Finite Group Databasebeta

← C7×#14446 #13191662

Subgroups — C7×#14446 #13191662

Order 1792.

1246 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#389C211yesmaximal, characteristic
2C2×C7×#387C212yesmaximal
3C7×#1445C212yesmaximal
4C7×#1442C212yesmaximal
5C7×#1441C212yesmaximal
6C7×#1436C212yesmaximal
7C7×#1436C212yesmaximal
8C7×C4⋊#95C211yesmaximal, characteristic
9C7×C4⋊#95C211yesmaximal, characteristic
10C22×C7×C4⋊C4C2212yes—
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C42×C7C2212yes—
18C22×C42×C7C2211yescharacteristic
19C7×#389C418yescomplemented
20C7×#387—28no—
21C2×C7×#95C2212yes—
22C2×C7×#95C2212yes—
23C2×C7×#95C2212yes—
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—
33#14446C711yesmaximal, characteristic, direct product factor, Sylow
34C23×C4×C7C2312yes—
35C23×C4×C7C2312yes—
36C23×C4×C7C2312yes—
37C23×C4×C7C2312yes—
38C23×C4×C7C2312yes—
39C23×C4×C7C2312yes—
40C23×C4×C7C2311yescharacteristic
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2311yescharacteristic
43C2×C7×C4⋊C4—24no—
44C2×C7×C4⋊C4—22no—
45C2×C7×C4⋊C4—22no—
46C2×C7×C4⋊C4—24no—
47C2×C7×C4⋊C4—22no—
48C2×C7×C4⋊C4—22no—
49C2×C7×C4⋊C4—41no—
50C2×C7×C4⋊C4—41no—
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—41no—
58C2×C7×C4⋊C4—41no—
59C2×C7×C4⋊C4C2×C414yes—
60C2×C7×C4⋊C4C2×C418yes—
61C2×C7×C4⋊C4C2×C414yes—
62C2×C7×C4⋊C4D414yes—
63C2×C7×C4⋊C4Q814yes—
64C2×C42×C7—24no—
65C2×C42×C7—41no—
66C2×C42×C7—41no—
67C2×C42×C7—42no—
68C2×C42×C7—42no—
69C2×C42×C7C2×C414yes—
70C7×#95—24no—
71C7×#95—24no—
72C7×#95—24no—
73C7×#95—24no—
74C7×#95—24no—
75C7×#95—24no—
76C7×#95—24no—
77C7×#95—42no—
78C7×#95—42no—
79C7×#95—42no—
80C7×#95—42no—
81C7×#95C2×C418yes—
82C2×#389C2×C711yescharacteristic
83C2×#387C2×C712yes—
84#1445C2×C712yes—
85#1442C2×C712yes—
86#1441C2×C712yes—
87#1436C2×C712yes—
88#1436C2×C712yes—
89C4⋊#95C2×C711yescharacteristic
90C4⋊#95C2×C711yescharacteristic
91C24×C7C2411yescharacteristic
92C22×C4×C7—21no—
93C22×C4×C7—21no—
94C22×C4×C7—21no—
95C22×C4×C7—21no—
96C22×C4×C7—21no—
97C22×C4×C7—21no—
98C22×C4×C7—21no—
99C22×C4×C7—21no—
100C22×C4×C7—21no—
101C22×C4×C7—21no—
102C22×C4×C7—21no—
103C22×C4×C7—21no—
104C22×C4×C7—22no—
105C22×C4×C7—22no—
106C22×C4×C7—22no—
107C22×C4×C7—22no—
108C22×C4×C7—22no—
109C22×C4×C7—22no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
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×C7C22×C414yes—
143C22×C4×C7C22×C414yes—
144C22×C4×C7C22×C412yes—
145C22×C4×C7C22×C412yes—
146C22×C4×C7C22×C412yes—
147C22×C4×C7C2×D414yes—
148C22×C4×C7C2×D412yes—
149C22×C4×C7C2×Q814yes—
150C22×C4×C7C2×Q812yes—
151C22×C4×C7#4112yes—
152C22×C4×C7#4112yes—
153C22×C4×C7#4112yes—
154C22×C4×C7#4112yes—
155C7×C4⋊C4—28no—
156C7×C4⋊C4—216no—
157C7×C4⋊C4—44no—
158C7×C4⋊C4—44no—
159C7×C4⋊C4—44no—
160C7×C4⋊C4—44no—
161C7×C4⋊C4—44no—
162C42×C7—44no—
163C42×C7—48no—
164C22×C4⋊C4C22×C712yes—
165C22×C4⋊C4C22×C711yescharacteristic
166C22×C4⋊C4C22×C711yescharacteristic
167C22×C4⋊C4C22×C711yescharacteristic
168C22×C4⋊C4C22×C711yescharacteristic
169C22×C4⋊C4C22×C711yescharacteristic
170C22×C4⋊C4C22×C711yescharacteristic
171C22×C42C22×C712yes—
172C22×C42C22×C711yescharacteristic
173#389C4×C718yescomplemented
174#387—28no—
175C2×#95C22×C712yes—
176C2×#95C22×C712yes—
177C2×#95C22×C712yes—
178C2×#95C22×C712yes—
179C2×#95C22×C712yes—
180C2×#95C22×C712yes—
181C2×#95C22×C712yes—
182C2×#95C22×C712yes—
183C2×#95C22×C712yes—
184C2×#95C22×C712yes—
185C2×#95C22×C712yes—
186C2×#95C22×C712yes—
187C23×C7C23×C411yescharacteristic
188C23×C7C22×D411yescharacteristic
189C23×C7C22×Q811yescharacteristic
190C23×C7C2×#4111yescharacteristic
191C23×C7C2×#4111yescharacteristic
192C23×C7C2×#4111yescharacteristic
193C23×C7C2×#4111yescharacteristic
194C23×C7H(5,𝔽2)11yescharacteristic
195C23×C7H(5,𝔽2)11yescharacteristic
196C23×C7H(5,𝔽2)11yescharacteristic
197C23×C7H(5,𝔽2)11yescharacteristic
198C23×C72−1+411yescharacteristic
199C23×C72−1+411yescharacteristic
200C23×C72−1+411yescharacteristic
201C23×C72−1+411yescharacteristic
202C2×C4×C7—22no—
203C2×C4×C7—22no—
204C2×C4×C7—22no—
205C2×C4×C7—22no—
206C2×C4×C7—22no—
207C2×C4×C7—22no—
208C2×C4×C7—22no—
209C2×C4×C7—22no—
210C2×C4×C7—22no—
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—22no—
218C2×C4×C7—22no—
219C2×C4×C7—22no—
220C2×C4×C7—24no—
221C2×C4×C7—24no—
222C2×C4×C7—24no—
223C2×C4×C7—24no—
224C2×C4×C7—24no—
225C2×C4×C7—24no—
226C2×C4×C7—24no—
227C2×C4×C7—24no—
228C2×C4×C7—24no—
229C2×C4×C7—24no—
230C2×C4×C7—24no—
231C2×C4×C7—24no—
232C2×C4×C7—42no—
233C2×C4×C7—42no—
234C2×C4×C7—42no—
235C2×C4×C7—42no—
236C2×C4×C7—42no—
237C2×C4×C7—42no—
238C2×C4×C7—42no—
239C2×C4×C7—42no—
240C2×C4×C7—42no—
241C2×C4×C7—42no—
242C2×C4×C7—42no—
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#11714yes—
263C2×C4×C7C4×D414yes—
264C2×C4×C7C4×Q814yes—
265C23×C4C23×C712yes—
266C23×C4C23×C712yes—
267C23×C4C23×C712yes—
268C23×C4C23×C712yes—
269C23×C4C23×C712yes—
270C23×C4C23×C712yes—
271C23×C4C23×C711yescharacteristic
272C23×C4C23×C711yescharacteristic
273C23×C4C23×C711yescharacteristic
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—41no—
281C2×C4⋊C4—41no—
282C2×C4⋊C4—41no—
283C2×C4⋊C4—41no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—41no—
286C2×C4⋊C4—41no—
287C2×C4⋊C4—41no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4C2×C4×C714yes—
291C2×C4⋊C4C2×C4×C718yes—
292C2×C4⋊C4C2×C4×C714yes—
293C2×C4⋊C4C7×D414yes—
294C2×C4⋊C4C7×Q814yes—
295C2×C42—24no—
296C2×C42—41no—
297C2×C42—41no—
298C2×C42—42no—
299C2×C42—42no—
300C2×C42C2×C4×C714yes—
301#95—24no—
302#95—24no—
303#95—24no—
304#95—24no—
305#95—24no—
306#95—24no—
307#95—24no—
308#95—42no—
309#95—42no—
310#95—42no—
311#95—42no—
312#95C2×C4×C718yes—
313C22×C7C2×#11711yescharacteristic
314C22×C7C2×C4×D411yescharacteristic
315C22×C7C2×C4×Q811yescharacteristic
316C22×C7#51811yescharacteristic
317C22×C7#51911yescharacteristic
318C22×C7#52011yescharacteristic
319C22×C7#52011yescharacteristic
320C22×C7#53411yescharacteristic
321C22×C7#53711yescharacteristic
322C22×C7#53811yescharacteristic
323C22×C7#53811yescharacteristic
324C22×C7#53911yescharacteristic
325C22×C7#53911yescharacteristic
326C22×C7#53911yescharacteristic
327C22×C7#53911yescharacteristic
328C22×C7#53911yescharacteristic
329C22×C7#53911yescharacteristic
330C22×C7#54311yescharacteristic
331C22×C7#54411yescharacteristic
332C22×C7#54711yescharacteristic
333C22×C7#54711yescharacteristic
334C22×C7D4×Q811yescharacteristic
335C22×C7#55011yescharacteristic
336C22×C7#55411yescharacteristic
337C22×C7#55511yescharacteristic
338C22×C7#55611yescharacteristic
339C22×C7#55611yescharacteristic
340C22×C7#55611yescharacteristic
341C22×C7#55711yescharacteristic
342C22×C7#55711yescharacteristic
343C22×C7#55911yescharacteristic
344C22×C7#56211yescharacteristic
345C22×C7#56311yescharacteristic
346C22×C7#56311yescharacteristic
347C22×C7#56411yescharacteristic
348C4×C7—24no—
349C4×C7—24no—
350C4×C7—24no—
351C4×C7—44no—
352C4×C7—44no—
353C4×C7—44no—
354C4×C7—44no—
355C4×C7—82no—
356C4×C7—82no—
357C24C24×C711yescharacteristic
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
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×C4C22×C4×C714yes—
409C22×C4C22×C4×C714yes—
410C22×C4C22×C4×C712yes—
411C22×C4C22×C4×C712yes—
412C22×C4C22×C4×C712yes—
413C22×C4C2×C7×D414yes—
414C22×C4C2×C7×D412yes—
415C22×C4C2×C7×Q814yes—
416C22×C4C2×C7×Q812yes—
417C22×C4C7×#4112yes—
418C22×C4C7×#4112yes—
419C22×C4C7×#4112yes—
420C22×C4C7×#4112yes—
421C4⋊C4—28no—
422C4⋊C4—216no—
423C4⋊C4—44no—
424C4⋊C4—44no—
425C4⋊C4—44no—
426C4⋊C4—44no—
427C4⋊C4—44no—
428C42—44no—
429C42—48no—
430C2×C7#231311yescharacteristic
431C2×C7#232511yescharacteristic
432C2×C7#232911yescharacteristic
433C2×C7#235411yescharacteristic
434C2×C7#235511yescharacteristic
435C2×C7#236511yescharacteristic
436C2×C7#238211yescharacteristic
437C2×C7#272411yescharacteristic
438C2×C7#272611yescharacteristic
439C2×C7#272711yescharacteristic
440C2×C7#273211yescharacteristic
441C2×C7#280511yescharacteristic
442C2×C7#280811yescharacteristic
443C2×C7#280911yescharacteristic
444C2×C7#281011yescharacteristic
445C23C23×C4×C711yescharacteristic
446C23C22×C7×D411yescharacteristic
447C23C22×C7×Q811yescharacteristic
448C23C2×C7×#4111yescharacteristic
449C23C2×C7×#4111yescharacteristic
450C23C2×C7×#4111yescharacteristic
451C23C2×C7×#4111yescharacteristic
452C23C7×H(5,𝔽2)11yescharacteristic
453C23C7×H(5,𝔽2)11yescharacteristic
454C23C7×H(5,𝔽2)11yescharacteristic
455C23C7×H(5,𝔽2)11yescharacteristic
456C23C7×2−1+411yescharacteristic
457C23C7×2−1+411yescharacteristic
458C23C7×2−1+411yescharacteristic
459C23C7×2−1+411yescharacteristic
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
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×C4C7×#11714yes—
521C2×C4C4×C7×D414yes—
522C2×C4C4×C7×Q814yes—
523C7#1444611yescharacteristic, direct product factor, Sylow
524C22C2×C7×#11711yescharacteristic
525C22C2×C4×C7×D411yescharacteristic
526C22C2×C4×C7×Q811yescharacteristic
527C22C7×#51811yescharacteristic
528C22C7×#51911yescharacteristic
529C22C7×#52011yescharacteristic
530C22C7×#52011yescharacteristic
531C22C7×#53411yescharacteristic
532C22C7×#53711yescharacteristic
533C22C7×#53811yescharacteristic
534C22C7×#53811yescharacteristic
535C22C7×#53911yescharacteristic
536C22C7×#53911yescharacteristic
537C22C7×#53911yescharacteristic
538C22C7×#53911yescharacteristic
539C22C7×#53911yescharacteristic
540C22C7×#53911yescharacteristic
541C22C7×#54311yescharacteristic
542C22C7×#54411yescharacteristic
543C22C7×#54711yescharacteristic
544C22C7×#54711yescharacteristic
545C22C7×D4×Q811yescharacteristic
546C22C7×#55011yescharacteristic
547C22C7×#55411yescharacteristic
548C22C7×#55511yescharacteristic
549C22C7×#55611yescharacteristic
550C22C7×#55611yescharacteristic
551C22C7×#55611yescharacteristic
552C22C7×#55711yescharacteristic
553C22C7×#55711yescharacteristic
554C22C7×#55911yescharacteristic
555C22C7×#56211yescharacteristic
556C22C7×#56311yescharacteristic
557C22C7×#56311yescharacteristic
558C22C7×#56411yescharacteristic
559C4—24no—
560C4—24no—
561C4—24no—
562C4—44no—
563C4—44no—
564C4—44no—
565C4—44no—
566C4—82no—
567C4—82no—
568C2C7×#231311yescharacteristic
569C2C7×#232511yescharacteristic
570C2C7×#232911yescharacteristic
571C2C7×#235411yescharacteristic
572C2C7×#235511yescharacteristic
573C2C7×#236511yescharacteristic
574C2C7×#238211yescharacteristic
575C2C7×#272411yescharacteristic
576C2C7×#272611yescharacteristic
577C2C7×#272711yescharacteristic
578C2C7×#273211yescharacteristic
579C2C7×#280511yescharacteristic
580C2C7×#280811yescharacteristic
581C2C7×#280911yescharacteristic
582C2C7×#281011yescharacteristic
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
19. C7×#389C4semidirect
33. #14446C7direct (N × H)
173. #389C4×C7semidirect
523. C7#14446direct (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×#14452
C7×#14422
C7×#14412
C7×#14362
C7×C4⋊#952
#144467