Finite Group Databasebeta

← C7×#14441 #13191657

Subgroups — C7×#14441 #13191657

Order 1792.

1390 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#389C212yesmaximal
2C2×C7×#389C211yesmaximal, characteristic
3C2×C7×#387C212yesmaximal
4C7×#1444C212yesmaximal
5C7×#1441C212yesmaximal
6C7×#1441C212yesmaximal
7C7×#1436C212yesmaximal
8C7×C4⋊#95C211yesmaximal, characteristic
9C7×C4⋊#95C211yesmaximal, characteristic
10C22×C7×C4⋊C4C2212yes—
11C22×C7×C4⋊C4C2212yes—
12C22×C7×C4⋊C4C2212yes—
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C42×C7C2212yes—
20C22×C42×C7C2211yescharacteristic
21C7×#389—28no—
22C7×#389C418yescomplemented
23C7×#387—28no—
24C2×C7×#95C2212yes—
25C2×C7×#95C2212yes—
26C2×C7×#95C2212yes—
27C2×C7×#95C2212yes—
28C2×C7×#95C2212yes—
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34#14441C711yesmaximal, characteristic, direct product factor, Sylow
35C23×C4×C7C2312yes—
36C23×C4×C7C2312yes—
37C23×C4×C7C2312yes—
38C23×C4×C7C2312yes—
39C23×C4×C7C2312yes—
40C23×C4×C7C2311yescharacteristic
41C23×C4×C7C2312yes—
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C2×C7×C4⋊C4—24no—
45C2×C7×C4⋊C4—24no—
46C2×C7×C4⋊C4—24no—
47C2×C7×C4⋊C4—24no—
48C2×C7×C4⋊C4—24no—
49C2×C7×C4⋊C4—22no—
50C2×C7×C4⋊C4—22no—
51C2×C7×C4⋊C4—41no—
52C2×C7×C4⋊C4—41no—
53C2×C7×C4⋊C4—41no—
54C2×C7×C4⋊C4—41no—
55C2×C7×C4⋊C4—41no—
56C2×C7×C4⋊C4—41no—
57C2×C7×C4⋊C4—42no—
58C2×C7×C4⋊C4—41no—
59C2×C7×C4⋊C4—41no—
60C2×C7×C4⋊C4—41no—
61C2×C7×C4⋊C4—41no—
62C2×C7×C4⋊C4—42no—
63C2×C7×C4⋊C4—42no—
64C2×C7×C4⋊C4C2×C418yes—
65C2×C7×C4⋊C4C2×C414yes—
66C2×C7×C4⋊C4C2×C414yes—
67C2×C7×C4⋊C4D414yes—
68C2×C7×C4⋊C4D414yes—
69C2×C7×C4⋊C4Q814yes—
70C2×C7×C4⋊C4Q814yes—
71C2×C42×C7—24no—
72C2×C42×C7—24no—
73C2×C42×C7—41no—
74C2×C42×C7—41no—
75C2×C42×C7—42no—
76C2×C42×C7C2×C414yes—
77C7×#95—24no—
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×#95C2×C418yes—
87C2×#389C2×C712yes—
88C2×#389C2×C711yescharacteristic
89C2×#387C2×C712yes—
90#1444C2×C712yes—
91#1441C2×C712yes—
92#1441C2×C712yes—
93#1436C2×C712yes—
94C4⋊#95C2×C711yescharacteristic
95C4⋊#95C2×C711yescharacteristic
96C24×C7C2411yescharacteristic
97C22×C4×C7—22no—
98C22×C4×C7—22no—
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—22no—
106C22×C4×C7—21no—
107C22×C4×C7—21no—
108C22×C4×C7—21no—
109C22×C4×C7—21no—
110C22×C4×C7—21no—
111C22×C4×C7—21no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
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—22no—
136C22×C4×C7—22no—
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—22no—
145C22×C4×C7C22×C414yes—
146C22×C4×C7C22×C414yes—
147C22×C4×C7C22×C412yes—
148C22×C4×C7C22×C412yes—
149C22×C4×C7C22×C412yes—
150C22×C4×C7C2×D414yes—
151C22×C4×C7C2×D412yes—
152C22×C4×C7C2×D414yes—
153C22×C4×C7C2×D412yes—
154C22×C4×C7C2×Q814yes—
155C22×C4×C7C2×Q812yes—
156C22×C4×C7C2×Q814yes—
157C22×C4×C7C2×Q812yes—
158C22×C4×C7#4112yes—
159C22×C4×C7#4112yes—
160C7×C4⋊C4—216no—
161C7×C4⋊C4—44no—
162C7×C4⋊C4—44no—
163C7×C4⋊C4—44no—
164C7×C4⋊C4—48no—
165C7×C4⋊C4—44no—
166C7×C4⋊C4—44no—
167C7×C4⋊C4—48no—
168C7×C4⋊C4C4⋊C4116yescomplemented
169C42×C7—44no—
170C42×C7—48no—
171C22×C4⋊C4C22×C712yes—
172C22×C4⋊C4C22×C712yes—
173C22×C4⋊C4C22×C711yescharacteristic
174C22×C4⋊C4C22×C711yescharacteristic
175C22×C4⋊C4C22×C712yes—
176C22×C4⋊C4C22×C711yescharacteristic
177C22×C4⋊C4C22×C711yescharacteristic
178C22×C4⋊C4C22×C711yescharacteristic
179C22×C4⋊C4C22×C711yescharacteristic
180C22×C42C22×C712yes—
181C22×C42C22×C711yescharacteristic
182#389—28no—
183#389C4×C718yescomplemented
184#387—28no—
185C2×#95C22×C712yes—
186C2×#95C22×C712yes—
187C2×#95C22×C712yes—
188C2×#95C22×C712yes—
189C2×#95C22×C712yes—
190C2×#95C22×C712yes—
191C2×#95C22×C712yes—
192C2×#95C22×C712yes—
193C2×#95C22×C712yes—
194C2×#95C22×C712yes—
195C23×C7C23×C411yescharacteristic
196C23×C7C22×D411yescharacteristic
197C23×C7C22×D411yescharacteristic
198C23×C7C22×Q811yescharacteristic
199C23×C7C22×Q811yescharacteristic
200C23×C7C2×#4111yescharacteristic
201C23×C7C2×#4111yescharacteristic
202C23×C7H(5,𝔽2)11yescharacteristic
203C23×C7H(5,𝔽2)11yescharacteristic
204C23×C7H(5,𝔽2)11yescharacteristic
205C23×C7H(5,𝔽2)11yescharacteristic
206C23×C72−1+411yescharacteristic
207C23×C72−1+411yescharacteristic
208C23×C72−1+411yescharacteristic
209C23×C72−1+411yescharacteristic
210C2×C4×C7—24no—
211C2×C4×C7—22no—
212C2×C4×C7—22no—
213C2×C4×C7—22no—
214C2×C4×C7—22no—
215C2×C4×C7—22no—
216C2×C4×C7—22no—
217C2×C4×C7—24no—
218C2×C4×C7—22no—
219C2×C4×C7—22no—
220C2×C4×C7—22no—
221C2×C4×C7—22no—
222C2×C4×C7—22no—
223C2×C4×C7—22no—
224C2×C4×C7—22no—
225C2×C4×C7—22no—
226C2×C4×C7—22no—
227C2×C4×C7—22no—
228C2×C4×C7—22no—
229C2×C4×C7—22no—
230C2×C4×C7—24no—
231C2×C4×C7—24no—
232C2×C4×C7—24no—
233C2×C4×C7—24no—
234C2×C4×C7—24no—
235C2×C4×C7—24no—
236C2×C4×C7—24no—
237C2×C4×C7—24no—
238C2×C4×C7—24no—
239C2×C4×C7—24no—
240C2×C4×C7—24no—
241C2×C4×C7—24no—
242C2×C4×C7—24no—
243C2×C4×C7—42no—
244C2×C4×C7—42no—
245C2×C4×C7—42no—
246C2×C4×C7—42no—
247C2×C4×C7—42no—
248C2×C4×C7—42no—
249C2×C4×C7—42no—
250C2×C4×C7—42no—
251C2×C4×C7—42no—
252C2×C4×C7—42no—
253C2×C4×C7—42no—
254C2×C4×C7—42no—
255C2×C4×C7—42no—
256C2×C4×C7—42no—
257C2×C4×C7—42no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
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×C7C2×C4⋊C414yes—
270C2×C4×C7C2×C4⋊C418yes—
271C2×C4×C7C4×D414yes—
272C2×C4×C7C4×Q814yes—
273C23×C4C23×C712yes—
274C23×C4C23×C712yes—
275C23×C4C23×C712yes—
276C23×C4C23×C712yes—
277C23×C4C23×C712yes—
278C23×C4C23×C712yes—
279C23×C4C23×C711yescharacteristic
280C23×C4C23×C711yescharacteristic
281C23×C4C23×C711yescharacteristic
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4C2×C4×C718yes—
303C2×C4⋊C4C2×C4×C714yes—
304C2×C4⋊C4C2×C4×C714yes—
305C2×C4⋊C4C7×D414yes—
306C2×C4⋊C4C7×D414yes—
307C2×C4⋊C4C7×Q814yes—
308C2×C4⋊C4C7×Q814yes—
309C2×C42—24no—
310C2×C42—24no—
311C2×C42—41no—
312C2×C42—41no—
313C2×C42—42no—
314C2×C42C2×C4×C714yes—
315#95—24no—
316#95—24no—
317#95—24no—
318#95—24no—
319#95—24no—
320#95—24no—
321#95—24no—
322#95—42no—
323#95—42no—
324#95C2×C4×C718yes—
325C22×C7C22×C4⋊C411yescharacteristic
326C22×C7C2×C4×D411yescharacteristic
327C22×C7C2×C4×Q811yescharacteristic
328C22×C7#51811yescharacteristic
329C22×C7#51911yescharacteristic
330C22×C7#52011yescharacteristic
331C22×C7#52011yescharacteristic
332C22×C7#53411yescharacteristic
333C22×C7#53711yescharacteristic
334C22×C7#53711yescharacteristic
335C22×C7#53711yescharacteristic
336C22×C7#53811yescharacteristic
337C22×C7#53811yescharacteristic
338C22×C7#53911yescharacteristic
339C22×C7#53911yescharacteristic
340C22×C7#54311yescharacteristic
341C22×C7#54411yescharacteristic
342C22×C7#54411yescharacteristic
343C22×C7#54411yescharacteristic
344C22×C7D4211yescharacteristic
345C22×C7#54711yescharacteristic
346C22×C7#54711yescharacteristic
347C22×C7D4×Q811yescharacteristic
348C22×C7D4×Q811yescharacteristic
349C22×C7D4×Q811yescharacteristic
350C22×C7#55011yescharacteristic
351C22×C7#55411yescharacteristic
352C22×C7#55611yescharacteristic
353C22×C7#55711yescharacteristic
354C22×C7#55711yescharacteristic
355C22×C7Q8211yescharacteristic
356C22×C7#56211yescharacteristic
357C22×C7#56311yescharacteristic
358C22×C7#56311yescharacteristic
359C22×C7#56411yescharacteristic
360C4×C7—24no—
361C4×C7—24no—
362C4×C7—24no—
363C4×C7—28no—
364C4×C7—44no—
365C4×C7—44no—
366C4×C7—44no—
367C4×C7—82no—
368C4×C7—82no—
369C24C24×C711yescharacteristic
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4C22×C4×C714yes—
419C22×C4C22×C4×C714yes—
420C22×C4C22×C4×C712yes—
421C22×C4C22×C4×C712yes—
422C22×C4C22×C4×C712yes—
423C22×C4C2×C7×D414yes—
424C22×C4C2×C7×D412yes—
425C22×C4C2×C7×D414yes—
426C22×C4C2×C7×D412yes—
427C22×C4C2×C7×Q814yes—
428C22×C4C2×C7×Q812yes—
429C22×C4C2×C7×Q814yes—
430C22×C4C2×C7×Q812yes—
431C22×C4C7×#4112yes—
432C22×C4C7×#4112yes—
433C4⋊C4—216no—
434C4⋊C4—44no—
435C4⋊C4—44no—
436C4⋊C4—44no—
437C4⋊C4—48no—
438C4⋊C4—44no—
439C4⋊C4—44no—
440C4⋊C4—48no—
441C4⋊C4C7×C4⋊C4116yescomplemented
442C42—44no—
443C42—48no—
444C2×C7#231611yescharacteristic
445C2×C7#232511yescharacteristic
446C2×C7#232911yescharacteristic
447C2×C7D4×C4⋊C411yescharacteristic
448C2×C7Q8×C4⋊C411yescharacteristic
449C2×C7#236511yescharacteristic
450C2×C7#238211yescharacteristic
451C2×C7#268211yescharacteristic
452C2×C7#268311yescharacteristic
453C2×C7#272611yescharacteristic
454C2×C7#272611yescharacteristic
455C2×C7#272711yescharacteristic
456C2×C7#273411yescharacteristic
457C2×C7#280511yescharacteristic
458C2×C7#280611yescharacteristic
459C23C23×C4×C711yescharacteristic
460C23C22×C7×D411yescharacteristic
461C23C22×C7×D411yescharacteristic
462C23C22×C7×Q811yescharacteristic
463C23C22×C7×Q811yescharacteristic
464C23C2×C7×#4111yescharacteristic
465C23C2×C7×#4111yescharacteristic
466C23C7×H(5,𝔽2)11yescharacteristic
467C23C7×H(5,𝔽2)11yescharacteristic
468C23C7×H(5,𝔽2)11yescharacteristic
469C23C7×H(5,𝔽2)11yescharacteristic
470C23C7×2−1+411yescharacteristic
471C23C7×2−1+411yescharacteristic
472C23C7×2−1+411yescharacteristic
473C23C7×2−1+411yescharacteristic
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4C2×C7×C4⋊C414yes—
534C2×C4C2×C7×C4⋊C418yes—
535C2×C4C4×C7×D414yes—
536C2×C4C4×C7×Q814yes—
537C7#1444111yescharacteristic, direct product factor, Sylow
538C22C22×C7×C4⋊C411yescharacteristic
539C22C2×C4×C7×D411yescharacteristic
540C22C2×C4×C7×Q811yescharacteristic
541C22C7×#51811yescharacteristic
542C22C7×#51911yescharacteristic
543C22C7×#52011yescharacteristic
544C22C7×#52011yescharacteristic
545C22C7×#53411yescharacteristic
546C22C7×#53711yescharacteristic
547C22C7×#53711yescharacteristic
548C22C7×#53711yescharacteristic
549C22C7×#53811yescharacteristic
550C22C7×#53811yescharacteristic
551C22C7×#53911yescharacteristic
552C22C7×#53911yescharacteristic
553C22C7×#54311yescharacteristic
554C22C7×#54411yescharacteristic
555C22C7×#54411yescharacteristic
556C22C7×#54411yescharacteristic
557C22C7×D4211yescharacteristic
558C22C7×#54711yescharacteristic
559C22C7×#54711yescharacteristic
560C22C7×D4×Q811yescharacteristic
561C22C7×D4×Q811yescharacteristic
562C22C7×D4×Q811yescharacteristic
563C22C7×#55011yescharacteristic
564C22C7×#55411yescharacteristic
565C22C7×#55611yescharacteristic
566C22C7×#55711yescharacteristic
567C22C7×#55711yescharacteristic
568C22C7×Q8211yescharacteristic
569C22C7×#56211yescharacteristic
570C22C7×#56311yescharacteristic
571C22C7×#56311yescharacteristic
572C22C7×#56411yescharacteristic
573C4—24no—
574C4—24no—
575C4—24no—
576C4—28no—
577C4—44no—
578C4—44no—
579C4—44no—
580C4—82no—
581C4—82no—
582C2C7×#231611yescharacteristic
583C2C7×#232511yescharacteristic
584C2C7×#232911yescharacteristic
585C2C7×D4×C4⋊C411yescharacteristic
586C2C7×Q8×C4⋊C411yescharacteristic
587C2C7×#236511yescharacteristic
588C2C7×#238211yescharacteristic
589C2C7×#268211yescharacteristic
590C2C7×#268311yescharacteristic
591C2C7×#272611yescharacteristic
592C2C7×#272611yescharacteristic
593C2C7×#272711yescharacteristic
594C2C7×#273411yescharacteristic
595C2C7×#280511yescharacteristic
596C2C7×#280611yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
22. C7×#389C4semidirect
34. #14441C7direct (N × H)
168. C7×C4⋊C4C4⋊C4semidirect
183. #389C4×C7semidirect
441. C4⋊C4C7×C4⋊C4semidirect
537. C7#14441direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×C7×#3872
C7×#14442
C7×#14412
C7×#14362
C7×C4⋊#952
#144417