Finite Group Databasebeta

← C7×#14737 #13191953

Subgroups — C7×#14737 #13191953

Order 1792.

2110 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#397C211yesmaximal, characteristic, complemented
2C2×C7×#386C211yesmaximal, characteristic
3C2×C7×#386C211yesmaximal, characteristic
4C2×C7×#386C211yesmaximal, characteristic
5C2×C7×#385C211yesmaximal, characteristic, complemented
6C22×C7×#95C211yesmaximal, characteristic, complemented
7C7×#1445C211yesmaximal, characteristic, complemented
8C7×#1443C211yesmaximal, characteristic, complemented
9C7×#1443C211yesmaximal, characteristic, complemented
10C7×#1442C211yesmaximal, characteristic, complemented
11C7×#1440C211yesmaximal, characteristic, complemented
12C7×#1440C211yesmaximal, characteristic, complemented
13C7×#1439C211yesmaximal, characteristic, complemented
14C7×C22⋊#95C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C24×C4×C7C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31C7×#397—24no—
32C7×#386—24no—
33C7×#386—24no—
34C7×#386—24no—
35C7×#385—24no—
36C2×C7×#95—24no—
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2211yescharacteristic
41C2×C7×#95C2211yescharacteristic
42C2×C7×#95C2211yescharacteristic
43C2×C7×#95C2211yescharacteristic
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
57#14737C711yesmaximal, characteristic, direct product factor, Sylow
58C25×C7C2311yescharacteristic
59C25×C7C2311yescharacteristic
60C22×C7×D4—22no—
61C22×C7×D4—22no—
62C22×C7×D4—22no—
63C22×C7×D4—22no—
64C22×C7×D4—22no—
65C22×C7×D4—22no—
66C22×C7×D4D414yes—
67C23×C4×C7—22no—
68C23×C4×C7—22no—
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—22no—
79C23×C4×C7—22no—
80C23×C4×C7—22no—
81C23×C4×C7—22no—
82C23×C4×C7—41no—
83C23×C4×C7—41no—
84C23×C4×C7—41no—
85C23×C4×C7—41no—
86C23×C4×C7—41no—
87C23×C4×C7—41no—
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2311yescharacteristic
92C23×C4×C7C2311yescharacteristic
93C23×C4×C7C2311yescharacteristic
94C23×C4×C7C2311yescharacteristic
95C23×C4×C7C2311yescharacteristic
96C23×C4×C7C2311yescharacteristic
97C23×C4×C7C2311yescharacteristic
98C23×C4×C7C2311yescharacteristic
99C23×C4×C7C2311yescharacteristic
100C23×C4×C7C2311yescharacteristic
101C2×C7×C4⋊C4—22no—
102C2×C7×C4⋊C4—22no—
103C2×C7×C4⋊C4—22no—
104C2×C7×C4⋊C4—22no—
105C2×C7×C4⋊C4—41no—
106C2×C7×C4⋊C4—41no—
107C2×C7×C22⋊C4—22no—
108C2×C7×C22⋊C4—22no—
109C2×C7×C22⋊C4—22no—
110C2×C7×C22⋊C4—22no—
111C2×C7×C22⋊C4—22no—
112C2×C7×C22⋊C4—22no—
113C2×C7×C22⋊C4—22no—
114C2×C7×C22⋊C4—22no—
115C2×C7×C22⋊C4—22no—
116C2×C7×C22⋊C4—22no—
117C2×C7×C22⋊C4—22no—
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—41no—
128C2×C7×C22⋊C4—41no—
129C2×C7×C22⋊C4—41no—
130C2×C7×C22⋊C4—41no—
131C2×C7×C22⋊C4—41no—
132C2×C7×C22⋊C4—41no—
133C2×C7×C22⋊C4D414yes—
134C7×#95—22no—
135C7×#95—22no—
136C7×#95—22no—
137C7×#95—22no—
138C7×#95—22no—
139C7×#95—22no—
140C7×#95—22no—
141C7×#95—22no—
142C7×#95—22no—
143C7×#95—22no—
144C7×#95—22no—
145C7×#95—22no—
146C7×#95—22no—
147C7×#95—22no—
148C7×#95—22no—
149C7×#95—41no—
150C7×#95—41no—
151C7×#95—41no—
152C7×#95—41no—
153C7×#95D414yescomplemented
154C2×#397C2×C711yescharacteristic, complemented
155C2×#386C2×C711yescharacteristic
156C2×#386C2×C711yescharacteristic
157C2×#386C2×C711yescharacteristic
158C2×#385C2×C711yescharacteristic, complemented
159C22×#95C2×C711yescharacteristic, complemented
160#1445C2×C711yescharacteristic, complemented
161#1443C2×C711yescharacteristic, complemented
162#1443C2×C711yescharacteristic, complemented
163#1442C2×C711yescharacteristic, complemented
164#1440C2×C711yescharacteristic, complemented
165#1440C2×C711yescharacteristic, complemented
166#1439C2×C711yescharacteristic, complemented
167C22⋊#95C2×C711yescharacteristic, complemented
168C22⋊#95C2×C711yescharacteristic, complemented
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—21no—
173C24×C7—21no—
174C24×C7—21no—
175C24×C7—21no—
176C24×C7—21no—
177C24×C7—21no—
178C24×C7—21no—
179C24×C7—21no—
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×C7C2×D412yes—
192C24×C7C2×D412yes—
193C24×C7C2×D412yes—
194C24×C7#4112yes—
195C24×C7#4112yes—
196C24×C7#4112yes—
197C24×C7#4112yes—
198C24×C7#4112yes—
199C24×C7C2411yescharacteristic
200C2×C7×D4—28no—
201C2×C7×D4—28no—
202C2×C7×D4—28no—
203C2×C7×D4—44no—
204C2×C7×D4—44no—
205C2×C7×D4—44no—
206C2×C7×D4—44no—
207C22×C4×C7—28no—
208C22×C4×C7—28no—
209C22×C4×C7—28no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
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—21no—
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—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—21no—
288C22×C4×C7—21no—
289C22×C4×C7—21no—
290C22×C4×C7—21no—
291C22×C4×C7—21no—
292C22×C4×C7—44no—
293C22×C4×C7—44no—
294C22×C4×C7—44no—
295C22×C4×C7—44no—
296C22×C4×C7—44no—
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×C7—44no—
309C22×C4×C7—44no—
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×C7#4112yes—
317C22×C4×C7#4112yes—
318C22×C4×C7#4112yes—
319C7×C4⋊C4—44no—
320C7×C4⋊C4—44no—
321C7×C22⋊C4—28no—
322C7×C22⋊C4—44no—
323C7×C22⋊C4—44no—
324C7×C22⋊C4—44no—
325C7×C22⋊C4—44no—
326C7×C22⋊C4—44no—
327C7×C22⋊C4—44no—
328C7×C22⋊C4—44no—
329C7×C22⋊C4—44no—
330C23×D4C22×C711yescharacteristic
331C24×C4C22×C711yescharacteristic
332C24×C4C22×C711yescharacteristic
333C24×C4C22×C711yescharacteristic
334C22×C4⋊C4C22×C711yescharacteristic
335C22×C4⋊C4C22×C711yescharacteristic
336C22×C22⋊C4C22×C711yescharacteristic
337C22×C22⋊C4C22×C711yescharacteristic
338C22×C22⋊C4C22×C711yescharacteristic
339C22×C22⋊C4C22×C711yescharacteristic
340C22×C22⋊C4C22×C711yescharacteristic
341C22×C22⋊C4C22×C711yescharacteristic
342C22×C22⋊C4C22×C711yescharacteristic
343C22×C22⋊C4C22×C711yescharacteristic
344C22×C22⋊C4C22×C711yescharacteristic
345#397—24no—
346#386—24no—
347#386—24no—
348#386—24no—
349#385—24no—
350C2×#95—24no—
351C2×#95C22×C711yescharacteristic
352C2×#95C22×C711yescharacteristic
353C2×#95C22×C711yescharacteristic
354C2×#95C22×C711yescharacteristic
355C2×#95C22×C711yescharacteristic
356C2×#95C22×C711yescharacteristic
357C2×#95C22×C711yescharacteristic
358C2×#95C22×C711yescharacteristic
359C2×#95C22×C711yescharacteristic
360C2×#95C22×C711yescharacteristic
361C2×#95C22×C711yescharacteristic
362C2×#95C22×C711yescharacteristic
363C2×#95C22×C711yescharacteristic
364C2×#95C22×C711yescharacteristic
365C2×#95C22×C711yescharacteristic
366C2×#95C22×C711yescharacteristic
367C2×#95C22×C711yescharacteristic
368C2×#95C22×C711yescharacteristic
369C2×#95C22×C711yescharacteristic
370C2×#95C22×C711yescharacteristic
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—22no—
378C23×C7—22no—
379C23×C7—22no—
380C23×C7—22no—
381C23×C7—22no—
382C23×C7—22no—
383C23×C7—22no—
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—41no—
407C23×C7—41no—
408C23×C7—41no—
409C23×C7—41no—
410C23×C7—41no—
411C23×C7—41no—
412C23×C7—41no—
413C23×C7—41no—
414C23×C7—41no—
415C23×C7—41no—
416C23×C7—41no—
417C23×C7—41no—
418C23×C7—41no—
419C23×C7—41no—
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#12114yes—
435C23×C7#12314yes—
436C23×C7#12314yes—
437C23×C7#12314yes—
438C23×C7#12414yes—
439C23×C7#12614yes—
440C23×C7#12614yes—
441C23×C7C22×D411yescharacteristic
442C23×C7C22×D411yescharacteristic
443C23×C7C22×D411yescharacteristic
444C23×C7C2×#4111yescharacteristic
445C23×C7C2×#4111yescharacteristic
446C23×C7C2×#4111yescharacteristic
447C23×C7C2×#4111yescharacteristic
448C23×C7C2×#4111yescharacteristic
449C23×C7C2×#4111yescharacteristic
450C23×C7C2×#4111yescharacteristic
451C23×C7C2×#4111yescharacteristic
452C23×C7H(5,𝔽2)11yescharacteristic
453C23×C7H(5,𝔽2)11yescharacteristic
454C23×C7H(5,𝔽2)11yescharacteristic
455C23×C72−1+411yescharacteristic
456C7×D4—416no—
457C2×C4×C7—22no—
458C2×C4×C7—22no—
459C2×C4×C7—22no—
460C2×C4×C7—22no—
461C2×C4×C7—22no—
462C2×C4×C7—22no—
463C2×C4×C7—22no—
464C2×C4×C7—22no—
465C2×C4×C7—22no—
466C2×C4×C7—22no—
467C2×C4×C7—22no—
468C2×C4×C7—22no—
469C2×C4×C7—22no—
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—416no—
485C2×C4×C7—416no—
486C2×C4×C7—416no—
487C2×C4×C7—41no—
488C2×C4×C7—41no—
489C2×C4×C7—41no—
490C2×C4×C7—41no—
491C2×C4×C7—41no—
492C2×C4×C7—41no—
493C2×C4×C7—41no—
494C2×C4×C7—41no—
495C2×C4×C7—41no—
496C2×C4×C7—41no—
497C2×C4×C7—41no—
498C2×C4×C7—41no—
499C2×C4×C7—41no—
500C2×C4×C7—41no—
501C2×C4×C7—41no—
502C2×C4×C7—41no—
503C2×C4×C7—41no—
504C2×C4×C7—41no—
505C2×C4×C7—41no—
506C2×C4×C7—41no—
507C2×C4×C7—41no—
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—
551C25C23×C711yescharacteristic
552C25C23×C711yescharacteristic
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4C7×D414yes—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—22no—
574C23×C4—22no—
575C23×C4—41no—
576C23×C4—41no—
577C23×C4—41no—
578C23×C4—41no—
579C23×C4—41no—
580C23×C4—41no—
581C23×C4C23×C711yescharacteristic
582C23×C4C23×C711yescharacteristic
583C23×C4C23×C711yescharacteristic
584C23×C4C23×C711yescharacteristic
585C23×C4C23×C711yescharacteristic
586C23×C4C23×C711yescharacteristic
587C23×C4C23×C711yescharacteristic
588C23×C4C23×C711yescharacteristic
589C23×C4C23×C711yescharacteristic
590C23×C4C23×C711yescharacteristic
591C23×C4C23×C711yescharacteristic
592C23×C4C23×C711yescharacteristic
593C23×C4C23×C711yescharacteristic
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4C7×D414yes—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—22no—
634#95—22no—
635#95—22no—
636#95—22no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—41no—
643#95—41no—
644#95—41no—
645#95—41no—
646#95C7×D414yescomplemented
647C22×C7—24no—
648C22×C7—24no—
649C22×C7—24no—
650C22×C7—24no—
651C22×C7—24no—
652C22×C7—24no—
653C22×C7—24no—
654C22×C7—24no—
655C22×C7—24no—
656C22×C7—24no—
657C22×C7—24no—
658C22×C7—24no—
659C22×C7—24no—
660C22×C7—24no—
661C22×C7—42no—
662C22×C7—42no—
663C22×C7—42no—
664C22×C7—42no—
665C22×C7—42no—
666C22×C7—42no—
667C22×C7—42no—
668C22×C7—81no—
669C22×C7—81no—
670C22×C7—81no—
671C22×C7—81no—
672C22×C7—81no—
673C22×C7—81no—
674C22×C7—81no—
675C22×C7—81no—
676C22×C7#39718yescomplemented
677C22×C7C2×#12111yescharacteristic
678C22×C7C2×#12311yescharacteristic
679C22×C7C2×#12311yescharacteristic
680C22×C7C2×#12311yescharacteristic
681C22×C7#52511yescharacteristic
682C22×C7#52511yescharacteristic
683C22×C7#52511yescharacteristic
684C22×C7C2×#12411yescharacteristic
685C22×C7C2×#12611yescharacteristic
686C22×C7C2×#12611yescharacteristic
687C22×C7#52911yescharacteristic
688C22×C7#52911yescharacteristic
689C22×C7#52911yescharacteristic
690C22×C7#53811yescharacteristic
691C22×C7#53811yescharacteristic
692C22×C7#53811yescharacteristic
693C22×C7#53911yescharacteristic
694C22×C7#53911yescharacteristic
695C22×C7#53911yescharacteristic
696C22×C7D4211yescharacteristic
697C22×C7D4211yescharacteristic
698C22×C7#54611yescharacteristic
699C22×C7#54611yescharacteristic
700C22×C7#54611yescharacteristic
701C22×C7#54611yescharacteristic
702C22×C7#54611yescharacteristic
703C22×C7#54711yescharacteristic
704C22×C7#54711yescharacteristic
705C22×C7#54811yescharacteristic
706C22×C7#55111yescharacteristic
707C22×C7#55111yescharacteristic
708C22×C7#55211yescharacteristic
709C22×C7#55311yescharacteristic
710C22×C7#55311yescharacteristic
711C22×C7#55311yescharacteristic
712C4×C7—42no—
713C4×C7—42no—
714C4×C7—42no—
715C4×C7—42no—
716C4×C7—42no—
717C4×C7—42no—
718C4×C7—42no—
719C4×C7—42no—
720C4×C7—42no—
721C4×C7—81no—
722C4×C7—81no—
723C4×C7—81no—
724C4×C7—81no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24C2×C7×D412yes—
748C24C2×C7×D412yes—
749C24C2×C7×D412yes—
750C24C7×#4112yes—
751C24C7×#4112yes—
752C24C7×#4112yes—
753C24C7×#4112yes—
754C24C7×#4112yes—
755C24C24×C711yescharacteristic
756C2×D4—28no—
757C2×D4—28no—
758C2×D4—28no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
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—21no—
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—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—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4C2×C7×D412yes—
867C22×C4C2×C7×D412yes—
868C22×C4C2×C7×D412yes—
869C22×C4C2×C7×D412yes—
870C22×C4C2×C7×D412yes—
871C22×C4C2×C7×D412yes—
872C22×C4C7×#4112yes—
873C22×C4C7×#4112yes—
874C22×C4C7×#4112yes—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C22⋊C4—28no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C2×C7—28no—
887C2×C7—82no—
888C2×C7C2×#39711yescharacteristic
889C2×C7#241811yescharacteristic
890C2×C7#241911yescharacteristic
891C2×C7#242411yescharacteristic
892C2×C7#242511yescharacteristic
893C2×C7#244311yescharacteristic
894C2×C7#244311yescharacteristic
895C2×C7#244411yescharacteristic
896C2×C7#244411yescharacteristic
897C2×C7#247211yescharacteristic
898C2×C7#248111yescharacteristic
899C2×C7#248811yescharacteristic
900C2×C7#251011yescharacteristic
901C2×C7#264311yescharacteristic
902C2×C7#285211yescharacteristic
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
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—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23C7×#12114yes—
967C23C7×#12314yes—
968C23C7×#12314yes—
969C23C7×#12314yes—
970C23C7×#12414yes—
971C23C7×#12614yes—
972C23C7×#12614yes—
973C23C22×C7×D411yescharacteristic
974C23C22×C7×D411yescharacteristic
975C23C22×C7×D411yescharacteristic
976C23C2×C7×#4111yescharacteristic
977C23C2×C7×#4111yescharacteristic
978C23C2×C7×#4111yescharacteristic
979C23C2×C7×#4111yescharacteristic
980C23C2×C7×#4111yescharacteristic
981C23C2×C7×#4111yescharacteristic
982C23C2×C7×#4111yescharacteristic
983C23C2×C7×#4111yescharacteristic
984C23C7×H(5,𝔽2)11yescharacteristic
985C23C7×H(5,𝔽2)11yescharacteristic
986C23C7×H(5,𝔽2)11yescharacteristic
987C23C7×2−1+411yescharacteristic
988D4—416no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—416no—
1017C2×C4—416no—
1018C2×C4—416no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
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—
1083C7#1473711yescharacteristic, direct product factor, Sylow
1084C22—24no—
1085C22—24no—
1086C22—24no—
1087C22—24no—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—24no—
1097C22—24no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22C7×#39718yescomplemented
1114C22C2×C7×#12111yescharacteristic
1115C22C2×C7×#12311yescharacteristic
1116C22C2×C7×#12311yescharacteristic
1117C22C2×C7×#12311yescharacteristic
1118C22C7×#52511yescharacteristic
1119C22C7×#52511yescharacteristic
1120C22C7×#52511yescharacteristic
1121C22C2×C7×#12411yescharacteristic
1122C22C2×C7×#12611yescharacteristic
1123C22C2×C7×#12611yescharacteristic
1124C22C7×#52911yescharacteristic
1125C22C7×#52911yescharacteristic
1126C22C7×#52911yescharacteristic
1127C22C7×#53811yescharacteristic
1128C22C7×#53811yescharacteristic
1129C22C7×#53811yescharacteristic
1130C22C7×#53911yescharacteristic
1131C22C7×#53911yescharacteristic
1132C22C7×#53911yescharacteristic
1133C22C7×D4211yescharacteristic
1134C22C7×D4211yescharacteristic
1135C22C7×#54611yescharacteristic
1136C22C7×#54611yescharacteristic
1137C22C7×#54611yescharacteristic
1138C22C7×#54611yescharacteristic
1139C22C7×#54611yescharacteristic
1140C22C7×#54711yescharacteristic
1141C22C7×#54711yescharacteristic
1142C22C7×#54811yescharacteristic
1143C22C7×#55111yescharacteristic
1144C22C7×#55111yescharacteristic
1145C22C7×#55211yescharacteristic
1146C22C7×#55311yescharacteristic
1147C22C7×#55311yescharacteristic
1148C22C7×#55311yescharacteristic
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C2—28no—
1163C2—82no—
1164C2C2×C7×#39711yescharacteristic
1165C2C7×#241811yescharacteristic
1166C2C7×#241911yescharacteristic
1167C2C7×#242411yescharacteristic
1168C2C7×#242511yescharacteristic
1169C2C7×#244311yescharacteristic
1170C2C7×#244311yescharacteristic
1171C2C7×#244411yescharacteristic
1172C2C7×#244411yescharacteristic
1173C2C7×#247211yescharacteristic
1174C2C7×#248111yescharacteristic
1175C2C7×#248811yescharacteristic
1176C2C7×#251011yescharacteristic
1177C2C7×#264311yescharacteristic
1178C2C7×#285211yescharacteristic
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
1. C2×C7×#397C2semidirect
5. C2×C7×#385C2semidirect
6. C22×C7×#95C2semidirect
7. C7×#1445C2semidirect
8. C7×#1443C2semidirect
9. C7×#1443C2semidirect
10. C7×#1442C2semidirect
11. C7×#1440C2semidirect
12. C7×#1440C2semidirect
13. C7×#1439C2semidirect
14. C7×C22⋊#95C2semidirect
15. C7×C22⋊#95C2semidirect
57. #14737C7direct (N × H)
153. C7×#95D4semidirect
154. C2×#397C2×C7semidirect
158. C2×#385C2×C7semidirect
159. C22×#95C2×C7semidirect
160. #1445C2×C7semidirect
161. #1443C2×C7semidirect
162. #1443C2×C7semidirect
163. #1442C2×C7semidirect
164. #1440C2×C7semidirect
165. #1440C2×C7semidirect
166. #1439C2×C7semidirect
167. C22⋊#95C2×C7semidirect
168. C22⋊#95C2×C7semidirect
646. #95C7×D4semidirect
676. C22×C7#397semidirect
1083. C7#14737direct (N × H)
1113. C22C7×#397semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3972
C2×C7×#3862
C2×C7×#3852
C22×C7×#952
C7×#14452
C7×#14432
C7×#14422
C7×#14402
C7×#14392
C7×C22⋊#952
#147377