Finite Group Databasebeta

← C7×#13975 #13191191

Subgroups — C7×#13975 #13191191

Order 1792.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic
2C2×C7×#386C211yesmaximal, characteristic
3C2×C7×#386C211yesmaximal, characteristic
4C2×C7×#385C211yesmaximal, characteristic, complemented
5C2×C7×#385C211yesmaximal, characteristic, complemented
6C2×C7×#380C211yesmaximal, characteristic, complemented
7C22×C7×#95C211yesmaximal, characteristic, complemented
8C7×#1444C211yesmaximal, characteristic, complemented
9C7×#1442C211yesmaximal, characteristic, complemented
10C7×#1439C211yesmaximal, characteristic, complemented
11C7×#1439C211yesmaximal, characteristic, complemented
12C7×#1436C211yesmaximal, characteristic, complemented
13C7×#1436C211yesmaximal, characteristic, complemented
14C7×C22⋊#95C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C24×C4×C7C2211yescharacteristic
20C24×C4×C7C2211yescharacteristic
21C2×C4×C7×D4—24no—
22C2×C4×C7×D4—24no—
23C2×C4×C7×D4—24no—
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C4⋊C4C2211yescharacteristic
27C22×C7×C4⋊C4C2211yescharacteristic
28C22×C7×C4⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31C22×C7×C22⋊C4C2211yescharacteristic
32C22×C7×C22⋊C4C2211yescharacteristic
33C22×C7×C22⋊C4C2211yescharacteristic
34C22×C7×C22⋊C4C2211yescharacteristic
35C22×C7×C22⋊C4C2211yescharacteristic
36C22×C7×C22⋊C4C2211yescharacteristic
37C22×C42×C7C2211yescharacteristic
38C7×#386—24no—
39C7×#386C418yescomplemented
40C7×#385—24no—
41C7×#385—24no—
42C7×#380—24no—
43C2×C7×#95—24no—
44C2×C7×#95C2211yescharacteristic
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47C2×C7×#95C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56C2×C7×#95C2211yescharacteristic
57C2×C7×#95C2211yescharacteristic
58C2×C7×#95C2211yescharacteristic
59C2×C7×#95C2211yescharacteristic
60#13975C711yesmaximal, characteristic, direct product factor, Sylow
61C25×C7C2311yescharacteristic
62C25×C7C2311yescharacteristic
63C22×C7×D4—22no—
64C22×C7×D4—22no—
65C22×C7×D4—22no—
66C22×C7×D4—22no—
67C22×C7×D4C2×C414yes—
68C22×C7×D4D414yes—
69C22×C7×D4Q814yes—
70C23×C4×C7—22no—
71C23×C4×C7—22no—
72C23×C4×C7—22no—
73C23×C4×C7—22no—
74C23×C4×C7—22no—
75C23×C4×C7—22no—
76C23×C4×C7—22no—
77C23×C4×C7—22no—
78C23×C4×C7—22no—
79C23×C4×C7—22no—
80C23×C4×C7—22no—
81C23×C4×C7—22no—
82C23×C4×C7—22no—
83C23×C4×C7—22no—
84C23×C4×C7—22no—
85C23×C4×C7—22no—
86C23×C4×C7—22no—
87C23×C4×C7—22no—
88C23×C4×C7—41no—
89C23×C4×C7—41no—
90C23×C4×C7—41no—
91C23×C4×C7—41no—
92C23×C4×C7—41no—
93C23×C4×C7—41no—
94C23×C4×C7—41no—
95C23×C4×C7—41no—
96C23×C4×C7C2×C414yescomplemented
97C23×C4×C7D414yes—
98C23×C4×C7C2311yescharacteristic
99C23×C4×C7C2311yescharacteristic
100C23×C4×C7C2311yescharacteristic
101C23×C4×C7C2311yescharacteristic
102C23×C4×C7C2311yescharacteristic
103C23×C4×C7C2311yescharacteristic
104C23×C4×C7C2311yescharacteristic
105C23×C4×C7C2311yescharacteristic
106C23×C4×C7C2311yescharacteristic
107C23×C4×C7C2311yescharacteristic
108C23×C4×C7C2311yescharacteristic
109C23×C4×C7C2311yescharacteristic
110C23×C4×C7C2311yescharacteristic
111C4×C7×D4—232no—
112C2×C7×C4⋊C4—22no—
113C2×C7×C4⋊C4—22no—
114C2×C7×C4⋊C4—22no—
115C2×C7×C4⋊C4—22no—
116C2×C7×C4⋊C4—22no—
117C2×C7×C4⋊C4—22no—
118C2×C7×C4⋊C4—22no—
119C2×C7×C4⋊C4—22no—
120C2×C7×C4⋊C4—22no—
121C2×C7×C4⋊C4—22no—
122C2×C7×C4⋊C4—22no—
123C2×C7×C4⋊C4—41no—
124C2×C7×C4⋊C4—41no—
125C2×C7×C4⋊C4—41no—
126C2×C7×C4⋊C4—41no—
127C2×C7×C22⋊C4—22no—
128C2×C7×C22⋊C4—22no—
129C2×C7×C22⋊C4—22no—
130C2×C7×C22⋊C4—22no—
131C2×C7×C22⋊C4—22no—
132C2×C7×C22⋊C4—22no—
133C2×C7×C22⋊C4—22no—
134C2×C7×C22⋊C4—22no—
135C2×C7×C22⋊C4—22no—
136C2×C7×C22⋊C4—22no—
137C2×C7×C22⋊C4—22no—
138C2×C7×C22⋊C4—22no—
139C2×C7×C22⋊C4—22no—
140C2×C7×C22⋊C4—22no—
141C2×C7×C22⋊C4—22no—
142C2×C7×C22⋊C4—22no—
143C2×C7×C22⋊C4—41no—
144C2×C7×C22⋊C4—41no—
145C2×C7×C22⋊C4—41no—
146C2×C7×C22⋊C4—41no—
147C2×C7×C22⋊C4C2×C414yescomplemented
148C2×C7×C22⋊C4C2×C414yescomplemented
149C2×C7×C22⋊C4C2×C414yescomplemented
150C2×C7×C22⋊C4D414yes—
151C2×C42×C7—22no—
152C2×C42×C7—22no—
153C2×C42×C7—22no—
154C7×#95—22no—
155C7×#95—22no—
156C7×#95—22no—
157C7×#95—22no—
158C7×#95—22no—
159C7×#95—22no—
160C7×#95—22no—
161C7×#95—22no—
162C7×#95—22no—
163C7×#95—22no—
164C7×#95—22no—
165C7×#95—41no—
166C7×#95—41no—
167C7×#95C2×C414yescomplemented
168C7×#95C2×C414yescomplemented
169C7×#95D414yescomplemented
170C22×C4×D4C2×C711yescharacteristic
171C2×#386C2×C711yescharacteristic
172C2×#386C2×C711yescharacteristic
173C2×#385C2×C711yescharacteristic, complemented
174C2×#385C2×C711yescharacteristic, complemented
175C2×#380C2×C711yescharacteristic, complemented
176C22×#95C2×C711yescharacteristic, complemented
177#1444C2×C711yescharacteristic, complemented
178#1442C2×C711yescharacteristic, complemented
179#1439C2×C711yescharacteristic, complemented
180#1439C2×C711yescharacteristic, complemented
181#1436C2×C711yescharacteristic, complemented
182#1436C2×C711yescharacteristic, complemented
183C22⋊#95C2×C711yescharacteristic, complemented
184C22⋊#95C2×C711yescharacteristic, complemented
185C24×C7—21no—
186C24×C7—21no—
187C24×C7—21no—
188C24×C7—21no—
189C24×C7—21no—
190C24×C7—21no—
191C24×C7—21no—
192C24×C7—21no—
193C24×C7—21no—
194C24×C7—21no—
195C24×C7—21no—
196C24×C7—21no—
197C24×C7—21no—
198C24×C7—21no—
199C24×C7—21no—
200C24×C7—21no—
201C24×C7—21no—
202C24×C7—21no—
203C24×C7—21no—
204C24×C7—21no—
205C24×C7C22×C412yes—
206C24×C7C22×C412yes—
207C24×C7C2×D412yes—
208C24×C7C2×D412yes—
209C24×C7C2×D412yes—
210C24×C7C2×D412yes—
211C24×C7C2×Q812yes—
212C24×C7C2×Q812yes—
213C24×C7#4112yes—
214C24×C7#4112yes—
215C24×C7C2411yescharacteristic
216C2×C7×D4—28no—
217C2×C7×D4—28no—
218C2×C7×D4—28no—
219C2×C7×D4—28no—
220C2×C7×D4—28no—
221C2×C7×D4—28no—
222C2×C7×D4C4⋊C4116yescomplemented
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—28no—
236C22×C4×C7—28no—
237C22×C4×C7—28no—
238C22×C4×C7—28no—
239C22×C4×C7—21no—
240C22×C4×C7—21no—
241C22×C4×C7—21no—
242C22×C4×C7—21no—
243C22×C4×C7—21no—
244C22×C4×C7—21no—
245C22×C4×C7—21no—
246C22×C4×C7—21no—
247C22×C4×C7—21no—
248C22×C4×C7—21no—
249C22×C4×C7—21no—
250C22×C4×C7—21no—
251C22×C4×C7—21no—
252C22×C4×C7—21no—
253C22×C4×C7—21no—
254C22×C4×C7—21no—
255C22×C4×C7—21no—
256C22×C4×C7—21no—
257C22×C4×C7—21no—
258C22×C4×C7—21no—
259C22×C4×C7—21no—
260C22×C4×C7—21no—
261C22×C4×C7—21no—
262C22×C4×C7—21no—
263C22×C4×C7—21no—
264C22×C4×C7—21no—
265C22×C4×C7—21no—
266C22×C4×C7—21no—
267C22×C4×C7—21no—
268C22×C4×C7—21no—
269C22×C4×C7—21no—
270C22×C4×C7—21no—
271C22×C4×C7—21no—
272C22×C4×C7—21no—
273C22×C4×C7—21no—
274C22×C4×C7—21no—
275C22×C4×C7—21no—
276C22×C4×C7—21no—
277C22×C4×C7—21no—
278C22×C4×C7—21no—
279C22×C4×C7—21no—
280C22×C4×C7—21no—
281C22×C4×C7—21no—
282C22×C4×C7—21no—
283C22×C4×C7—21no—
284C22×C4×C7—21no—
285C22×C4×C7—21no—
286C22×C4×C7—21no—
287C22×C4×C7—28no—
288C22×C4×C7—28no—
289C22×C4×C7—21no—
290C22×C4×C7—21no—
291C22×C4×C7—21no—
292C22×C4×C7—21no—
293C22×C4×C7—21no—
294C22×C4×C7—21no—
295C22×C4×C7—21no—
296C22×C4×C7—21no—
297C22×C4×C7—21no—
298C22×C4×C7—21no—
299C22×C4×C7—21no—
300C22×C4×C7—21no—
301C22×C4×C7—21no—
302C22×C4×C7—21no—
303C22×C4×C7—44no—
304C22×C4×C7—44no—
305C22×C4×C7—44no—
306C22×C4×C7—44no—
307C22×C4×C7—44no—
308C22×C4×C7—44no—
309C22×C4×C7—44no—
310C22×C4×C7—44no—
311C22×C4×C7—44no—
312C22×C4×C7—44no—
313C22×C4×C7—44no—
314C22×C4×C7—44no—
315C22×C4×C7—44no—
316C22×C4×C7—44no—
317C22×C4×C7—44no—
318C22×C4×C7—44no—
319C22×C4×C7—44no—
320C22×C4×C7—44no—
321C22×C4×C7—44no—
322C22×C4×C7—44no—
323C22×C4×C7—44no—
324C22×C4×C7—44no—
325C22×C4×C7C22×C412yes—
326C22×C4×C7C22×C412yes—
327C22×C4×C7C22×C412yes—
328C22×C4×C7C22×C412yes—
329C22×C4×C7C22×C412yes—
330C22×C4×C7C2×D412yes—
331C22×C4×C7C2×D412yes—
332C22×C4×C7C2×D412yes—
333C22×C4×C7C2×D412yes—
334C22×C4×C7C2×D412yes—
335C22×C4×C7C2×D412yes—
336C22×C4×C7C2×D412yes—
337C22×C4×C7C2×D412yes—
338C22×C4×C7C2×Q812yes—
339C22×C4×C7#4112yes—
340C22×C4×C7#4112yes—
341C22×C4×C7#4112yes—
342C7×C4⋊C4—28no—
343C7×C4⋊C4—44no—
344C7×C4⋊C4—44no—
345C7×C4⋊C4—44no—
346C7×C4⋊C4—44no—
347C7×C22⋊C4—28no—
348C7×C22⋊C4—28no—
349C7×C22⋊C4—28no—
350C7×C22⋊C4—28no—
351C7×C22⋊C4—44no—
352C7×C22⋊C4—44no—
353C7×C22⋊C4—44no—
354C7×C22⋊C4—44no—
355C42×C7—28no—
356C23×D4C22×C711yescharacteristic
357C24×C4C22×C711yescharacteristic
358C24×C4C22×C711yescharacteristic
359C24×C4C22×C711yescharacteristic
360C24×C4C22×C711yescharacteristic
361C2×C4×D4—24no—
362C2×C4×D4—24no—
363C2×C4×D4—24no—
364C22×C4⋊C4C22×C711yescharacteristic
365C22×C4⋊C4C22×C711yescharacteristic
366C22×C4⋊C4C22×C711yescharacteristic
367C22×C4⋊C4C22×C711yescharacteristic
368C22×C4⋊C4C22×C711yescharacteristic
369C22×C22⋊C4C22×C711yescharacteristic
370C22×C22⋊C4C22×C711yescharacteristic
371C22×C22⋊C4C22×C711yescharacteristic
372C22×C22⋊C4C22×C711yescharacteristic
373C22×C22⋊C4C22×C711yescharacteristic
374C22×C22⋊C4C22×C711yescharacteristic
375C22×C22⋊C4C22×C711yescharacteristic
376C22×C22⋊C4C22×C711yescharacteristic
377C22×C42C22×C711yescharacteristic
378#386—24no—
379#386C4×C718yescomplemented
380#385—24no—
381#385—24no—
382#380—24no—
383C2×#95—24no—
384C2×#95C22×C711yescharacteristic
385C2×#95C22×C711yescharacteristic
386C2×#95C22×C711yescharacteristic
387C2×#95C22×C711yescharacteristic
388C2×#95C22×C711yescharacteristic
389C2×#95C22×C711yescharacteristic
390C2×#95C22×C711yescharacteristic
391C2×#95C22×C711yescharacteristic
392C2×#95C22×C711yescharacteristic
393C2×#95C22×C711yescharacteristic
394C2×#95C22×C711yescharacteristic
395C2×#95C22×C711yescharacteristic
396C2×#95C22×C711yescharacteristic
397C2×#95C22×C711yescharacteristic
398C2×#95C22×C711yescharacteristic
399C2×#95C22×C711yescharacteristic
400C23×C7—22no—
401C23×C7—22no—
402C23×C7—22no—
403C23×C7—22no—
404C23×C7—22no—
405C23×C7—22no—
406C23×C7—22no—
407C23×C7—22no—
408C23×C7—22no—
409C23×C7—22no—
410C23×C7—22no—
411C23×C7—22no—
412C23×C7—22no—
413C23×C7—22no—
414C23×C7—22no—
415C23×C7—22no—
416C23×C7—22no—
417C23×C7—22no—
418C23×C7—22no—
419C23×C7—22no—
420C23×C7—22no—
421C23×C7—22no—
422C23×C7—22no—
423C23×C7—22no—
424C23×C7—22no—
425C23×C7—22no—
426C23×C7—22no—
427C23×C7—22no—
428C23×C7—22no—
429C23×C7—22no—
430C23×C7—22no—
431C23×C7—22no—
432C23×C7—22no—
433C23×C7—22no—
434C23×C7—22no—
435C23×C7—22no—
436C23×C7—22no—
437C23×C7—22no—
438C23×C7—22no—
439C23×C7—22no—
440C23×C7—22no—
441C23×C7—22no—
442C23×C7—22no—
443C23×C7—22no—
444C23×C7—22no—
445C23×C7—22no—
446C23×C7—41no—
447C23×C7—41no—
448C23×C7—41no—
449C23×C7—41no—
450C23×C7—41no—
451C23×C7—41no—
452C23×C7—41no—
453C23×C7—41no—
454C23×C7—41no—
455C23×C7—41no—
456C23×C7—41no—
457C23×C7—41no—
458C23×C7—41no—
459C23×C7—41no—
460C23×C7—41no—
461C23×C7—41no—
462C23×C7C2×C4⋊C414yes—
463C23×C7C2×C4⋊C414yes—
464C23×C7C4×D414yes—
465C23×C7C4×D414yes—
466C23×C7#12014yes—
467C23×C7C22⋊Q814yes—
468C23×C7C22⋊Q814yes—
469C23×C7#12314yes—
470C23×C7C23×C411yescharacteristic
471C23×C7C22×D411yescharacteristic
472C23×C7C22×D411yescharacteristic
473C23×C7C22×D411yescharacteristic
474C23×C7C22×D411yescharacteristic
475C23×C7C22×Q811yescharacteristic
476C23×C7C2×#4111yescharacteristic
477C23×C7C2×#4111yescharacteristic
478C23×C7C2×#4111yescharacteristic
479C23×C7C2×#4111yescharacteristic
480C23×C7C2×#4111yescharacteristic
481C23×C7H(5,𝔽2)11yescharacteristic
482C23×C7H(5,𝔽2)11yescharacteristic
483C23×C7H(5,𝔽2)11yescharacteristic
484C23×C72−1+411yescharacteristic
485C7×D4—232no—
486C2×C4×C7—22no—
487C2×C4×C7—22no—
488C2×C4×C7—22no—
489C2×C4×C7—22no—
490C2×C4×C7—22no—
491C2×C4×C7—22no—
492C2×C4×C7—22no—
493C2×C4×C7—22no—
494C2×C4×C7—22no—
495C2×C4×C7—22no—
496C2×C4×C7—22no—
497C2×C4×C7—22no—
498C2×C4×C7—22no—
499C2×C4×C7—22no—
500C2×C4×C7—22no—
501C2×C4×C7—22no—
502C2×C4×C7—22no—
503C2×C4×C7—22no—
504C2×C4×C7—22no—
505C2×C4×C7—22no—
506C2×C4×C7—22no—
507C2×C4×C7—22no—
508C2×C4×C7—22no—
509C2×C4×C7—22no—
510C2×C4×C7—22no—
511C2×C4×C7—22no—
512C2×C4×C7—22no—
513C2×C4×C7—22no—
514C2×C4×C7—22no—
515C2×C4×C7—22no—
516C2×C4×C7—22no—
517C2×C4×C7—22no—
518C2×C4×C7—22no—
519C2×C4×C7—22no—
520C2×C4×C7—22no—
521C2×C4×C7—22no—
522C2×C4×C7—22no—
523C2×C4×C7—22no—
524C2×C4×C7—22no—
525C2×C4×C7—22no—
526C2×C4×C7—22no—
527C2×C4×C7—22no—
528C2×C4×C7—416no—
529C2×C4×C7—416no—
530C2×C4×C7—416no—
531C2×C4×C7—416no—
532C2×C4×C7—41no—
533C2×C4×C7—41no—
534C2×C4×C7—41no—
535C2×C4×C7—41no—
536C2×C4×C7—41no—
537C2×C4×C7—41no—
538C2×C4×C7—41no—
539C2×C4×C7—41no—
540C2×C4×C7—41no—
541C2×C4×C7—41no—
542C2×C4×C7—41no—
543C2×C4×C7—41no—
544C2×C4×C7—41no—
545C2×C4×C7—41no—
546C2×C4×C7—41no—
547C2×C4×C7—41no—
548C2×C4×C7—41no—
549C2×C4×C7—41no—
550C2×C4×C7—41no—
551C2×C4×C7—41no—
552C2×C4×C7—41no—
553C2×C4×C7—41no—
554C2×C4×C7—41no—
555C2×C4×C7—41no—
556C2×C4×C7—41no—
557C2×C4×C7—41no—
558C2×C4×C7—41no—
559C2×C4×C7—41no—
560C2×C4×C7—41no—
561C2×C4×C7—41no—
562C2×C4×C7—41no—
563C2×C4×C7—41no—
564C2×C4×C7—41no—
565C2×C4×C7—41no—
566C2×C4×C7—41no—
567C2×C4×C7—41no—
568C2×C4×C7—41no—
569C2×C4×C7—41no—
570C2×C4×C7—41no—
571C2×C4×C7—41no—
572C2×C4×C7—41no—
573C2×C4×C7—41no—
574C2×C4×C7—41no—
575C2×C4×C7—41no—
576C2×C4×C7—41no—
577C2×C4×C7—41no—
578C2×C4×C7C2×C4⋊C414yes—
579C2×C4×C7C4×D414yescomplemented
580C2×C4×C7#12114yes—
581C25C23×C711yescharacteristic
582C25C23×C711yescharacteristic
583C22×D4—22no—
584C22×D4—22no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4C2×C4×C714yes—
588C22×D4C7×D414yes—
589C22×D4C7×Q814yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—22no—
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—22no—
599C23×C4—22no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—22no—
603C23×C4—22no—
604C23×C4—22no—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—41no—
609C23×C4—41no—
610C23×C4—41no—
611C23×C4—41no—
612C23×C4—41no—
613C23×C4—41no—
614C23×C4—41no—
615C23×C4—41no—
616C23×C4C2×C4×C714yescomplemented
617C23×C4C7×D414yes—
618C23×C4C23×C711yescharacteristic
619C23×C4C23×C711yescharacteristic
620C23×C4C23×C711yescharacteristic
621C23×C4C23×C711yescharacteristic
622C23×C4C23×C711yescharacteristic
623C23×C4C23×C711yescharacteristic
624C23×C4C23×C711yescharacteristic
625C23×C4C23×C711yescharacteristic
626C23×C4C23×C711yescharacteristic
627C23×C4C23×C711yescharacteristic
628C23×C4C23×C711yescharacteristic
629C23×C4C23×C711yescharacteristic
630C23×C4C23×C711yescharacteristic
631C4×D4—232no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4C2×C4×C714yescomplemented
668C2×C22⋊C4C2×C4×C714yescomplemented
669C2×C22⋊C4C2×C4×C714yescomplemented
670C2×C22⋊C4C7×D414yes—
671C2×C42—22no—
672C2×C42—22no—
673C2×C42—22no—
674#95—22no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—22no—
685#95—41no—
686#95—41no—
687#95C2×C4×C714yescomplemented
688#95C2×C4×C714yescomplemented
689#95C7×D414yescomplemented
690C22×C7—24no—
691C22×C7—24no—
692C22×C7—24no—
693C22×C7—24no—
694C22×C7—24no—
695C22×C7—24no—
696C22×C7—24no—
697C22×C7—24no—
698C22×C7—24no—
699C22×C7—24no—
700C22×C7—24no—
701C22×C7—24no—
702C22×C7—24no—
703C22×C7—24no—
704C22×C7—24no—
705C22×C7—24no—
706C22×C7—24no—
707C22×C7—42no—
708C22×C7—42no—
709C22×C7—42no—
710C22×C7—42no—
711C22×C7—42no—
712C22×C7—42no—
713C22×C7—42no—
714C22×C7—42no—
715C22×C7—42no—
716C22×C7—42no—
717C22×C7—42no—
718C22×C7—42no—
719C22×C7#38518yescomplemented
720C22×C7C22×C4⋊C411yescharacteristic
721C22×C7C2×C4×D411yescharacteristic
722C22×C7C2×C4×D411yescharacteristic
723C22×C7C2×C4×D411yescharacteristic
724C22×C7C4×#4111yescharacteristic
725C22×C7#51811yescharacteristic
726C22×C7#52011yescharacteristic
727C22×C7C2×#12011yescharacteristic
728C22×C7C2×#12111yescharacteristic
729C22×C7C2×C22⋊Q811yescharacteristic
730C22×C7C2×C22⋊Q811yescharacteristic
731C22×C7C2×#12311yescharacteristic
732C22×C7#52511yescharacteristic
733C22×C7#52911yescharacteristic
734C22×C7#53211yescharacteristic
735C22×C7#53411yescharacteristic
736C22×C7#53711yescharacteristic
737C22×C7#53811yescharacteristic
738C22×C7#53911yescharacteristic
739C22×C7D4211yescharacteristic
740C22×C7D4211yescharacteristic
741C22×C7#54611yescharacteristic
742C22×C7#54611yescharacteristic
743C22×C7#54611yescharacteristic
744C22×C7#54611yescharacteristic
745C22×C7#54611yescharacteristic
746C22×C7#54711yescharacteristic
747C22×C7#54711yescharacteristic
748C22×C7D4×Q811yescharacteristic
749C22×C7#55111yescharacteristic
750C22×C7#55111yescharacteristic
751C22×C7#55211yescharacteristic
752C22×C7#55411yescharacteristic
753C22×C7#55411yescharacteristic
754C22×C7#55411yescharacteristic
755C4×C7—24no—
756C4×C7—24no—
757C4×C7—24no—
758C4×C7—42no—
759C4×C7—42no—
760C4×C7—42no—
761C4×C7—42no—
762C4×C7—42no—
763C4×C7—42no—
764C4×C7—42no—
765C4×C7—42no—
766C4×C7—81no—
767C4×C7—81no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24C22×C4×C712yes—
789C24C22×C4×C712yes—
790C24C2×C7×D412yes—
791C24C2×C7×D412yes—
792C24C2×C7×D412yes—
793C24C2×C7×D412yes—
794C24C2×C7×Q812yes—
795C24C2×C7×Q812yes—
796C24C7×#4112yes—
797C24C7×#4112yes—
798C24C24×C711yescharacteristic
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4C7×C4⋊C4116yescomplemented
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—28no—
819C22×C4—28no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—28no—
871C22×C4—28no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4C22×C4×C712yes—
909C22×C4C22×C4×C712yes—
910C22×C4C22×C4×C712yes—
911C22×C4C22×C4×C712yes—
912C22×C4C22×C4×C712yes—
913C22×C4C2×C7×D412yes—
914C22×C4C2×C7×D412yes—
915C22×C4C2×C7×D412yes—
916C22×C4C2×C7×D412yes—
917C22×C4C2×C7×D412yes—
918C22×C4C2×C7×D412yes—
919C22×C4C2×C7×D412yes—
920C22×C4C2×C7×D412yes—
921C22×C4C2×C7×Q812yes—
922C22×C4C7×#4112yes—
923C22×C4C7×#4112yes—
924C22×C4C7×#4112yes—
925C4⋊C4—28no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C42—28no—
939C2×C7—28no—
940C2×C7—44no—
941C2×C7C2×#38511yescharacteristic
942C2×C7C4×#12111yescharacteristic
943C2×C7#232511yescharacteristic
944C2×C7D4×C4⋊C411yescharacteristic
945C2×C7#234911yescharacteristic
946C2×C7#235811yescharacteristic
947C2×C7#235911yescharacteristic
948C2×C7#241011yescharacteristic
949C2×C7#241711yescharacteristic
950C2×C7#241811yescharacteristic
951C2×C7#241911yescharacteristic
952C2×C7#243011yescharacteristic
953C2×C7#244911yescharacteristic
954C2×C7#245011yescharacteristic
955C2×C7#256411yescharacteristic
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23C2×C7×C4⋊C414yes—
1019C23C2×C7×C4⋊C414yes—
1020C23C4×C7×D414yes—
1021C23C4×C7×D414yes—
1022C23C7×#12014yes—
1023C23C7×C22⋊Q814yes—
1024C23C7×C22⋊Q814yes—
1025C23C7×#12314yes—
1026C23C23×C4×C711yescharacteristic
1027C23C22×C7×D411yescharacteristic
1028C23C22×C7×D411yescharacteristic
1029C23C22×C7×D411yescharacteristic
1030C23C22×C7×D411yescharacteristic
1031C23C22×C7×Q811yescharacteristic
1032C23C2×C7×#4111yescharacteristic
1033C23C2×C7×#4111yescharacteristic
1034C23C2×C7×#4111yescharacteristic
1035C23C2×C7×#4111yescharacteristic
1036C23C2×C7×#4111yescharacteristic
1037C23C7×H(5,𝔽2)11yescharacteristic
1038C23C7×H(5,𝔽2)11yescharacteristic
1039C23C7×H(5,𝔽2)11yescharacteristic
1040C23C7×2−1+411yescharacteristic
1041D4—232no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—416no—
1085C2×C4—416no—
1086C2×C4—416no—
1087C2×C4—416no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4C2×C7×C4⋊C414yes—
1135C2×C4C4×C7×D414yescomplemented
1136C2×C4C7×#12114yes—
1137C7#1397511yescharacteristic, direct product factor, Sylow
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—24no—
1153C22—24no—
1154C22—24no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22C7×#38518yescomplemented
1168C22C22×C7×C4⋊C411yescharacteristic
1169C22C2×C4×C7×D411yescharacteristic
1170C22C2×C4×C7×D411yescharacteristic
1171C22C2×C4×C7×D411yescharacteristic
1172C22C4×C7×#4111yescharacteristic
1173C22C7×#51811yescharacteristic
1174C22C7×#52011yescharacteristic
1175C22C2×C7×#12011yescharacteristic
1176C22C2×C7×#12111yescharacteristic
1177C22C2×C7×C22⋊Q811yescharacteristic
1178C22C2×C7×C22⋊Q811yescharacteristic
1179C22C2×C7×#12311yescharacteristic
1180C22C7×#52511yescharacteristic
1181C22C7×#52911yescharacteristic
1182C22C7×#53211yescharacteristic
1183C22C7×#53411yescharacteristic
1184C22C7×#53711yescharacteristic
1185C22C7×#53811yescharacteristic
1186C22C7×#53911yescharacteristic
1187C22C7×D4211yescharacteristic
1188C22C7×D4211yescharacteristic
1189C22C7×#54611yescharacteristic
1190C22C7×#54611yescharacteristic
1191C22C7×#54611yescharacteristic
1192C22C7×#54611yescharacteristic
1193C22C7×#54611yescharacteristic
1194C22C7×#54711yescharacteristic
1195C22C7×#54711yescharacteristic
1196C22C7×D4×Q811yescharacteristic
1197C22C7×#55111yescharacteristic
1198C22C7×#55111yescharacteristic
1199C22C7×#55211yescharacteristic
1200C22C7×#55411yescharacteristic
1201C22C7×#55411yescharacteristic
1202C22C7×#55411yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—42no—
1210C4—42no—
1211C4—42no—
1212C4—42no—
1213C4—42no—
1214C4—81no—
1215C4—81no—
1216C2—28no—
1217C2—44no—
1218C2C2×C7×#38511yescharacteristic
1219C2C4×C7×#12111yescharacteristic
1220C2C7×#232511yescharacteristic
1221C2C7×D4×C4⋊C411yescharacteristic
1222C2C7×#234911yescharacteristic
1223C2C7×#235811yescharacteristic
1224C2C7×#235911yescharacteristic
1225C2C7×#241011yescharacteristic
1226C2C7×#241711yescharacteristic
1227C2C7×#241811yescharacteristic
1228C2C7×#241911yescharacteristic
1229C2C7×#243011yescharacteristic
1230C2C7×#244911yescharacteristic
1231C2C7×#245011yescharacteristic
1232C2C7×#256411yescharacteristic
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
4. C2×C7×#385C2semidirect
5. C2×C7×#385C2semidirect
6. C2×C7×#380C2semidirect
7. C22×C7×#95C2semidirect
8. C7×#1444C2semidirect
9. C7×#1442C2semidirect
10. C7×#1439C2semidirect
11. C7×#1439C2semidirect
12. C7×#1436C2semidirect
13. C7×#1436C2semidirect
14. C7×C22⋊#95C2semidirect
15. C7×C22⋊#95C2semidirect
39. C7×#386C4semidirect
60. #13975C7direct (N × H)
96. C23×C4×C7C2×C4semidirect
147. C2×C7×C22⋊C4C2×C4semidirect
148. C2×C7×C22⋊C4C2×C4semidirect
149. C2×C7×C22⋊C4C2×C4semidirect
167. C7×#95C2×C4semidirect
168. C7×#95C2×C4semidirect
169. C7×#95D4semidirect
173. C2×#385C2×C7semidirect
174. C2×#385C2×C7semidirect
175. C2×#380C2×C7semidirect
176. C22×#95C2×C7semidirect
177. #1444C2×C7semidirect
178. #1442C2×C7semidirect
179. #1439C2×C7semidirect
180. #1439C2×C7semidirect
181. #1436C2×C7semidirect
182. #1436C2×C7semidirect
183. C22⋊#95C2×C7semidirect
184. C22⋊#95C2×C7semidirect
222. C2×C7×D4C4⋊C4semidirect
379. #386C4×C7semidirect
579. C2×C4×C7C4×D4semidirect
616. C23×C4C2×C4×C7semidirect
667. C2×C22⋊C4C2×C4×C7semidirect
668. C2×C22⋊C4C2×C4×C7semidirect
669. C2×C22⋊C4C2×C4×C7semidirect
687. #95C2×C4×C7semidirect
688. #95C2×C4×C7semidirect
689. #95C7×D4semidirect
719. C22×C7#385semidirect
805. C2×D4C7×C4⋊C4semidirect
1135. C2×C4C4×C7×D4semidirect
1137. C7#13975direct (N × H)
1167. C22C7×#385semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C2×C7×#3862
C2×C7×#3852
C2×C7×#3802
C22×C7×#952
C7×#14442
C7×#14422
C7×#14392
C7×#14362
C7×C22⋊#952
#139757