Finite Group Databasebeta

← C7×#13872 #13191088

Subgroups — C7×#13872 #13191088

Order 1792.

2950 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic
2C23×C7×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C7×#386C212yesmaximal
4C2×C7×#380C212yesmaximal, complemented
5C2×C7×#380C211yesmaximal, characteristic, complemented
6C7×#1441C212yesmaximal, complemented
7C7×#1439C212yesmaximal, complemented
8C7×C4⋊#95C212yesmaximal, complemented
9C7×C22⋊#95C212yesmaximal, complemented
10C23×C7×D4C2211yescharacteristic
11C24×C4×C7C2211yescharacteristic
12C24×C4×C7C2212yes—
13C24×C4×C7C2211yescharacteristic
14C2×C4×C7×D4—24no—
15C2×C4×C7×D4—24no—
16C2×C4×C7×D4C418yescomplemented
17C22×C7×C4⋊C4—24no—
18C22×C7×C4⋊C4—28no—
19C22×C7×C4⋊C4C2212yes—
20C22×C7×C4⋊C4C2212yes—
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2214yes—
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C42×C7C2211yescharacteristic
28C7×#386—28no—
29C7×#380—24no—
30C7×#380—28no—
31C2×C7×#95C2214yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2214yes—
34C2×C7×#95C2214yes—
35#13872C711yesmaximal, characteristic, direct product factor, Sylow
36C25×C7C2311yescharacteristic
37C25×C7C2311yescharacteristic
38C22×C7×D4—22no—
39C22×C7×D4—22no—
40C22×C7×D4—22no—
41C22×C7×D4—22no—
42C22×C7×D4C2×C414yes—
43C22×C7×D4D414yes—
44C22×C7×D4Q814yes—
45C23×C4×C7—24no—
46C23×C4×C7—24no—
47C23×C4×C7—24no—
48C23×C4×C7—28no—
49C23×C4×C7—22no—
50C23×C4×C7—22no—
51C23×C4×C7—24no—
52C23×C4×C7—24no—
53C23×C4×C7—24no—
54C23×C4×C7—24no—
55C23×C4×C7—44no—
56C23×C4×C7C2×C414yes—
57C23×C4×C7C2×C414yescomplemented
58C23×C4×C7D414yes—
59C23×C4×C7D414yes—
60C23×C4×C7C2314yes—
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2314yes—
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C4×C7×D4—232no—
68C2×C7×C4⋊C4—232no—
69C2×C7×C4⋊C4—28no—
70C2×C7×C4⋊C4—24no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—24no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—24no—
76C2×C7×C4⋊C4—24no—
77C2×C7×C4⋊C4—24no—
78C2×C7×C4⋊C4C2×C414yescomplemented
79C2×C7×C4⋊C4D418yescomplemented
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—28no—
86C2×C7×C22⋊C4—24no—
87C2×C7×C22⋊C4—24no—
88C2×C7×C22⋊C4—28no—
89C2×C7×C22⋊C4—44no—
90C2×C7×C22⋊C4C2×C414yes—
91C2×C7×C22⋊C4C2×C414yescomplemented
92C2×C42×C7—22no—
93C2×C42×C7—22no—
94C2×C42×C7C2×C414yescomplemented
95C7×#95—28no—
96C7×#95—24no—
97C7×#95—28no—
98C7×#95—44no—
99C22×C4×D4C2×C711yescharacteristic
100C23×C4⋊C4C2×C711yescharacteristic, complemented
101C2×#386C2×C712yes—
102C2×#380C2×C711yescharacteristic, complemented
103C2×#380C2×C712yescomplemented
104#1441C2×C712yescomplemented
105#1439C2×C712yescomplemented
106C4⋊#95C2×C712yescomplemented
107C22⋊#95C2×C712yescomplemented
108C24×C7—22no—
109C24×C7—22no—
110C24×C7—22no—
111C24×C7—22no—
112C24×C7—22no—
113C24×C7—21no—
114C24×C7—21no—
115C24×C7—22no—
116C24×C7—21no—
117C24×C7—21no—
118C24×C7—22no—
119C24×C7—22no—
120C24×C7C22×C412yes—
121C24×C7C22×C412yes—
122C24×C7C2×D412yes—
123C24×C7C2×D412yes—
124C24×C7C2×D412yes—
125C24×C7C2×D412yes—
126C24×C7C2×Q812yes—
127C24×C7C2×Q812yes—
128C24×C7#4112yes—
129C24×C7#4112yes—
130C24×C7C2411yescharacteristic
131C2×C7×D4—28no—
132C2×C7×D4—28no—
133C2×C7×D4—28no—
134C2×C7×D4—28no—
135C2×C7×D4—28no—
136C2×C7×D4—28no—
137C2×C7×D4C4⋊C4116yescomplemented
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—216no—
145C22×C4×C7—28no—
146C22×C4×C7—216no—
147C22×C4×C7—28no—
148C22×C4×C7—216no—
149C22×C4×C7—22no—
150C22×C4×C7—24no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—24no—
156C22×C4×C7—24no—
157C22×C4×C7—22no—
158C22×C4×C7—24no—
159C22×C4×C7—22no—
160C22×C4×C7—24no—
161C22×C4×C7—24no—
162C22×C4×C7—22no—
163C22×C4×C7—28no—
164C22×C4×C7—216no—
165C22×C4×C7—24no—
166C22×C4×C7—24no—
167C22×C4×C7—24no—
168C22×C4×C7—24no—
169C22×C4×C7—24no—
170C22×C4×C7—24no—
171C22×C4×C7—24no—
172C22×C4×C7—416no—
173C22×C4×C7—416no—
174C22×C4×C7—48no—
175C22×C4×C7—48no—
176C22×C4×C7—44no—
177C22×C4×C7—48no—
178C22×C4×C7—44no—
179C22×C4×C7C22⋊C4116yescomplemented
180C22×C4×C7C22×C412yes—
181C22×C4×C7C22×C412yes—
182C22×C4×C7C22×C412yes—
183C22×C4×C7C22×C412yes—
184C22×C4×C7C22×C412yes—
185C22×C4×C7C2×D418yes—
186C22×C4×C7C2×D412yes—
187C22×C4×C7C2×D412yes—
188C22×C4×C7C2×D412yes—
189C22×C4×C7C2×D412yes—
190C22×C4×C7C2×D412yes—
191C22×C4×C7C2×D414yes—
192C22×C4×C7C2×Q812yes—
193C22×C4×C7#4114yes—
194C7×C4⋊C4—216no—
195C7×C4⋊C4—28no—
196C7×C4⋊C4—216no—
197C7×C4⋊C4—48no—
198C7×C22⋊C4—28no—
199C7×C22⋊C4—28no—
200C7×C22⋊C4—416no—
201C7×C22⋊C4—48no—
202C42×C7—28no—
203C23×D4C22×C711yescharacteristic
204C24×C4C22×C711yescharacteristic
205C24×C4C22×C712yes—
206C24×C4C22×C711yescharacteristic
207C2×C4×D4—24no—
208C2×C4×D4—24no—
209C2×C4×D4C4×C718yescomplemented
210C22×C4⋊C4—24no—
211C22×C4⋊C4—28no—
212C22×C4⋊C4C22×C712yes—
213C22×C4⋊C4C22×C712yes—
214C22×C4⋊C4C22×C711yescharacteristic
215C22×C4⋊C4C22×C712yes—
216C22×C22⋊C4C22×C712yes—
217C22×C22⋊C4C22×C714yes—
218C22×C22⋊C4C22×C711yescharacteristic
219C22×C22⋊C4C22×C711yescharacteristic
220C22×C42C22×C711yescharacteristic
221#386—28no—
222#380—24no—
223#380—28no—
224C2×#95C22×C714yes—
225C2×#95C22×C714yes—
226C2×#95C22×C712yes—
227C2×#95C22×C714yes—
228C23×C7—24no—
229C23×C7—24no—
230C23×C7—22no—
231C23×C7—24no—
232C23×C7—22no—
233C23×C7—22no—
234C23×C7—22no—
235C23×C7—24no—
236C23×C7—24no—
237C23×C7—24no—
238C23×C7—24no—
239C23×C7—24no—
240C23×C7—24no—
241C23×C7—24no—
242C23×C7—24no—
243C23×C7—24no—
244C23×C7—22no—
245C23×C7—22no—
246C23×C7—24no—
247C23×C7—24no—
248C23×C7—22no—
249C23×C7—22no—
250C23×C7—22no—
251C23×C7—22no—
252C23×C7—24no—
253C23×C7—24no—
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—41no—
257C23×C7—42no—
258C23×C7—41no—
259C23×C7—41no—
260C23×C7—41no—
261C23×C7—42no—
262C23×C7—42no—
263C23×C7—42no—
264C23×C7—42no—
265C23×C7—42no—
266C23×C7C2×C22⋊C414yes—
267C23×C7C2×C4⋊C414yes—
268C23×C7C2×C4⋊C414yescomplemented
269C23×C7#11714yes—
270C23×C7#12114yes—
271C23×C7#12114yes—
272C23×C7C22⋊Q814yes—
273C23×C7C22⋊Q814yes—
274C23×C7C23×C411yescharacteristic
275C23×C7C22×D411yescharacteristic
276C23×C7C22×D411yescharacteristic
277C23×C7C22×D411yescharacteristic
278C23×C7C22×D412yes—
279C23×C7C22×Q811yescharacteristic
280C23×C7C2×#4111yescharacteristic
281C23×C7C2×#4111yescharacteristic
282C23×C7C2×#4112yes—
283C23×C7H(5,𝔽2)12yes—
284C23×C72−1+412yes—
285C7×D4—232no—
286C2×C4×C7—22no—
287C2×C4×C7—22no—
288C2×C4×C7—24no—
289C2×C4×C7—22no—
290C2×C4×C7—24no—
291C2×C4×C7—22no—
292C2×C4×C7—22no—
293C2×C4×C7—22no—
294C2×C4×C7—22no—
295C2×C4×C7—22no—
296C2×C4×C7—232no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—24no—
300C2×C4×C7—24no—
301C2×C4×C7—28no—
302C2×C4×C7—28no—
303C2×C4×C7—28no—
304C2×C4×C7—432no—
305C2×C4×C7—41no—
306C2×C4×C7—44no—
307C2×C4×C7—42no—
308C2×C4×C7—41no—
309C2×C4×C7—41no—
310C2×C4×C7—44no—
311C2×C4×C7—41no—
312C2×C4×C7—42no—
313C2×C4×C7—44no—
314C2×C4×C7—44no—
315C2×C4×C7—416no—
316C2×C4×C7—44no—
317C2×C4×C7—44no—
318C2×C4×C7—44no—
319C2×C4×C7—44no—
320C2×C4×C7—44no—
321C2×C4×C7—44no—
322C2×C4×C7—44no—
323C2×C4×C7C2×C22⋊C414yes—
324C2×C4×C7C2×C22⋊C414yes—
325C2×C4×C7C2×C4⋊C414yescomplemented
326C2×C4×C7C4×D418yes—
327C2×C4×C7#12014yes—
328C2×C4×C7#12118yes—
329C2×C4×C7#12314yes—
330C25C23×C711yescharacteristic
331C25C23×C711yescharacteristic
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4C2×C4×C714yes—
337C22×D4C7×D414yes—
338C22×D4C7×Q814yes—
339C23×C4—24no—
340C23×C4—24no—
341C23×C4—24no—
342C23×C4—28no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—24no—
348C23×C4—24no—
349C23×C4—44no—
350C23×C4C2×C4×C714yes—
351C23×C4C2×C4×C714yescomplemented
352C23×C4C7×D414yes—
353C23×C4C7×D414yes—
354C23×C4C23×C714yes—
355C23×C4C23×C711yescharacteristic
356C23×C4C23×C711yescharacteristic
357C23×C4C23×C714yes—
358C23×C4C23×C711yescharacteristic
359C23×C4C23×C711yescharacteristic
360C23×C4C23×C711yescharacteristic
361C4×D4—232no—
362C2×C4⋊C4—232no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4C2×C4×C714yescomplemented
373C2×C4⋊C4C7×D418yescomplemented
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4C2×C4×C714yes—
385C2×C22⋊C4C2×C4×C714yescomplemented
386C2×C42—22no—
387C2×C42—22no—
388C2×C42C2×C4×C714yescomplemented
389#95—28no—
390#95—24no—
391#95—28no—
392#95—44no—
393C22×C7—24no—
394C22×C7—28no—
395C22×C7—28no—
396C22×C7—24no—
397C22×C7—24no—
398C22×C7—28no—
399C22×C7—28no—
400C22×C7—24no—
401C22×C7—24no—
402C22×C7—24no—
403C22×C7—28no—
404C22×C7—24no—
405C22×C7—42no—
406C22×C7—44no—
407C22×C7—42no—
408C22×C7—42no—
409C22×C7—44no—
410C22×C7—44no—
411C22×C7—42no—
412C22×C7—42no—
413C22×C7—42no—
414C22×C7#38018yescomplemented
415C22×C7C22×C22⋊C411yescharacteristic
416C22×C7C22×C4⋊C411yescharacteristic
417C22×C7C2×#11711yescharacteristic
418C22×C7C2×C4×D412yes—
419C22×C7#52012yes—
420C22×C7C2×#12011yescharacteristic
421C22×C7C2×#12111yescharacteristic
422C22×C7C2×#12111yescharacteristic
423C22×C7C2×#12112yes—
424C22×C7C2×C22⋊Q811yescharacteristic
425C22×C7C2×C22⋊Q811yescharacteristic
426C22×C7C2×#12311yescharacteristic
427C22×C7#53511yescharacteristic
428C22×C7#53611yescharacteristic
429C22×C7#53712yes—
430C22×C7D4212yes—
431C22×C7#54612yes—
432C22×C7#54712yes—
433C22×C7#54812yes—
434C22×C7D4×Q812yes—
435C22×C7#55212yes—
436C22×C7#55312yes—
437C22×C7#55412yes—
438C4×C7—24no—
439C4×C7—24no—
440C4×C7—42no—
441C4×C7—48no—
442C4×C7—42no—
443C4×C7—84no—
444C4×C7#38618yescomplemented
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24—21no—
452C24—22no—
453C24—21no—
454C24—21no—
455C24—22no—
456C24—22no—
457C24C22×C4×C712yes—
458C24C22×C4×C712yes—
459C24C2×C7×D412yes—
460C24C2×C7×D412yes—
461C24C2×C7×D412yes—
462C24C2×C7×D412yes—
463C24C2×C7×Q812yes—
464C24C2×C7×Q812yes—
465C24C7×#4112yes—
466C24C7×#4112yes—
467C24C24×C711yescharacteristic
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—28no—
472C2×D4—28no—
473C2×D4—28no—
474C2×D4C7×C4⋊C4116yescomplemented
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—216no—
482C22×C4—28no—
483C22×C4—216no—
484C22×C4—28no—
485C22×C4—216no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—28no—
501C22×C4—216no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—416no—
510C22×C4—416no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—44no—
514C22×C4—48no—
515C22×C4—44no—
516C22×C4C7×C22⋊C4116yescomplemented
517C22×C4C22×C4×C712yes—
518C22×C4C22×C4×C712yes—
519C22×C4C22×C4×C712yes—
520C22×C4C22×C4×C712yes—
521C22×C4C22×C4×C712yes—
522C22×C4C2×C7×D418yes—
523C22×C4C2×C7×D412yes—
524C22×C4C2×C7×D412yes—
525C22×C4C2×C7×D412yes—
526C22×C4C2×C7×D412yes—
527C22×C4C2×C7×D412yes—
528C22×C4C2×C7×D414yes—
529C22×C4C2×C7×Q812yes—
530C22×C4C7×#4114yes—
531C4⋊C4—216no—
532C4⋊C4—28no—
533C4⋊C4—216no—
534C4⋊C4—48no—
535C22⋊C4—28no—
536C22⋊C4—28no—
537C22⋊C4—416no—
538C22⋊C4—48no—
539C42—28no—
540C2×C7—28no—
541C2×C7—44no—
542C2×C7C2×#38011yescharacteristic
543C2×C7C2×#38611yescharacteristic
544C2×C7#231111yescharacteristic
545C2×C7D4×C4⋊C412yes—
546C2×C7#235212yes—
547C2×C7#240811yescharacteristic
548C2×C7#240911yescharacteristic
549C2×C7#241612yes—
550C2×C7#241712yes—
551C2×C7#248611yescharacteristic
552C2×C7#248711yescharacteristic
553C23—24no—
554C23—24no—
555C23—22no—
556C23—24no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—22no—
570C23—22no—
571C23—24no—
572C23—24no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—41no—
582C23—42no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23C2×C7×C22⋊C414yes—
592C23C2×C7×C4⋊C414yes—
593C23C2×C7×C4⋊C414yescomplemented
594C23C7×#11714yes—
595C23C7×#12114yes—
596C23C7×#12114yes—
597C23C7×C22⋊Q814yes—
598C23C7×C22⋊Q814yes—
599C23C23×C4×C711yescharacteristic
600C23C22×C7×D411yescharacteristic
601C23C22×C7×D411yescharacteristic
602C23C22×C7×D411yescharacteristic
603C23C22×C7×D412yes—
604C23C22×C7×Q811yescharacteristic
605C23C2×C7×#4111yescharacteristic
606C23C2×C7×#4111yescharacteristic
607C23C2×C7×#4112yes—
608C23C7×H(5,𝔽2)12yes—
609C23C7×2−1+412yes—
610D4—232no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—232no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—28no—
627C2×C4—28no—
628C2×C4—28no—
629C2×C4—432no—
630C2×C4—41no—
631C2×C4—44no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—44no—
636C2×C4—41no—
637C2×C4—42no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—416no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4C2×C7×C22⋊C414yes—
649C2×C4C2×C7×C22⋊C414yes—
650C2×C4C2×C7×C4⋊C414yescomplemented
651C2×C4C4×C7×D418yes—
652C2×C4C7×#12014yes—
653C2×C4C7×#12118yes—
654C2×C4C7×#12314yes—
655C7#1387211yescharacteristic, direct product factor, Sylow
656C22—24no—
657C22—24no—
658C22—28no—
659C22—28no—
660C22—24no—
661C22—24no—
662C22—24no—
663C22—24no—
664C22—28no—
665C22—28no—
666C22—24no—
667C22—28no—
668C22—42no—
669C22—42no—
670C22—44no—
671C22—44no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—44no—
677C22C7×#38018yescomplemented
678C22C22×C7×C22⋊C411yescharacteristic
679C22C22×C7×C4⋊C411yescharacteristic
680C22C2×C7×#11711yescharacteristic
681C22C2×C4×C7×D412yes—
682C22C7×#52012yes—
683C22C2×C7×#12011yescharacteristic
684C22C2×C7×#12111yescharacteristic
685C22C2×C7×#12111yescharacteristic
686C22C2×C7×#12112yes—
687C22C2×C7×C22⋊Q811yescharacteristic
688C22C2×C7×C22⋊Q811yescharacteristic
689C22C2×C7×#12311yescharacteristic
690C22C7×#53511yescharacteristic
691C22C7×#53611yescharacteristic
692C22C7×#53712yes—
693C22C7×D4212yes—
694C22C7×#54612yes—
695C22C7×#54712yes—
696C22C7×#54812yes—
697C22C7×D4×Q812yes—
698C22C7×#55212yes—
699C22C7×#55312yes—
700C22C7×#55412yes—
701C4—24no—
702C4—24no—
703C4—48no—
704C4—42no—
705C4—42no—
706C4—84no—
707C4C7×#38618yescomplemented
708C2—28no—
709C2—44no—
710C2C2×C7×#38011yescharacteristic
711C2C2×C7×#38611yescharacteristic
712C2C7×#231111yescharacteristic
713C2C7×D4×C4⋊C412yes—
714C2C7×#235212yes—
715C2C7×#240811yescharacteristic
716C2C7×#240911yescharacteristic
717C2C7×#241612yes—
718C2C7×#241712yes—
719C2C7×#248611yescharacteristic
720C2C7×#248711yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C7×C4⋊C4C2semidirect
4. C2×C7×#380C2semidirect
5. C2×C7×#380C2semidirect
6. C7×#1441C2semidirect
7. C7×#1439C2semidirect
8. C7×C4⋊#95C2semidirect
9. C7×C22⋊#95C2semidirect
16. C2×C4×C7×D4C4semidirect
35. #13872C7direct (N × H)
57. C23×C4×C7C2×C4semidirect
78. C2×C7×C4⋊C4C2×C4semidirect
79. C2×C7×C4⋊C4D4semidirect
91. C2×C7×C22⋊C4C2×C4semidirect
94. C2×C42×C7C2×C4semidirect
100. C23×C4⋊C4C2×C7semidirect
102. C2×#380C2×C7semidirect
103. C2×#380C2×C7semidirect
104. #1441C2×C7semidirect
105. #1439C2×C7semidirect
106. C4⋊#95C2×C7semidirect
107. C22⋊#95C2×C7semidirect
137. C2×C7×D4C4⋊C4semidirect
179. C22×C4×C7C22⋊C4semidirect
209. C2×C4×D4C4×C7semidirect
268. C23×C7C2×C4⋊C4semidirect
325. C2×C4×C7C2×C4⋊C4semidirect
351. C23×C4C2×C4×C7semidirect
372. C2×C4⋊C4C2×C4×C7semidirect
373. C2×C4⋊C4C7×D4semidirect
385. C2×C22⋊C4C2×C4×C7semidirect
388. C2×C42C2×C4×C7semidirect
414. C22×C7#380semidirect
444. C4×C7#386semidirect
474. C2×D4C7×C4⋊C4semidirect
516. C22×C4C7×C22⋊C4semidirect
593. C23C2×C7×C4⋊C4semidirect
650. C2×C4C2×C7×C4⋊C4semidirect
655. C7#13872direct (N × H)
677. C22C7×#380semidirect
707. C4C7×#386semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C23×C7×C4⋊C42
C2×C7×#3862
C2×C7×#3802
C7×#14412
C7×#14392
C7×C4⋊#952
C7×C22⋊#952
#138727