Finite Group Databasebeta

← D7×#1996 #13358433

Subgroups — D7×#1996 #13358433

Order 1792.

1698 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×C22⋊Q8C211yesmaximal, characteristic
2D7×#380C211yesmaximal, characteristic
3C4×D7×C22⋊C4C211yesmaximal, characteristic
4C7×#1996C211yesmaximal, characteristic, complemented
5#11729455C211yesmaximal, characteristic, complemented
6#11727283C211yesmaximal, characteristic, complemented
7#11727211C211yesmaximal, characteristic, complemented
8D7×#342C214yesmaximal
9#11726709C214yesmaximal, complemented
10C22×Q8×D7C411yescharacteristic, complemented
11C23×C4×D7C2211yescharacteristic
12C2×C7×C22⋊Q8C2211yescharacteristic
13C2×#6509C411yescharacteristic, complemented
14C2×#6487C2211yescharacteristic
15D7×C22⋊Q8—21no—
16D7×C22⋊Q8—21no—
17D7×C22⋊Q8—21no—
18D7×C22⋊Q8—21no—
19D7×C22⋊Q8—21no—
20D7×C22⋊Q8—21no—
21D7×C22⋊Q8—21no—
22D7×C22⋊Q8—21no—
23C2×#6460C411yescharacteristic, complemented
24C2×#6459C412yescomplemented
25C2×D7×C4⋊C4—21no—
26C2×D7×C4⋊C4C411yescharacteristic, complemented
27C2×D7×C4⋊C4C412yescomplemented
28C2×D7×C22⋊C4C2212yes—
29C2×D7×C22⋊C4C2212yes—
30C2×D7×C22⋊C4C2212yes—
31C2×#6441C2212yes—
32C2×C42×D7—21no—
33C7×#380C2211yescharacteristic
34C4×C7×C22⋊C4C2211yescharacteristic
35#89984C2211yescharacteristic
36C4×C22⋊Dic7C2211yescharacteristic
37#89759—21no—
38#89714C2212yes—
39C22⋊C4×Dic7C2212yes—
40C4×(C2×D7)⋊C4—21no—
41#89439—21no—
42#89438—21no—
43D7×#95—21no—
44D7×#95—21no—
45C7×#342C2214yes—
46#89322C2214yes—
47#89322C2214yes—
48#89321C2214yes—
49C2×#1996—71nomaximal, Sylow
50C24×D7C2311yescharacteristic
51C22×C7×Q8C2×C411yescharacteristic, complemented
52C23×C4×C7C2311yescharacteristic
53C23×Dic7C2311yescharacteristic
54C2×Q8×D7—21no—
55C2×Q8×D7—21no—
56C2×Q8×D7—21no—
57C2×Q8×D7—21no—
58C2×Q8×D7—44no—
59C22×C4×D7—22no—
60C22×C4×D7—22no—
61C22×C4×D7—44no—
62C22×C4×D7C2×C411yescharacteristic
63C22×C4×D7C2×C412yes—
64C22×C4×D7C2×C412yes—
65C22×C4×D7C2×C411yescharacteristic
66C22×C4×D7C2×C411yescharacteristic
67C22×C4×D7C2×C411yescharacteristic
68C22×C4×D7D411yescharacteristic
69C22×C4×D7D411yescharacteristic
70C22×C4×D7D411yescharacteristic
71C22×C4×D7D411yescharacteristic
72C22×C4×D7D411yescharacteristic
73C22×C4×D7D411yescharacteristic
74C22×C4×D7D411yescharacteristic
75C22×C4×D7D411yescharacteristic
76C22×Dic14C2×C412yescomplemented
77C22×Dic14C2×C411yescharacteristic, complemented
78C7×C22⋊Q8—21no—
79C7×C22⋊Q8—21no—
80C7×C22⋊Q8—21no—
81C7×C22⋊Q8—21no—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4C2×C412yescomplemented
84C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
85C2×C7×C22⋊C4C2312yes—
86C2×C7×C22⋊C4C2312yes—
87C2×C7×C22⋊C4C2312yes—
88C2×C42×C7—21no—
89C2×C22⋊Dic7C2312yes—
90C2×C22⋊Dic7C2312yes—
91C2×C22⋊Dic7C2312yes—
92#6509—21no—
93#6509—21no—
94#6509—21no—
95#6509—21no—
96C2×(C2×D7)⋊C4—22no—
97C2×(C2×D7)⋊C4—22no—
98C2×(C2×D7)⋊C4C2×C412yes—
99C2×(C2×D7)⋊C4C2×C412yes—
100C2×C4⋊Dic7—21no—
101C2×C4⋊Dic7C2×C412yescomplemented
102C2×C4⋊Dic7C2×C411yescharacteristic, complemented
103#6487—21no—
104#6487—21no—
105#6487—21no—
106#6487—21no—
107C2×Dic7⋊C4—22no—
108C2×Dic7⋊C4C2×C412yescomplemented
109C2×Dic7⋊C4C2×C412yescomplemented
110C2×Dic7⋊C4C2×C412yescomplemented
111C2×C4×Dic7—21no—
112C2×C4×Dic7—22no—
113#6460—21no—
114#6460—21no—
115#6460—21no—
116#6460—21no—
117#6459—22no—
118#6459—22no—
119#6459—22no—
120#6459—22no—
121D7×C4⋊C4—22no—
122D7×C4⋊C4—22no—
123D7×C4⋊C4—22no—
124D7×C4⋊C4—22no—
125D7×C4⋊C4—21no—
126D7×C4⋊C4—21no—
127D7×C4⋊C4—21no—
128D7×C4⋊C4—21no—
129D7×C4⋊C4—44no—
130D7×C22⋊C4—22no—
131D7×C22⋊C4—22no—
132D7×C22⋊C4—22no—
133D7×C22⋊C4—22no—
134D7×C22⋊C4—24no—
135D7×C22⋊C4—28no—
136D7×C22⋊C4Q818yescomplemented
137#6441—22no—
138#6441—22no—
139#6441—22no—
140#6441—22no—
141C42×D7—44no—
142C7×#95—21no—
143C7×#95—21no—
144C7⋊#95—21no—
145C7⋊#95—21no—
146C7⋊#95—22no—
147C7⋊#95—22no—
148C22×C22⋊Q8—71no—
149C2×#380—71no—
150C2×C4×C22⋊C4—71no—
151#1996—71no—
152#1996—71no—
153#1996—74no—
154#1996—71no—
155#1996D711yescharacteristic, direct product factor
156C2×#342—74no—
157C24×C7C2411yescharacteristic
158C23×D7—42no—
159C23×D7—42no—
160C23×D7C22×C411yescharacteristic
161C23×D7C22×C411yescharacteristic
162C23×D7C2×D411yescharacteristic
163C23×D7C2×D411yescharacteristic
164C23×D7C2×D411yescharacteristic
165C23×D7C2×D411yescharacteristic
166C23×D7C2×Q814yes—
167C23×D7#4114yes—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8—42no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—42no—
174C22×C4×C7C22×C411yescharacteristic
175C22×C4×C7C22×C412yes—
176C22×C4×C7C22×C412yes—
177C22×C4×C7C22×C411yescharacteristic
178C22×C4×C7C2×D411yescharacteristic
179C22×C4×C7C2×D411yescharacteristic
180C22×C4×C7C2×D411yescharacteristic
181C22×C4×C7C2×D411yescharacteristic
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—42no—
185C22×Dic7C22×C411yescharacteristic
186C22×Dic7C22×C412yes—
187C22×Dic7C22×C412yes—
188C22×Dic7C22×C411yescharacteristic
189C22×Dic7C2×D411yescharacteristic
190C22×Dic7C2×D411yescharacteristic
191C22×Dic7C2×D411yescharacteristic
192C22×Dic7C2×D411yescharacteristic
193Q8×D7—44no—
194Q8×D7—44no—
195Q8×D7—44no—
196Q8×D7—44no—
197C2×C4×D7—24no—
198C2×C4×D7—24no—
199C2×C4×D7—24no—
200C2×C4×D7—22no—
201C2×C4×D7—22no—
202C2×C4×D7—22no—
203C2×C4×D7—22no—
204C2×C4×D7—28no—
205C2×C4×D7—42no—
206C2×C4×D7—42no—
207C2×C4×D7—42no—
208C2×C4×D7—42no—
209C2×C4×D7—42no—
210C2×C4×D7—42no—
211C2×C4×D7—42no—
212C2×C4×D7—42no—
213C2×C4×D7—42no—
214C2×C4×D7—44no—
215C2×C4×D7—44no—
216C2×C4×D7—44no—
217C2×C4×D7—44no—
218C2×C4×D7—44no—
219C2×C4×D7—44no—
220C2×C4×D7—44no—
221C2×C4×D7C22⋊C411yescharacteristic
222C2×C4×D7C22⋊C411yescharacteristic
223C2×C4×D7C22⋊C411yescharacteristic
224C2×C4×D7C22⋊C411yescharacteristic
225C2×C4×D7C22⋊C411yescharacteristic
226C2×C4×D7C22⋊C411yescharacteristic
227C2×C4×D7C22⋊C411yescharacteristic
228C2×C4×D7C22⋊C411yescharacteristic
229C2×C4×D7C22⋊C411yescharacteristic
230C2×C4×D7C22⋊C411yescharacteristic
231C2×C4×D7C22⋊C411yescharacteristic
232C2×C4×D7C22⋊C411yescharacteristic
233C2×C4×D7C22⋊C411yescharacteristic
234C2×C4×D7C22⋊C411yescharacteristic
235C2×C4×D7C22⋊C411yescharacteristic
236C2×C4×D7C22⋊C411yescharacteristic
237C2×Dic14—21no—
238C2×Dic14—21no—
239C2×Dic14—22no—
240C2×Dic14—22no—
241C2×Dic14—44no—
242C2×Dic14—42no—
243C7×C4⋊C4—22no—
244C7×C4⋊C4—22no—
245C7×C4⋊C4—21no—
246C7×C4⋊C4—21no—
247C7×C4⋊C4—42no—
248C7×C22⋊C4—22no—
249C7×C22⋊C4—22no—
250C7×C22⋊C4—22no—
251C7×C22⋊C4—24no—
252C7×C22⋊C4C2×Q814yescomplemented
253C42×C7—42no—
254C22⋊Dic7—22no—
255C22⋊Dic7—22no—
256C22⋊Dic7—22no—
257C22⋊Dic7—24no—
258C22⋊Dic7C2×Q814yescomplemented
259(C2×D7)⋊C4—22no—
260(C2×D7)⋊C4—22no—
261(C2×D7)⋊C4—22no—
262(C2×D7)⋊C4—22no—
263(C2×D7)⋊C4—28no—
264(C2×D7)⋊C4—44no—
265C4⋊Dic7—21no—
266C4⋊Dic7—21no—
267C4⋊Dic7—22no—
268C4⋊Dic7—22no—
269C4⋊Dic7—42no—
270Dic7⋊C4—22no—
271Dic7⋊C4—22no—
272Dic7⋊C4—22no—
273Dic7⋊C4—22no—
274Dic7⋊C4—22no—
275Dic7⋊C4—22no—
276Dic7⋊C4—44no—
277C4×Dic7—44no—
278C4×Dic7—42no—
279C23×Q8—71no—
280C24×C4—71no—
281C2×C22⋊Q8—71no—
282C2×C22⋊Q8—71no—
283C2×C22⋊Q8—72no—
284C2×C22⋊Q8—71no—
285C2×C22⋊Q8—72no—
286C2×C22⋊Q8—141no—
287C2×C22⋊Q8—141no—
288C2×C22⋊Q8—141no—
289C2×C22⋊Q8—141no—
290C2×C22⋊Q8—141no—
291C2×C22⋊Q8—141no—
292C2×C22⋊Q8—141no—
293C2×C22⋊Q8—141no—
294C2×C22⋊Q8C2×D711yescharacteristic
295C22×C4⋊C4—71no—
296C22×C4⋊C4—72no—
297C22×C4⋊C4—141no—
298C22×C22⋊C4—72no—
299C22×C22⋊C4—72no—
300C22×C22⋊C4—72no—
301C22×C42—141no—
302#380—71no—
303#380—72no—
304#380—141no—
305#380—141no—
306#380C2×D711yescharacteristic
307C4×C22⋊C4—71no—
308C4×C22⋊C4—72no—
309C4×C22⋊C4—141no—
310C4×C22⋊C4—141no—
311C4×C22⋊C4C2×D711yescharacteristic
312C2×#95—141no—
313C2×#95—141no—
314#342—74no—
315#342—74no—
316#342—74no—
317#342C2×D714yes—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7C23×C411yescharacteristic
321C23×C7C22×D411yescharacteristic
322C23×C7C22×D411yescharacteristic
323C23×C7C22×Q812yes—
324C23×C7C2×#4112yes—
325C22×D7—22no—
326C22×D7—22no—
327C22×D7—22no—
328C22×D7—22no—
329C22×D7—22no—
330C22×D7—22no—
331C22×D7—48no—
332C22×D7—48no—
333C22×D7—41no—
334C22×D7—41no—
335C22×D7—41no—
336C22×D7—41no—
337C22×D7—41no—
338C22×D7—41no—
339C22×D7C2×C22⋊C411yescharacteristic
340C22×D7C2×C22⋊C411yescharacteristic
341C22×D7C2×C22⋊C411yescharacteristic
342C22×D7C2×C22⋊C411yescharacteristic
343C22×D7C4×Q814yes—
344C22×D7C4×Q814yes—
345C22×D7C22⋊Q814yes—
346C22×D7C22⋊Q814yes—
347C22×D7#12412yes—
348C22×D7#12412yes—
349C22×D7C4⋊Q812yes—
350C22×D7C4⋊Q812yes—
351C7×Q8—42no—
352C7×Q8—42no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—24no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—42no—
363C2×C4×C7—42no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—42no—
368C2×C4×C7—42no—
369C2×C4×C7C2×C22⋊C411yescharacteristic
370C2×C4×C7C2×C22⋊C411yescharacteristic
371C2×C4×C7C2×C22⋊C411yescharacteristic
372C2×C4×C7C2×C22⋊C411yescharacteristic
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—24no—
379C2×Dic7—41no—
380C2×Dic7—41no—
381C2×Dic7—41no—
382C2×Dic7—42no—
383C2×Dic7—42no—
384C2×Dic7—42no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7C2×C22⋊C411yescharacteristic
390C2×Dic7C2×C22⋊C411yescharacteristic
391C2×Dic7C2×C22⋊C411yescharacteristic
392C2×Dic7C2×C22⋊C411yescharacteristic
393C4×D7—22no—
394C4×D7—22no—
395C4×D7—22no—
396C4×D7—22no—
397C4×D7—22no—
398C4×D7—22no—
399C4×D7—22no—
400C4×D7—22no—
401C4×D7—22no—
402C4×D7—41no—
403C4×D7—41no—
404C4×D7—41no—
405C4×D7—41no—
406C4×D7—41no—
407C4×D7—41no—
408C4×D7—416no—
409C4×D7—44no—
410C4×D7—44no—
411C4×D7—44no—
412C4×D7—44no—
413C4×D7—88no—
414C4×D7#9914yes—
415Dic14—44no—
416Dic14—42no—
417Dic14—42no—
418Dic14—44no—
419C25—71no—
420C22×Q8—72no—
421C22×Q8—71no—
422C22×Q8—141no—
423C22×Q8—141no—
424C22×Q8—141no—
425C22×Q8—141no—
426C22×Q8—284no—
427C22×Q8C4×D711yescharacteristic, complemented
428C23×C4—71no—
429C23×C4—71no—
430C23×C4—71no—
431C23×C4—71no—
432C23×C4—71no—
433C23×C4—71no—
434C23×C4—71no—
435C23×C4—71no—
436C23×C4—71no—
437C23×C4—71no—
438C23×C4—71no—
439C23×C4—71no—
440C23×C4—71no—
441C23×C4—72no—
442C23×C4—72no—
443C23×C4—142no—
444C23×C4—142no—
445C23×C4—284no—
446C23×C4C22×D711yescharacteristic
447C22⋊Q8—21no—
448C22⋊Q8—21no—
449C22⋊Q8—21no—
450C22⋊Q8—21no—
451C22⋊Q8—142no—
452C22⋊Q8—142no—
453C22⋊Q8—142no—
454C22⋊Q8—142no—
455C22⋊Q8—142no—
456C22⋊Q8—142no—
457C22⋊Q8—142no—
458C22⋊Q8—142no—
459C22⋊Q8—141no—
460C22⋊Q8—141no—
461C22⋊Q8—141no—
462C22⋊Q8—141no—
463C22⋊Q8—141no—
464C22⋊Q8—141no—
465C22⋊Q8—141no—
466C22⋊Q8—141no—
467C22⋊Q8—141no—
468C22⋊Q8—141no—
469C22⋊Q8—141no—
470C22⋊Q8—141no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—72no—
473C2×C4⋊C4—72no—
474C2×C4⋊C4—72no—
475C2×C4⋊C4—72no—
476C2×C4⋊C4—71no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—142no—
482C2×C4⋊C4—142no—
483C2×C4⋊C4—142no—
484C2×C4⋊C4—142no—
485C2×C4⋊C4—142no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4—284no—
488C2×C4⋊C4C4×D711yescharacteristic, complemented
489C2×C4⋊C4C4×D712yescomplemented
490C2×C22⋊C4—72no—
491C2×C22⋊C4—78no—
492C2×C22⋊C4—72no—
493C2×C22⋊C4—72no—
494C2×C22⋊C4—72no—
495C2×C22⋊C4—72no—
496C2×C22⋊C4—142no—
497C2×C22⋊C4—142no—
498C2×C22⋊C4—142no—
499C2×C22⋊C4—142no—
500C2×C22⋊C4—144no—
501C2×C22⋊C4—148no—
502C2×C22⋊C4—142no—
503C2×C22⋊C4—142no—
504C2×C22⋊C4C22×D712yes—
505C2×C22⋊C4C22×D712yes—
506C2×C22⋊C4C22×D712yes—
507C2×C42—21no—
508C2×C42—142no—
509C2×C42—141no—
510C2×C42—284no—
511#95—21no—
512#95—21no—
513#95—142no—
514#95—142no—
515#95—141no—
516#95—141no—
517C22×C7—21no—
518C22×C7—21no—
519C22×C7—21no—
520C22×C7—21no—
521C22×C7—21no—
522C22×C7—21no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7C22×C22⋊C411yescharacteristic
526C22×C7C2×C4×Q812yes—
527C22×C7C2×C22⋊Q812yes—
528C22×C7C2×#12411yescharacteristic
529C22×C7C2×C4⋊Q811yescharacteristic
530C2×D7—21no—
531C2×D7—21no—
532C2×D7—21no—
533C2×D7—21no—
534C2×D7—21no—
535C2×D7—21no—
536C2×D7—28no—
537C2×D7—24no—
538C2×D7—28no—
539C2×D7—24no—
540C2×D7—44no—
541C2×D7—44no—
542C2×D7—42no—
543C2×D7—42no—
544C2×D7#39112yes—
545C2×D7#39112yes—
546C2×D7#39112yes—
547C2×D7#39112yes—
548C2×D7C2×#9912yes—
549C2×D7#41012yes—
550C4×C7—21no—
551C4×C7—21no—
552C4×C7—21no—
553C4×C7—44no—
554C4×C7—42no—
555C4×C7—42no—
556C4×C7—82no—
557C4×C7C2×#9912yes—
558Dic7—21no—
559Dic7—21no—
560Dic7—21no—
561Dic7—44no—
562Dic7—42no—
563Dic7—42no—
564Dic7—82no—
565Dic7C2×#9912yes—
566C24—71no—
567C24—71no—
568C24—71no—
569C24—71no—
570C24—71no—
571C24—71no—
572C24—74no—
573C24—74no—
574C24—282no—
575C24—282no—
576C24C23×D711yescharacteristic
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—42no—
580C2×Q8—142no—
581C2×Q8—142no—
582C2×Q8—141no—
583C2×Q8—141no—
584C2×Q8—282no—
585C2×Q8—284no—
586C2×Q8—284no—
587C2×Q8—284no—
588C2×Q8—284no—
589C2×Q8—284no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—42no—
593C22×C4—71no—
594C22×C4—71no—
595C22×C4—71no—
596C22×C4—71no—
597C22×C4—71no—
598C22×C4—71no—
599C22×C4—71no—
600C22×C4—71no—
601C22×C4—71no—
602C22×C4—71no—
603C22×C4—71no—
604C22×C4—71no—
605C22×C4—71no—
606C22×C4—71no—
607C22×C4—71no—
608C22×C4—71no—
609C22×C4—71no—
610C22×C4—71no—
611C22×C4—71no—
612C22×C4—71no—
613C22×C4—71no—
614C22×C4—71no—
615C22×C4—72no—
616C22×C4—72no—
617C22×C4—144no—
618C22×C4—144no—
619C22×C4—144no—
620C22×C4—148no—
621C22×C4—142no—
622C22×C4—142no—
623C22×C4—142no—
624C22×C4—142no—
625C22×C4—142no—
626C22×C4—142no—
627C22×C4—282no—
628C22×C4—282no—
629C22×C4—282no—
630C22×C4—282no—
631C22×C4—282no—
632C22×C4—282no—
633C22×C4—282no—
634C22×C4—282no—
635C22×C4—282no—
636C22×C4—284no—
637C22×C4—284no—
638C22×C4—284no—
639C22×C4—284no—
640C22×C4—284no—
641C22×C4—284no—
642C22×C4—284no—
643C22×C4—282no—
644C22×C4C2×C4×D711yescharacteristic
645C22×C4C2×C4×D712yes—
646C22×C4C2×C4×D712yes—
647C22×C4C2×C4×D711yescharacteristic
648C22×C4D4×D711yescharacteristic
649C22×C4D4×D711yescharacteristic
650C22×C4D4×D711yescharacteristic
651C22×C4D4×D711yescharacteristic
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—42no—
657C4⋊C4—142no—
658C4⋊C4—142no—
659C4⋊C4—142no—
660C4⋊C4—142no—
661C4⋊C4—142no—
662C4⋊C4—142no—
663C4⋊C4—142no—
664C4⋊C4—142no—
665C4⋊C4—141no—
666C4⋊C4—141no—
667C4⋊C4—282no—
668C4⋊C4—284no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—24no—
673C22⋊C4—74no—
674C22⋊C4—148no—
675C22⋊C4—142no—
676C22⋊C4—142no—
677C22⋊C4—142no—
678C22⋊C4—142no—
679C22⋊C4—142no—
680C22⋊C4—142no—
681C22⋊C4—142no—
682C22⋊C4—144no—
683C22⋊C4—284no—
684C22⋊C4Q8×D714yescomplemented
685C42—42no—
686C42—282no—
687C42—284no—
688C2×C7—22no—
689C2×C7—21no—
690C2×C7—22no—
691C2×C7—21no—
692C2×C7C2×#39111yescharacteristic
693C2×C7C22×#9911yescharacteristic
694C2×C7C2×#41011yescharacteristic
695D7—22no—
696D7—22no—
697D7—22no—
698D7#199614yesdirect product factor
699C23—41no—
700C23—41no—
701C23—71no—
702C23—72no—
703C23—71no—
704C23—71no—
705C23—71no—
706C23—74no—
707C23—74no—
708C23—72no—
709C23—72no—
710C23—74no—
711C23—74no—
712C23—72no—
713C23—142no—
714C23—142no—
715C23—142no—
716C23—142no—
717C23—142no—
718C23—142no—
719C23—281no—
720C23—281no—
721C23—281no—
722C23—281no—
723C23—281no—
724C23—281no—
725C23—288no—
726C23—288no—
727C23C22×C4×D711yescharacteristic
728C23C2×D4×D711yescharacteristic
729C23C2×D4×D711yescharacteristic
730C23C2×Q8×D712yes—
731C23D7×#4112yes—
732Q8—42no—
733Q8—42no—
734Q8—282no—
735Q8—284no—
736Q8—284no—
737Q8—282no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—71no—
755C2×C4—74no—
756C2×C4—71no—
757C2×C4—71no—
758C2×C4—71no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—142no—
766C2×C4—142no—
767C2×C4—142no—
768C2×C4—142no—
769C2×C4—142no—
770C2×C4—142no—
771C2×C4—142no—
772C2×C4—142no—
773C2×C4—144no—
774C2×C4—281no—
775C2×C4—281no—
776C2×C4—281no—
777C2×C4—281no—
778C2×C4—281no—
779C2×C4—281no—
780C2×C4—284no—
781C2×C4—284no—
782C2×C4—2816no—
783C2×C4—284no—
784C2×C4—284no—
785C2×C4—281no—
786C2×C4—281no—
787C2×C4—281no—
788C2×C4—282no—
789C2×C4—282no—
790C2×C4—282no—
791C2×C4—282no—
792C2×C4—282no—
793C2×C4—282no—
794C2×C4—282no—
795C2×C4—568no—
796C2×C4D7×C22⋊C411yescharacteristic
797C2×C4D7×C22⋊C411yescharacteristic
798C2×C4D7×C22⋊C411yescharacteristic
799C2×C4D7×C22⋊C411yescharacteristic
800C7C2×#199611yescharacteristic, complemented, Sylow
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—42no—
808C22—42no—
809C22—72no—
810C22—72no—
811C22—72no—
812C22—72no—
813C22—72no—
814C22—72no—
815C22—148no—
816C22—144no—
817C22—144no—
818C22—148no—
819C22—141no—
820C22—141no—
821C22—141no—
822C22—141no—
823C22—141no—
824C22—141no—
825C22—284no—
826C22—282no—
827C22—282no—
828C22—284no—
829C22C2×D7×C22⋊C411yescharacteristic
830C22C4×Q8×D712yes—
831C22D7×C22⋊Q812yes—
832C22D7×#12411yescharacteristic
833C22D7×C4⋊Q811yescharacteristic
834C4—21no—
835C4—21no—
836C4—21no—
837C4—44no—
838C4—42no—
839C4—42no—
840C4—72no—
841C4—82no—
842C4—141no—
843C4—141no—
844C4—141no—
845C4—284no—
846C4—282no—
847C4—282no—
848C4—562no—
849C4D7×#9912yes—
850C2—22no—
851C2—21no—
852C2—21no—
853C2—22no—
854C2—74no—
855C2—142no—
856C2—142no—
857C2—142no—
858C2D7×#39111yescharacteristic
859C2C2×D7×#9911yescharacteristic
860C2D7×#41011yescharacteristic
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC7×#1996C2
socleC22×C7C22×C22⋊C4
prime radicalC24×D7C23
cosocleC24×C7C24
hypercenter#1996D7
hypocenterC7C2×#1996
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
4. C7×#1996C2semidirect
5. #11729455C2semidirect
6. #11727283C2semidirect
7. #11727211C2semidirect
9. #11726709C2semidirect
10. C22×Q8×D7C4semidirect
13. C2×#6509C4semidirect
23. C2×#6460C4semidirect
24. C2×#6459C4semidirect
26. C2×D7×C4⋊C4C4semidirect
27. C2×D7×C4⋊C4C4semidirect
51. C22×C7×Q8C2×C4semidirect
76. C22×Dic14C2×C4semidirect
77. C22×Dic14C2×C4semidirect
83. C2×C7×C4⋊C4C2×C4semidirect
84. C2×C7×C4⋊C4C2×C4semidirect
101. C2×C4⋊Dic7C2×C4semidirect
102. C2×C4⋊Dic7C2×C4semidirect
108. C2×Dic7⋊C4C2×C4semidirect
109. C2×Dic7⋊C4C2×C4semidirect
110. C2×Dic7⋊C4C2×C4semidirect
136. D7×C22⋊C4Q8semidirect
155. #1996D7direct (N × H)
252. C7×C22⋊C4C2×Q8semidirect
258. C22⋊Dic7C2×Q8semidirect
427. C22×Q8C4×D7semidirect
488. C2×C4⋊C4C4×D7semidirect
489. C2×C4⋊C4C4×D7semidirect
684. C22⋊C4Q8×D7semidirect
698. D7#1996direct (N × H)
800. C7C2×#1996semidirect

Maximal subgroups

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

subgroupindex
C2×D7×C22⋊Q82
D7×#3802
C4×D7×C22⋊C42
C7×#19962
#117294552
#117272832
#117272112
D7×#3422
#117267092
C2×#19967