Finite Group Databasebeta

← C7×#14733 #13191949

Subgroups — C7×#14733 #13191949

Order 1792.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic
2C2×C7×#398C211yesmaximal, characteristic, complemented
3C2×C7×#396C211yesmaximal, characteristic, complemented
4C2×C7×#385C211yesmaximal, characteristic, complemented
5C2×C7×#385C211yesmaximal, characteristic, complemented
6C2×C7×#380C211yesmaximal, characteristic, complemented
7C7×#1441C211yesmaximal, characteristic, complemented
8C7×#1439C211yesmaximal, characteristic, complemented
9C7×#1439C211yesmaximal, characteristic, complemented
10C7×#1439C211yesmaximal, characteristic, complemented
11C7×#1438C211yesmaximal, characteristic
12C7×#1438C211yesmaximal, characteristic
13C7×#1436C211yesmaximal, characteristic, complemented
14C7×#1436C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C2×C4×C7×D4—24no—
20C2×C4×C7×D4—24no—
21C2×C4×C7×D4—24no—
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
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×C7×C22⋊C4C2211yescharacteristic
38C22×C7×C22⋊C4C2211yescharacteristic
39C22×C42×C7C2211yescharacteristic
40C7×#398—24no—
41C7×#396—24no—
42C7×#385—24no—
43C7×#385—24no—
44C7×#380—24no—
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
59#14733C711yesmaximal, characteristic, direct product factor, Sylow
60C25×C7C2311yescharacteristic
61C25×C7C2311yescharacteristic
62C22×C7×D4—22no—
63C22×C7×D4—22no—
64C22×C7×D4—22no—
65C22×C7×D4—22no—
66C22×C7×D4—22no—
67C22×C7×D4—22no—
68C22×C7×D4Q814yes—
69C23×C4×C7—22no—
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—41no—
79C23×C4×C7—41no—
80C23×C4×C7—41no—
81C23×C4×C7—41no—
82C23×C4×C7D414yes—
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2311yescharacteristic
92C23×C4×C7C2311yescharacteristic
93C23×C4×C7C2311yescharacteristic
94C23×C4×C7C2311yescharacteristic
95C23×C4×C7C2311yescharacteristic
96C4×C7×D4—232no—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4—22no—
99C2×C7×C4⋊C4—22no—
100C2×C7×C4⋊C4—22no—
101C2×C7×C4⋊C4—22no—
102C2×C7×C4⋊C4—22no—
103C2×C7×C4⋊C4—22no—
104C2×C7×C4⋊C4—22no—
105C2×C7×C4⋊C4—22no—
106C2×C7×C4⋊C4—22no—
107C2×C7×C4⋊C4—22no—
108C2×C7×C4⋊C4—22no—
109C2×C7×C4⋊C4—22no—
110C2×C7×C4⋊C4—22no—
111C2×C7×C4⋊C4—22no—
112C2×C7×C4⋊C4—22no—
113C2×C7×C4⋊C4—41no—
114C2×C7×C4⋊C4—41no—
115C2×C7×C4⋊C4—41no—
116C2×C7×C4⋊C4—41no—
117C2×C7×C4⋊C4D414yes—
118C2×C7×C22⋊C4—22no—
119C2×C7×C22⋊C4—22no—
120C2×C7×C22⋊C4—22no—
121C2×C7×C22⋊C4—22no—
122C2×C7×C22⋊C4—22no—
123C2×C7×C22⋊C4—22no—
124C2×C7×C22⋊C4—22no—
125C2×C7×C22⋊C4—22no—
126C2×C7×C22⋊C4—22no—
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—41no—
140C2×C7×C22⋊C4—41no—
141C2×C7×C22⋊C4—41no—
142C2×C7×C22⋊C4—41no—
143C2×C7×C22⋊C4—41no—
144C2×C7×C22⋊C4—41no—
145C2×C7×C22⋊C4—41no—
146C2×C7×C22⋊C4—41no—
147C2×C7×C22⋊C4D414yes—
148C2×C42×C7—22no—
149C2×C42×C7—22no—
150C2×C42×C7—22no—
151C7×#95—22no—
152C7×#95—22no—
153C7×#95—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—41no—
163C7×#95—41no—
164C7×#95D414yescomplemented
165C22×C4×D4C2×C711yescharacteristic
166C2×#398C2×C711yescharacteristic, complemented
167C2×#396C2×C711yescharacteristic, complemented
168C2×#385C2×C711yescharacteristic, complemented
169C2×#385C2×C711yescharacteristic, complemented
170C2×#380C2×C711yescharacteristic, complemented
171#1441C2×C711yescharacteristic, complemented
172#1439C2×C711yescharacteristic, complemented
173#1439C2×C711yescharacteristic, complemented
174#1439C2×C711yescharacteristic, complemented
175#1438C2×C711yescharacteristic
176#1438C2×C711yescharacteristic
177#1436C2×C711yescharacteristic, complemented
178#1436C2×C711yescharacteristic, complemented
179C22⋊#95C2×C711yescharacteristic, complemented
180C24×C7—21no—
181C24×C7—21no—
182C24×C7—21no—
183C24×C7—21no—
184C24×C7—21no—
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×C7C2×D412yes—
205C24×C7C2×D412yes—
206C24×C7C2×Q812yes—
207C24×C7C2×Q812yes—
208C24×C7#4112yes—
209C24×C7#4112yes—
210C24×C7C2411yescharacteristic
211C2×C7×D4—28no—
212C2×C7×D4—28no—
213C2×C7×D4—28no—
214C2×C7×D4—28no—
215C2×C7×D4—28no—
216C2×C7×D4—28no—
217C2×C7×D4—28no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
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—28no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—21no—
236C22×C4×C7—21no—
237C22×C4×C7—21no—
238C22×C4×C7—21no—
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—28no—
268C22×C4×C7—28no—
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—21no—
288C22×C4×C7—21no—
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—44no—
298C22×C4×C7—44no—
299C22×C4×C7—44no—
300C22×C4×C7—44no—
301C22×C4×C7—44no—
302C22×C4×C7—44no—
303C22×C4×C7—44no—
304C22×C4×C7—44no—
305C22×C4×C7—44no—
306C22×C4×C7—44no—
307C22×C4×C7—44no—
308C22×C4×C7C2×D412yes—
309C22×C4×C7C2×D412yes—
310C22×C4×C7C2×D412yes—
311C22×C4×C7C2×D412yes—
312C22×C4×C7C2×D412yes—
313C22×C4×C7C2×D412yes—
314C22×C4×C7C2×D412yes—
315C22×C4×C7C2×D412yes—
316C22×C4×C7C2×D412yes—
317C22×C4×C7C2×D412yes—
318C22×C4×C7C2×Q812yes—
319C22×C4×C7#4112yes—
320C22×C4×C7#4112yes—
321C22×C4×C7#4112yes—
322C22×C4×C7#4112yes—
323C7×C4⋊C4—28no—
324C7×C4⋊C4—44no—
325C7×C4⋊C4—44no—
326C7×C4⋊C4—44no—
327C7×C4⋊C4—44no—
328C7×C4⋊C4—44no—
329C7×C4⋊C4—44no—
330C7×C22⋊C4—28no—
331C7×C22⋊C4—28no—
332C7×C22⋊C4—28no—
333C7×C22⋊C4—28no—
334C7×C22⋊C4—44no—
335C7×C22⋊C4—44no—
336C7×C22⋊C4—44no—
337C7×C22⋊C4—44no—
338C7×C22⋊C4—44no—
339C7×C22⋊C4—44no—
340C42×C7—28no—
341C23×D4C22×C711yescharacteristic
342C24×C4C22×C711yescharacteristic
343C24×C4C22×C711yescharacteristic
344C2×C4×D4—24no—
345C2×C4×D4—24no—
346C2×C4×D4—24no—
347C22×C4⋊C4C22×C711yescharacteristic
348C22×C4⋊C4C22×C711yescharacteristic
349C22×C4⋊C4C22×C711yescharacteristic
350C22×C4⋊C4C22×C711yescharacteristic
351C22×C4⋊C4C22×C711yescharacteristic
352C22×C4⋊C4C22×C711yescharacteristic
353C22×C4⋊C4C22×C711yescharacteristic
354C22×C22⋊C4C22×C711yescharacteristic
355C22×C22⋊C4C22×C711yescharacteristic
356C22×C22⋊C4C22×C711yescharacteristic
357C22×C22⋊C4C22×C711yescharacteristic
358C22×C22⋊C4C22×C711yescharacteristic
359C22×C22⋊C4C22×C711yescharacteristic
360C22×C22⋊C4C22×C711yescharacteristic
361C22×C22⋊C4C22×C711yescharacteristic
362C22×C22⋊C4C22×C711yescharacteristic
363C22×C22⋊C4C22×C711yescharacteristic
364C22×C42C22×C711yescharacteristic
365#398—24no—
366#396—24no—
367#385—24no—
368#385—24no—
369#380—24no—
370C2×#95C22×C711yescharacteristic
371C2×#95C22×C711yescharacteristic
372C2×#95C22×C711yescharacteristic
373C2×#95C22×C711yescharacteristic
374C2×#95C22×C711yescharacteristic
375C2×#95C22×C711yescharacteristic
376C2×#95C22×C711yescharacteristic
377C2×#95C22×C711yescharacteristic
378C2×#95C22×C711yescharacteristic
379C2×#95C22×C711yescharacteristic
380C2×#95C22×C711yescharacteristic
381C2×#95C22×C711yescharacteristic
382C2×#95C22×C711yescharacteristic
383C2×#95C22×C711yescharacteristic
384C23×C7—22no—
385C23×C7—22no—
386C23×C7—22no—
387C23×C7—22no—
388C23×C7—22no—
389C23×C7—22no—
390C23×C7—22no—
391C23×C7—22no—
392C23×C7—22no—
393C23×C7—22no—
394C23×C7—22no—
395C23×C7—22no—
396C23×C7—22no—
397C23×C7—22no—
398C23×C7—22no—
399C23×C7—22no—
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—41no—
421C23×C7—41no—
422C23×C7—41no—
423C23×C7—41no—
424C23×C7—41no—
425C23×C7—41no—
426C23×C7—41no—
427C23×C7—41no—
428C23×C7—41no—
429C23×C7—41no—
430C23×C7—41no—
431C23×C7—41no—
432C23×C7—41no—
433C23×C7—41no—
434C23×C7—41no—
435C23×C7—41no—
436C23×C7—41no—
437C23×C7—41no—
438C23×C7—41no—
439C23×C7—41no—
440C23×C7—41no—
441C23×C7—41no—
442C23×C7—41no—
443C23×C7—41no—
444C23×C7—41no—
445C23×C7—41no—
446C23×C7—41no—
447C23×C7—41no—
448C23×C7—41no—
449C23×C7—41no—
450C23×C7—41no—
451C23×C7—41no—
452C23×C7C22⋊Q814yes—
453C23×C7C22⋊Q814yes—
454C23×C7C22×D411yescharacteristic
455C23×C7C22×D411yescharacteristic
456C23×C7C22×D411yescharacteristic
457C23×C7C22×D411yescharacteristic
458C23×C7C22×Q811yescharacteristic
459C23×C7C2×#4111yescharacteristic
460C23×C7C2×#4111yescharacteristic
461C23×C7C2×#4111yescharacteristic
462C23×C7C2×#4111yescharacteristic
463C23×C7C2×#4111yescharacteristic
464C23×C7C2×#4111yescharacteristic
465C23×C7H(5,𝔽2)11yescharacteristic
466C23×C7H(5,𝔽2)11yescharacteristic
467C23×C7H(5,𝔽2)11yescharacteristic
468C23×C72−1+411yescharacteristic
469C7×D4—232no—
470C2×C4×C7—22no—
471C2×C4×C7—22no—
472C2×C4×C7—22no—
473C2×C4×C7—22no—
474C2×C4×C7—22no—
475C2×C4×C7—22no—
476C2×C4×C7—22no—
477C2×C4×C7—22no—
478C2×C4×C7—22no—
479C2×C4×C7—22no—
480C2×C4×C7—22no—
481C2×C4×C7—22no—
482C2×C4×C7—22no—
483C2×C4×C7—22no—
484C2×C4×C7—22no—
485C2×C4×C7—22no—
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—416no—
507C2×C4×C7—416no—
508C2×C4×C7—41no—
509C2×C4×C7—41no—
510C2×C4×C7—41no—
511C2×C4×C7—41no—
512C2×C4×C7—41no—
513C2×C4×C7—41no—
514C2×C4×C7—41no—
515C2×C4×C7—41no—
516C2×C4×C7—41no—
517C2×C4×C7—41no—
518C2×C4×C7—41no—
519C2×C4×C7—41no—
520C2×C4×C7—41no—
521C2×C4×C7—41no—
522C2×C4×C7—41no—
523C2×C4×C7—41no—
524C2×C4×C7—41no—
525C2×C4×C7—41no—
526C2×C4×C7—41no—
527C2×C4×C7—41no—
528C2×C4×C7—41no—
529C2×C4×C7—41no—
530C2×C4×C7—41no—
531C2×C4×C7—41no—
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#12014yes—
561C2×C4×C7#12114yes—
562C2×C4×C7C22⋊Q814yes—
563C25C23×C711yescharacteristic
564C25C23×C711yescharacteristic
565C22×D4—22no—
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—22no—
569C22×D4—22no—
570C22×D4—22no—
571C22×D4C7×Q814yes—
572C23×C4—22no—
573C23×C4—22no—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—41no—
582C23×C4—41no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4C7×D414yes—
586C23×C4C23×C711yescharacteristic
587C23×C4C23×C711yescharacteristic
588C23×C4C23×C711yescharacteristic
589C23×C4C23×C711yescharacteristic
590C23×C4C23×C711yescharacteristic
591C23×C4C23×C711yescharacteristic
592C23×C4C23×C711yescharacteristic
593C23×C4C23×C711yescharacteristic
594C23×C4C23×C711yescharacteristic
595C23×C4C23×C711yescharacteristic
596C23×C4C23×C711yescharacteristic
597C23×C4C23×C711yescharacteristic
598C23×C4C23×C711yescharacteristic
599C4×D4—232no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4C7×D414yes—
621C2×C22⋊C4—22no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—22no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—41no—
643C2×C22⋊C4—41no—
644C2×C22⋊C4—41no—
645C2×C22⋊C4—41no—
646C2×C22⋊C4—41no—
647C2×C22⋊C4—41no—
648C2×C22⋊C4—41no—
649C2×C22⋊C4—41no—
650C2×C22⋊C4C7×D414yes—
651C2×C42—22no—
652C2×C42—22no—
653C2×C42—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—41no—
666#95—41no—
667#95C7×D414yescomplemented
668C22×C7—24no—
669C22×C7—24no—
670C22×C7—24no—
671C22×C7—24no—
672C22×C7—24no—
673C22×C7—24no—
674C22×C7—42no—
675C22×C7—42no—
676C22×C7—42no—
677C22×C7—42no—
678C22×C7—42no—
679C22×C7—42no—
680C22×C7—42no—
681C22×C7—42no—
682C22×C7—42no—
683C22×C7—42no—
684C22×C7—42no—
685C22×C7—42no—
686C22×C7—42no—
687C22×C7—42no—
688C22×C7—42no—
689C22×C7—42no—
690C22×C7—42no—
691C22×C7—42no—
692C22×C7—42no—
693C22×C7—42no—
694C22×C7—42no—
695C22×C7—42no—
696C22×C7—42no—
697C22×C7—42no—
698C22×C7C2×#12011yescharacteristic
699C22×C7C2×#12111yescharacteristic
700C22×C7C2×C22⋊Q811yescharacteristic
701C22×C7C2×C22⋊Q811yescharacteristic
702C22×C7C2×C22⋊Q811yescharacteristic
703C22×C7#52511yescharacteristic
704C22×C7#52511yescharacteristic
705C22×C7#52511yescharacteristic
706C22×C7#52511yescharacteristic
707C22×C7#52511yescharacteristic
708C22×C7#52911yescharacteristic
709C22×C7#52911yescharacteristic
710C22×C7#53211yescharacteristic
711C22×C7#53411yescharacteristic
712C22×C7#53711yescharacteristic
713C22×C7#53811yescharacteristic
714C22×C7#53911yescharacteristic
715C22×C7#54011yescharacteristic
716C22×C7#54211yescharacteristic
717C22×C7D4211yescharacteristic
718C22×C7D4211yescharacteristic
719C22×C7#54611yescharacteristic
720C22×C7#54611yescharacteristic
721C22×C7#54611yescharacteristic
722C22×C7#54611yescharacteristic
723C22×C7#54711yescharacteristic
724C22×C7#54811yescharacteristic
725C22×C7D4×Q811yescharacteristic
726C22×C7#55011yescharacteristic
727C22×C7#55211yescharacteristic
728C22×C7#55311yescharacteristic
729C22×C7#55311yescharacteristic
730C22×C7#55411yescharacteristic
731C22×C7#55411yescharacteristic
732C22×C7#55411yescharacteristic
733C4×C7—24no—
734C4×C7—24no—
735C4×C7—24no—
736C4×C7—42no—
737C4×C7—42no—
738C4×C7—42no—
739C4×C7—42no—
740C4×C7—42no—
741C4×C7—42no—
742C4×C7—81no—
743C4×C7—81no—
744C4×C7—81no—
745C4×C7—81no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24C2×C7×D412yes—
771C24C2×C7×D412yes—
772C24C2×C7×Q812yes—
773C24C2×C7×Q812yes—
774C24C7×#4112yes—
775C24C7×#4112yes—
776C24C24×C711yescharacteristic
777C2×D4—28no—
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—28no—
781C2×D4—28no—
782C2×D4—28no—
783C2×D4—28no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—28no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
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—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
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—28no—
834C22×C4—28no—
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—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4C2×C7×D412yes—
875C22×C4C2×C7×D412yes—
876C22×C4C2×C7×D412yes—
877C22×C4C2×C7×D412yes—
878C22×C4C2×C7×D412yes—
879C22×C4C2×C7×D412yes—
880C22×C4C2×C7×D412yes—
881C22×C4C2×C7×D412yes—
882C22×C4C2×C7×D412yes—
883C22×C4C2×C7×D412yes—
884C22×C4C2×C7×Q812yes—
885C22×C4C7×#4112yes—
886C22×C4C7×#4112yes—
887C22×C4C7×#4112yes—
888C22×C4C7×#4112yes—
889C4⋊C4—28no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C42—28no—
907C2×C7—44no—
908C2×C7—44no—
909C2×C7#239211yescharacteristic
910C2×C7#240711yescharacteristic
911C2×C7#241011yescharacteristic
912C2×C7#241711yescharacteristic
913C2×C7#244911yescharacteristic
914C2×C7#245011yescharacteristic
915C2×C7#245211yescharacteristic
916C2×C7#245411yescharacteristic
917C2×C7#245611yescharacteristic
918C2×C7#246011yescharacteristic
919C2×C7#246411yescharacteristic
920C2×C7#246811yescharacteristic
921C2×C7#257911yescharacteristic
922C2×C7#263011yescharacteristic
923C2×C7#284811yescharacteristic
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23C7×C22⋊Q814yes—
993C23C7×C22⋊Q814yes—
994C23C22×C7×D411yescharacteristic
995C23C22×C7×D411yescharacteristic
996C23C22×C7×D411yescharacteristic
997C23C22×C7×D411yescharacteristic
998C23C22×C7×Q811yescharacteristic
999C23C2×C7×#4111yescharacteristic
1000C23C2×C7×#4111yescharacteristic
1001C23C2×C7×#4111yescharacteristic
1002C23C2×C7×#4111yescharacteristic
1003C23C2×C7×#4111yescharacteristic
1004C23C2×C7×#4111yescharacteristic
1005C23C7×H(5,𝔽2)11yescharacteristic
1006C23C7×H(5,𝔽2)11yescharacteristic
1007C23C7×H(5,𝔽2)11yescharacteristic
1008C23C7×2−1+411yescharacteristic
1009D4—232no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—416no—
1047C2×C4—416no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
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×C4C7×#12014yes—
1101C2×C4C7×#12114yes—
1102C2×C4C7×C22⋊Q814yes—
1103C7#1473311yescharacteristic, direct product factor, Sylow
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22C2×C7×#12011yescharacteristic
1135C22C2×C7×#12111yescharacteristic
1136C22C2×C7×C22⋊Q811yescharacteristic
1137C22C2×C7×C22⋊Q811yescharacteristic
1138C22C2×C7×C22⋊Q811yescharacteristic
1139C22C7×#52511yescharacteristic
1140C22C7×#52511yescharacteristic
1141C22C7×#52511yescharacteristic
1142C22C7×#52511yescharacteristic
1143C22C7×#52511yescharacteristic
1144C22C7×#52911yescharacteristic
1145C22C7×#52911yescharacteristic
1146C22C7×#53211yescharacteristic
1147C22C7×#53411yescharacteristic
1148C22C7×#53711yescharacteristic
1149C22C7×#53811yescharacteristic
1150C22C7×#53911yescharacteristic
1151C22C7×#54011yescharacteristic
1152C22C7×#54211yescharacteristic
1153C22C7×D4211yescharacteristic
1154C22C7×D4211yescharacteristic
1155C22C7×#54611yescharacteristic
1156C22C7×#54611yescharacteristic
1157C22C7×#54611yescharacteristic
1158C22C7×#54611yescharacteristic
1159C22C7×#54711yescharacteristic
1160C22C7×#54811yescharacteristic
1161C22C7×D4×Q811yescharacteristic
1162C22C7×#55011yescharacteristic
1163C22C7×#55211yescharacteristic
1164C22C7×#55311yescharacteristic
1165C22C7×#55311yescharacteristic
1166C22C7×#55411yescharacteristic
1167C22C7×#55411yescharacteristic
1168C22C7×#55411yescharacteristic
1169C4—24no—
1170C4—24no—
1171C4—24no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C2—44no—
1183C2—44no—
1184C2C7×#239211yescharacteristic
1185C2C7×#240711yescharacteristic
1186C2C7×#241011yescharacteristic
1187C2C7×#241711yescharacteristic
1188C2C7×#244911yescharacteristic
1189C2C7×#245011yescharacteristic
1190C2C7×#245211yescharacteristic
1191C2C7×#245411yescharacteristic
1192C2C7×#245611yescharacteristic
1193C2C7×#246011yescharacteristic
1194C2C7×#246411yescharacteristic
1195C2C7×#246811yescharacteristic
1196C2C7×#257911yescharacteristic
1197C2C7×#263011yescharacteristic
1198C2C7×#284811yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#398C2semidirect
3. C2×C7×#396C2semidirect
4. C2×C7×#385C2semidirect
5. C2×C7×#385C2semidirect
6. C2×C7×#380C2semidirect
7. C7×#1441C2semidirect
8. C7×#1439C2semidirect
9. C7×#1439C2semidirect
10. C7×#1439C2semidirect
13. C7×#1436C2semidirect
14. C7×#1436C2semidirect
15. C7×C22⋊#95C2semidirect
59. #14733C7direct (N × H)
164. C7×#95D4semidirect
166. C2×#398C2×C7semidirect
167. C2×#396C2×C7semidirect
168. C2×#385C2×C7semidirect
169. C2×#385C2×C7semidirect
170. C2×#380C2×C7semidirect
171. #1441C2×C7semidirect
172. #1439C2×C7semidirect
173. #1439C2×C7semidirect
174. #1439C2×C7semidirect
177. #1436C2×C7semidirect
178. #1436C2×C7semidirect
179. C22⋊#95C2×C7semidirect
667. #95C7×D4semidirect
1103. C7#14733direct (N × H)

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×#3982
C2×C7×#3962
C2×C7×#3852
C2×C7×#3802
C7×#14412
C7×#14392
C7×#14382
C7×#14362
C7×C22⋊#952
#147337