Finite Group Databasebeta

← C7×#14024 #13191240

Subgroups — C7×#14024 #13191240

Order 1792.

2054 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C4⋊Q8C211yesmaximal, characteristic
2C22×C4×C7×Q8C211yesmaximal, characteristic
3C2×C7×#391C211yesmaximal, characteristic
4C2×C7×#391C211yesmaximal, characteristic
5C2×C7×#391C211yesmaximal, characteristic
6C7×#1441C214yesmaximal
7C7×#1436C214yesmaximal
8C7×C4⋊#95C211yesmaximal, characteristic
9C4×C7×#95C211yesmaximal, characteristic
10C23×C7×Q8C2211yescharacteristic
11C23×C7×Q8C2211yescharacteristic
12C2×C7×C4⋊Q8—24no—
13C2×C7×C4⋊Q8—24no—
14C2×C7×C4⋊Q8C418yescomplemented
15C2×C4×C7×Q8—24no—
16C2×C4×C7×Q8—24no—
17C2×C4×C7×Q8—24no—
18C22×C7×C4⋊C4C2212yes—
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2214yes—
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C42×C7C2212yes—
23C22×C42×C7C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
26C7×#391—24no—
27C7×#391—24no—
28C7×#391—24no—
29C2×C7×#95C2212yes—
30C2×C7×#95C2214yes—
31C2×C7×#95C2214yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2214yes—
35C2×C7×#95C2212yes—
36#14024C711yesmaximal, characteristic, direct product factor, Sylow
37C22×C7×Q8—22no—
38C22×C7×Q8—22no—
39C22×C7×Q8—22no—
40C22×C7×Q8—22no—
41C22×C7×Q8—22no—
42C22×C7×Q8—22no—
43C22×C7×Q8—22no—
44C22×C7×Q8—22no—
45C22×C7×Q8—22no—
46C22×C7×Q8—22no—
47C22×C7×Q8C2×C414yes—
48C22×C7×Q8C2×C414yes—
49C22×C7×Q8D414yes—
50C22×C7×Q8D414yes—
51C23×C4×C7C2312yes—
52C23×C4×C7C2312yes—
53C23×C4×C7C2312yes—
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2312yes—
56C23×C4×C7C2312yes—
57C23×C4×C7C2312yes—
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C7×C4⋊Q8—232no—
61C4×C7×Q8—232no—
62C2×C7×C4⋊C4—24no—
63C2×C7×C4⋊C4—24no—
64C2×C7×C4⋊C4—24no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—28no—
68C2×C7×C4⋊C4—28no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4C2×C4116yes—
73C2×C7×C4⋊C4D414yes—
74C2×C42×C7—24no—
75C2×C42×C7—24no—
76C2×C42×C7—24no—
77C2×C42×C7—22no—
78C2×C42×C7—22no—
79C2×C42×C7—22no—
80C2×C42×C7—22no—
81C2×C42×C7—22no—
82C2×C42×C7—22no—
83C2×C42×C7—22no—
84C2×C42×C7C2×C414yes—
85C2×C42×C7D414yes—
86C7×#95—28no—
87C7×#95—28no—
88C7×#95—24no—
89C7×#95—24no—
90C7×#95—24no—
91C7×#95—28no—
92C7×#95Q818yescomplemented
93C22×C4⋊Q8C2×C711yescharacteristic
94C22×C4×Q8C2×C711yescharacteristic
95C2×#391C2×C711yescharacteristic
96C2×#391C2×C711yescharacteristic
97C2×#391C2×C711yescharacteristic
98#1441C2×C714yes—
99#1436C2×C714yes—
100C4⋊#95C2×C711yescharacteristic
101C4×#95C2×C711yescharacteristic
102C24×C7C2411yescharacteristic
103C2×C7×Q8—28no—
104C2×C7×Q8—28no—
105C2×C7×Q8—28no—
106C2×C7×Q8—28no—
107C2×C7×Q8—28no—
108C2×C7×Q8—28no—
109C2×C7×Q8—28no—
110C2×C7×Q8—28no—
111C2×C7×Q8—28no—
112C2×C7×Q8—44no—
113C2×C7×Q8—44no—
114C2×C7×Q8—44no—
115C2×C7×Q8—44no—
116C2×C7×Q8C22⋊C4116yes—
117C22×C4×C7—21no—
118C22×C4×C7—21no—
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—21no—
134C22×C4×C7—22no—
135C22×C4×C7—21no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—24no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—24no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—24no—
151C22×C4×C7—22no—
152C22×C4×C7—24no—
153C22×C4×C7C22×C414yes—
154C22×C4×C7C22×C414yes—
155C22×C4×C7C22×C414yes—
156C22×C4×C7C22×C412yes—
157C22×C4×C7C2×D414yes—
158C22×C4×C7C2×D412yes—
159C22×C4×C7C2×D414yes—
160C22×C4×C7C2×D414yes—
161C22×C4×C7C2×D412yes—
162C22×C4×C7C2×D412yes—
163C22×C4×C7C2×D412yes—
164C22×C4×C7C2×D412yes—
165C22×C4×C7C2×D412yes—
166C22×C4×C7C2×Q814yes—
167C22×C4×C7C2×Q814yes—
168C22×C4×C7C2×Q814yes—
169C22×C4×C7#4114yes—
170C22×C4×C7#4112yes—
171C22×C4×C7#4112yes—
172C7×C4⋊C4—216no—
173C7×C4⋊C4—232no—
174C7×C4⋊C4—28no—
175C7×C4⋊C4—44no—
176C42×C7—216no—
177C42×C7—28no—
178C42×C7—28no—
179C42×C7—44no—
180C23×Q8C22×C711yescharacteristic
181C23×Q8C22×C711yescharacteristic
182C2×C4⋊Q8—24no—
183C2×C4⋊Q8—24no—
184C2×C4⋊Q8C4×C718yescomplemented
185C2×C4×Q8—24no—
186C2×C4×Q8—24no—
187C2×C4×Q8—24no—
188C22×C4⋊C4C22×C712yes—
189C22×C4⋊C4C22×C711yescharacteristic
190C22×C4⋊C4C22×C714yes—
191C22×C4⋊C4C22×C711yescharacteristic
192C22×C42C22×C712yes—
193C22×C42C22×C711yescharacteristic
194C22×C42C22×C711yescharacteristic
195C22×C42C22×C711yescharacteristic
196#391—24no—
197#391—24no—
198#391—24no—
199C2×#95C22×C712yes—
200C2×#95C22×C714yes—
201C2×#95C22×C712yes—
202C2×#95C22×C714yes—
203C2×#95C22×C714yes—
204C2×#95C22×C712yes—
205C2×#95C22×C712yes—
206C23×C7C23×C411yescharacteristic
207C23×C7C22×D411yescharacteristic
208C23×C7C22×D411yescharacteristic
209C23×C7C22×D411yescharacteristic
210C23×C7C22×D411yescharacteristic
211C23×C7C22×Q812yes—
212C23×C7C2×#4111yescharacteristic
213C23×C7C2×#4111yescharacteristic
214C23×C7C2×#4112yes—
215C23×C72−1+412yes—
216C23×C72−1+412yes—
217C7×Q8—232no—
218C7×Q8—416no—
219C2×C4×C7—24no—
220C2×C4×C7—24no—
221C2×C4×C7—24no—
222C2×C4×C7—24no—
223C2×C4×C7—22no—
224C2×C4×C7—24no—
225C2×C4×C7—24no—
226C2×C4×C7—24no—
227C2×C4×C7—24no—
228C2×C4×C7—22no—
229C2×C4×C7—24no—
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—22no—
240C2×C4×C7—22no—
241C2×C4×C7—24no—
242C2×C4×C7—22no—
243C2×C4×C7—28no—
244C2×C4×C7—24no—
245C2×C4×C7—24no—
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—44no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
262C2×C4×C7—44no—
263C2×C4×C7—44no—
264C2×C4×C7C2×C22⋊C418yes—
265C2×C4×C7C2×C22⋊C414yes—
266C2×C4×C7C4×D414yes—
267C2×C4×C7C4×D414yes—
268C2×C4×C7C4×Q818yescomplemented
269C2×C4×C7#12014yes—
270C2×C4×C7#12114yes—
271C2×C4×C7#12114yes—
272C2×C4×C7#12314yes—
273C2×C4×C7C4⋊Q814yescomplemented
274C22×Q8—22no—
275C22×Q8—22no—
276C22×Q8—22no—
277C22×Q8—22no—
278C22×Q8—22no—
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8—22no—
282C22×Q8—22no—
283C22×Q8—22no—
284C22×Q8C2×C4×C714yes—
285C22×Q8C2×C4×C714yes—
286C22×Q8C7×D414yes—
287C22×Q8C7×D414yes—
288C23×C4C23×C712yes—
289C23×C4C23×C712yes—
290C23×C4C23×C712yes—
291C23×C4C23×C711yescharacteristic
292C23×C4C23×C712yes—
293C23×C4C23×C712yes—
294C23×C4C23×C712yes—
295C23×C4C23×C711yescharacteristic
296C23×C4C23×C711yescharacteristic
297C4⋊Q8—232no—
298C4×Q8—232no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4C2×C4×C7116yes—
310C2×C4⋊C4C7×D414yes—
311C2×C42—24no—
312C2×C42—24no—
313C2×C42—24no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42—22no—
320C2×C42—22no—
321C2×C42C2×C4×C714yes—
322C2×C42C7×D414yes—
323#95—28no—
324#95—28no—
325#95—24no—
326#95—24no—
327#95—24no—
328#95—28no—
329#95C7×Q818yescomplemented
330C22×C7C22×C22⋊C411yescharacteristic
331C22×C7C2×C4×D411yescharacteristic
332C22×C7C2×C4×D411yescharacteristic
333C22×C7C2×C4×Q812yes—
334C22×C7#51912yes—
335C22×C7C2×#12011yescharacteristic
336C22×C7C2×#12111yescharacteristic
337C22×C7C2×#12111yescharacteristic
338C22×C7C2×#12311yescharacteristic
339C22×C7C2×C4⋊Q811yescharacteristic
340C22×C7#53211yescharacteristic
341C22×C7#53312yes—
342C22×C7#53611yescharacteristic
343C22×C7#53611yescharacteristic
344C22×C7#54112yes—
345C22×C7#54712yes—
346C22×C7#54812yes—
347C22×C7#54812yes—
348C22×C7D4×Q812yes—
349C22×C7D4×Q812yes—
350C22×C7D4×Q812yes—
351C22×C7#55612yes—
352C22×C7#55712yes—
353C4×C7—28no—
354C4×C7—24no—
355C4×C7—28no—
356C4×C7—44no—
357C4×C7—42no—
358C4×C7—44no—
359C4×C7—44no—
360C4×C7—82no—
361C4×C7#38618yes—
362C24C24×C711yescharacteristic
363C2×Q8—28no—
364C2×Q8—28no—
365C2×Q8—28no—
366C2×Q8—28no—
367C2×Q8—28no—
368C2×Q8—28no—
369C2×Q8—28no—
370C2×Q8—28no—
371C2×Q8—28no—
372C2×Q8—44no—
373C2×Q8—44no—
374C2×Q8—44no—
375C2×Q8—44no—
376C2×Q8C7×C22⋊C4116yes—
377C22×C4—21no—
378C22×C4—21no—
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—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4C22×C4×C714yes—
414C22×C4C22×C4×C714yes—
415C22×C4C22×C4×C714yes—
416C22×C4C22×C4×C712yes—
417C22×C4C2×C7×D414yes—
418C22×C4C2×C7×D412yes—
419C22×C4C2×C7×D414yes—
420C22×C4C2×C7×D414yes—
421C22×C4C2×C7×D412yes—
422C22×C4C2×C7×D412yes—
423C22×C4C2×C7×D412yes—
424C22×C4C2×C7×D412yes—
425C22×C4C2×C7×D412yes—
426C22×C4C2×C7×Q814yes—
427C22×C4C2×C7×Q814yes—
428C22×C4C2×C7×Q814yes—
429C22×C4C7×#4114yes—
430C22×C4C7×#4112yes—
431C22×C4C7×#4112yes—
432C4⋊C4—216no—
433C4⋊C4—232no—
434C4⋊C4—28no—
435C4⋊C4—44no—
436C42—216no—
437C42—28no—
438C42—28no—
439C42—44no—
440C2×C7C2×#38611yescharacteristic
441C2×C7C4×C4⋊Q811yescharacteristic
442C2×C7#232711yescharacteristic
443C2×C7Q8×C22⋊C412yes—
444C2×C7#236512yes—
445C2×C7#242912yes—
446C2×C7#243211yescharacteristic
447C2×C7#243411yescharacteristic
448C2×C7#244612yes—
449C2×C7#254511yescharacteristic
450C2×C7#254611yescharacteristic
451C23C23×C4×C711yescharacteristic
452C23C22×C7×D411yescharacteristic
453C23C22×C7×D411yescharacteristic
454C23C22×C7×D411yescharacteristic
455C23C22×C7×D411yescharacteristic
456C23C22×C7×Q812yes—
457C23C2×C7×#4111yescharacteristic
458C23C2×C7×#4111yescharacteristic
459C23C2×C7×#4112yes—
460C23C7×2−1+412yes—
461C23C7×2−1+412yes—
462Q8—232no—
463Q8—416no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—28no—
489C2×C4—24no—
490C2×C4—24no—
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—44no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—44no—
508C2×C4—44no—
509C2×C4C2×C7×C22⋊C418yes—
510C2×C4C2×C7×C22⋊C414yes—
511C2×C4C4×C7×D414yes—
512C2×C4C4×C7×D414yes—
513C2×C4C4×C7×Q818yescomplemented
514C2×C4C7×#12014yes—
515C2×C4C7×#12114yes—
516C2×C4C7×#12114yes—
517C2×C4C7×#12314yes—
518C2×C4C7×C4⋊Q814yescomplemented
519C7#1402411yescharacteristic, direct product factor, Sylow
520C22C22×C7×C22⋊C411yescharacteristic
521C22C2×C4×C7×D411yescharacteristic
522C22C2×C4×C7×D411yescharacteristic
523C22C2×C4×C7×Q812yes—
524C22C7×#51912yes—
525C22C2×C7×#12011yescharacteristic
526C22C2×C7×#12111yescharacteristic
527C22C2×C7×#12111yescharacteristic
528C22C2×C7×#12311yescharacteristic
529C22C2×C7×C4⋊Q811yescharacteristic
530C22C7×#53211yescharacteristic
531C22C7×#53312yes—
532C22C7×#53611yescharacteristic
533C22C7×#53611yescharacteristic
534C22C7×#54112yes—
535C22C7×#54712yes—
536C22C7×#54812yes—
537C22C7×#54812yes—
538C22C7×D4×Q812yes—
539C22C7×D4×Q812yes—
540C22C7×D4×Q812yes—
541C22C7×#55612yes—
542C22C7×#55712yes—
543C4—24no—
544C4—28no—
545C4—28no—
546C4—44no—
547C4—42no—
548C4—44no—
549C4—44no—
550C4—82no—
551C4C7×#38618yes—
552C2C2×C7×#38611yescharacteristic
553C2C4×C7×C4⋊Q811yescharacteristic
554C2C7×#232711yescharacteristic
555C2C7×Q8×C22⋊C412yes—
556C2C7×#236512yes—
557C2C7×#242912yes—
558C2C7×#243211yescharacteristic
559C2C7×#243411yescharacteristic
560C2C7×#244612yes—
561C2C7×#254511yescharacteristic
562C2C7×#254611yescharacteristic
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
14. C2×C7×C4⋊Q8C4semidirect
36. #14024C7direct (N × H)
92. C7×#95Q8semidirect
184. C2×C4⋊Q8C4×C7semidirect
268. C2×C4×C7C4×Q8semidirect
273. C2×C4×C7C4⋊Q8semidirect
329. #95C7×Q8semidirect
513. C2×C4C4×C7×Q8semidirect
518. C2×C4C7×C4⋊Q8semidirect
519. C7#14024direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×C4⋊Q82
C22×C4×C7×Q82
C2×C7×#3912
C7×#14412
C7×#14362
C7×C4⋊#952
C4×C7×#952
#140247