55412yes—
603C22C7×#56212yes—
604C22C7×#56312yes—
605C4—24no—
606C4—28no—
607C4—44no—
608C4—44no—
609C4—42no—
610C4—44no—
611C4—82no—
612C4—82no—
613C2—44no—
614C2C7×#230811yescharacteristic
615C2C7×#232911yescharacteristic
616C2C7×#233211yescharacteristic
617C2C7×Q8×C22⋊C411yescharacteristic
618C2C7×#234111yescharacteristic
619C2C7×#236811yescharacteristic
620C2C7×#237811yescharacteristic
621C2C7×#272812yes—
622C2C7×#272912yes—
623C2C7×#273012yes—
624C2C7×#273212yes—
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#391C2semidirect
3. C7×#1445C2semidirect
4. C7×#1441C2semidirect
7. C7×#1436C2semidirect
13. C2×C7×C22⋊Q8C4semidirect
34. #14449C7direct (N × H)
74. C2×C7×C22⋊C4Q8semidirect
90. C2×#391C2×C7semidirect
91. #1445C2×C7semidirect
92. #1441C2×C7semidirect
95. #1436C2×C7semidirect
114. C2×C7×Q8C22⋊C4semidirect
183. C2×C22⋊Q8C4×C7semidirect
331. C2×C22⋊C4C7×Q8semidirect
404. C2×Q8C7×C22⋊C4semidirect
570. C7#14449direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×C22⋊Q82
C2×C7×#3912
C7×#14452
C7×#14412
C7×#14392
C7×#14372
C7×#14362
C7×C22⋊#952
#144497