Finite Group Databasebeta

← C7×#15162 #13192378

Subgroups — C7×#15162 #13192378

Order 1792.

1786 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#397C211yesmaximal, characteristic, complemented
2C2×C7×#394C211yesmaximal, characteristic
3C2×C7×#386C211yesmaximal, characteristic
4C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
5C7×#1443C211yesmaximal, characteristic, complemented
6C7×#1442C211yesmaximal, characteristic, complemented
7C7×#1440C211yesmaximal, characteristic, complemented
8C7×#1440C211yesmaximal, characteristic, complemented
9C7×#1439C211yesmaximal, characteristic, complemented
10C7×#1438C211yesmaximal, characteristic
11C7×#1437C211yesmaximal, characteristic, complemented
12C7×#1437C211yesmaximal, characteristic, complemented
13C7×#1436C211yesmaximal, characteristic, complemented
14C7×#1436C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊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
31C22×C42×C7C2211yescharacteristic
32C22×C42×C7C2211yescharacteristic
33C7×#397—24no—
34C7×#394—24no—
35C7×#386—24no—
36C4×C7×C22⋊C4—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
55#15162C711yesmaximal, characteristic, direct product factor, Sylow
56C25×C7C2311yescharacteristic
57C25×C7C2311yescharacteristic
58C22×C7×D4—22no—
59C22×C7×D4—22no—
60C22×C7×D4—22no—
61C22×C7×D4—22no—
62C22×C7×D4—22no—
63C22×C7×D4—41no—
64C22×C7×D4—41no—
65C23×C4×C7—22no—
66C23×C4×C7—22no—
67C23×C4×C7—41no—
68C23×C4×C7—41no—
69C23×C4×C7—41no—
70C23×C4×C7—41no—
71C23×C4×C7D414yes—
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C2×C7×C4⋊C4—22no—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—22no—
89C2×C7×C4⋊C4—41no—
90C2×C7×C4⋊C4—41no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—22no—
98C2×C7×C22⋊C4—22no—
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4—22no—
101C2×C7×C22⋊C4—22no—
102C2×C7×C22⋊C4—22no—
103C2×C7×C22⋊C4—22no—
104C2×C7×C22⋊C4—22no—
105C2×C7×C22⋊C4—22no—
106C2×C7×C22⋊C4—22no—
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—41no—
116C2×C7×C22⋊C4—41no—
117C2×C7×C22⋊C4—41no—
118C2×C7×C22⋊C4—41no—
119C2×C7×C22⋊C4—41no—
120C2×C7×C22⋊C4—41no—
121C2×C7×C22⋊C4—41no—
122C2×C7×C22⋊C4—41no—
123C2×C7×C22⋊C4D414yes—
124C2×C42×C7—22no—
125C2×C42×C7—22no—
126C2×C42×C7—41no—
127C2×C42×C7—41no—
128C2×C42×C7—41no—
129C2×C42×C7—41no—
130C7×#95—22no—
131C7×#95—22no—
132C7×#95—22no—
133C7×#95—22no—
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—41no—
145C7×#95—41no—
146C7×#95—41no—
147C7×#95—41no—
148C2×#397C2×C711yescharacteristic, complemented
149C2×#394C2×C711yescharacteristic
150C2×#386C2×C711yescharacteristic
151C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
152#1443C2×C711yescharacteristic, complemented
153#1442C2×C711yescharacteristic, complemented
154#1440C2×C711yescharacteristic, complemented
155#1440C2×C711yescharacteristic, complemented
156#1439C2×C711yescharacteristic, complemented
157#1438C2×C711yescharacteristic
158#1437C2×C711yescharacteristic, complemented
159#1437C2×C711yescharacteristic, complemented
160#1436C2×C711yescharacteristic, complemented
161#1436C2×C711yescharacteristic, complemented
162C22⋊#95C2×C711yescharacteristic, complemented
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—21no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7—21no—
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×C7C2×D412yes—
190C24×C7C2×D412yes—
191C24×C7#4112yes—
192C24×C7#4112yes—
193C24×C7C2411yescharacteristic
194C2×C7×D4—28no—
195C2×C7×D4—44no—
196C2×C7×D4—44no—
197C2×C7×D4—44no—
198C2×C7×D4—44no—
199C2×C7×D4—44no—
200C2×C7×D4—44no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
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—28no—
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—44no—
283C22×C4×C7—44no—
284C22×C4×C7—44no—
285C22×C4×C7—44no—
286C22×C4×C7—44no—
287C22×C4×C7—44no—
288C22×C4×C7C2×D412yes—
289C22×C4×C7C2×D412yes—
290C22×C4×C7C2×D412yes—
291C22×C4×C7C2×D412yes—
292C22×C4×C7#4112yes—
293C22×C4×C7#4112yes—
294C22×C4×C7#4112yes—
295C22×C4×C7#4112yes—
296C22×C4×C7#4112yes—
297C22×C4×C7#4112yes—
298C22×C4×C7#4112yes—
299C7×C4⋊C4—44no—
300C7×C4⋊C4—44no—
301C7×C22⋊C4—28no—
302C7×C22⋊C4—28no—
303C7×C22⋊C4—44no—
304C7×C22⋊C4—44no—
305C7×C22⋊C4—44no—
306C7×C22⋊C4—44no—
307C7×C22⋊C4—44no—
308C7×C22⋊C4—44no—
309C7×C22⋊C4—44no—
310C7×C22⋊C4—44no—
311C7×C22⋊C4—44no—
312C42×C7—44no—
313C42×C7—44no—
314C23×D4C22×C711yescharacteristic
315C24×C4C22×C711yescharacteristic
316C22×C4⋊C4C22×C711yescharacteristic
317C22×C4⋊C4C22×C711yescharacteristic
318C22×C22⋊C4C22×C711yescharacteristic
319C22×C22⋊C4C22×C711yescharacteristic
320C22×C22⋊C4C22×C711yescharacteristic
321C22×C22⋊C4C22×C711yescharacteristic
322C22×C22⋊C4C22×C711yescharacteristic
323C22×C22⋊C4C22×C711yescharacteristic
324C22×C22⋊C4C22×C711yescharacteristic
325C22×C22⋊C4C22×C711yescharacteristic
326C22×C22⋊C4C22×C711yescharacteristic
327C22×C22⋊C4C22×C711yescharacteristic
328C22×C22⋊C4C22×C711yescharacteristic
329C22×C42C22×C711yescharacteristic
330C22×C42C22×C711yescharacteristic
331#397—24no—
332#394—24no—
333#386—24no—
334C4×C22⋊C4—24no—
335C2×#95C22×C711yescharacteristic
336C2×#95C22×C711yescharacteristic
337C2×#95C22×C711yescharacteristic
338C2×#95C22×C711yescharacteristic
339C2×#95C22×C711yescharacteristic
340C2×#95C22×C711yescharacteristic
341C2×#95C22×C711yescharacteristic
342C2×#95C22×C711yescharacteristic
343C2×#95C22×C711yescharacteristic
344C2×#95C22×C711yescharacteristic
345C2×#95C22×C711yescharacteristic
346C2×#95C22×C711yescharacteristic
347C2×#95C22×C711yescharacteristic
348C2×#95C22×C711yescharacteristic
349C2×#95C22×C711yescharacteristic
350C2×#95C22×C711yescharacteristic
351C2×#95C22×C711yescharacteristic
352C2×#95C22×C711yescharacteristic
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—22no—
378C23×C7—41no—
379C23×C7—41no—
380C23×C7—41no—
381C23×C7—41no—
382C23×C7—41no—
383C23×C7—41no—
384C23×C7—41no—
385C23×C7—41no—
386C23×C7—41no—
387C23×C7—41no—
388C23×C7—41no—
389C23×C7—41no—
390C23×C7—41no—
391C23×C7—41no—
392C23×C7—41no—
393C23×C7—41no—
394C23×C7—41no—
395C23×C7—41no—
396C23×C7—41no—
397C23×C7—41no—
398C23×C7—41no—
399C23×C7—41no—
400C23×C7—41no—
401C23×C7—41no—
402C23×C7—41no—
403C23×C7—41no—
404C23×C7—41no—
405C23×C7—41no—
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#12114yes—
423C23×C7C22×D411yescharacteristic
424C23×C7C22×D411yescharacteristic
425C23×C7C2×#4111yescharacteristic
426C23×C7C2×#4111yescharacteristic
427C23×C7C2×#4111yescharacteristic
428C23×C7C2×#4111yescharacteristic
429C23×C7C2×#4111yescharacteristic
430C23×C7C2×#4111yescharacteristic
431C23×C7C2×#4111yescharacteristic
432C23×C7C2×#4111yescharacteristic
433C23×C7C2×#4111yescharacteristic
434C23×C7H(5,𝔽2)11yescharacteristic
435C23×C7H(5,𝔽2)11yescharacteristic
436C23×C7H(5,𝔽2)11yescharacteristic
437C23×C7H(5,𝔽2)11yescharacteristic
438C7×D4—416no—
439C2×C4×C7—22no—
440C2×C4×C7—22no—
441C2×C4×C7—22no—
442C2×C4×C7—22no—
443C2×C4×C7—22no—
444C2×C4×C7—22no—
445C2×C4×C7—22no—
446C2×C4×C7—22no—
447C2×C4×C7—22no—
448C2×C4×C7—22no—
449C2×C4×C7—22no—
450C2×C4×C7—22no—
451C2×C4×C7—22no—
452C2×C4×C7—22no—
453C2×C4×C7—22no—
454C2×C4×C7—22no—
455C2×C4×C7—22no—
456C2×C4×C7—22no—
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—416no—
470C2×C4×C7—41no—
471C2×C4×C7—41no—
472C2×C4×C7—41no—
473C2×C4×C7—41no—
474C2×C4×C7—41no—
475C2×C4×C7—41no—
476C2×C4×C7—41no—
477C2×C4×C7—41no—
478C2×C4×C7—41no—
479C2×C4×C7—41no—
480C2×C4×C7—41no—
481C2×C4×C7—41no—
482C2×C4×C7—41no—
483C2×C4×C7—41no—
484C2×C4×C7—41no—
485C2×C4×C7—41no—
486C2×C4×C7—41no—
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#12314yes—
531C25C23×C711yescharacteristic
532C25C23×C711yescharacteristic
533C22×D4—22no—
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—41no—
539C22×D4—41no—
540C23×C4—22no—
541C23×C4—22no—
542C23×C4—41no—
543C23×C4—41no—
544C23×C4—41no—
545C23×C4—41no—
546C23×C4C7×D414yes—
547C23×C4C23×C711yescharacteristic
548C23×C4C23×C711yescharacteristic
549C23×C4C23×C711yescharacteristic
550C23×C4C23×C711yescharacteristic
551C23×C4C23×C711yescharacteristic
552C23×C4C23×C711yescharacteristic
553C23×C4C23×C711yescharacteristic
554C23×C4C23×C711yescharacteristic
555C23×C4C23×C711yescharacteristic
556C23×C4C23×C711yescharacteristic
557C23×C4C23×C711yescharacteristic
558C23×C4C23×C711yescharacteristic
559C23×C4C23×C711yescharacteristic
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—41no—
591C2×C22⋊C4—41no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4—41no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—41no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4C7×D414yes—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—41no—
602C2×C42—41no—
603C2×C42—41no—
604C2×C42—41no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—41no—
620#95—41no—
621#95—41no—
622#95—41no—
623C22×C7—24no—
624C22×C7—24no—
625C22×C7—24no—
626C22×C7—42no—
627C22×C7—42no—
628C22×C7—42no—
629C22×C7—42no—
630C22×C7—42no—
631C22×C7—42no—
632C22×C7—42no—
633C22×C7—42no—
634C22×C7—42no—
635C22×C7—42no—
636C22×C7—42no—
637C22×C7—42no—
638C22×C7—42no—
639C22×C7—42no—
640C22×C7—42no—
641C22×C7—42no—
642C22×C7—42no—
643C22×C7—42no—
644C22×C7—42no—
645C22×C7—81no—
646C22×C7—81no—
647C22×C7—81no—
648C22×C7—81no—
649C22×C7—81no—
650C22×C7—81no—
651C22×C7—81no—
652C22×C7—81no—
653C22×C7C2×#12111yescharacteristic
654C22×C7C2×#12311yescharacteristic
655C22×C7#52511yescharacteristic
656C22×C7#52511yescharacteristic
657C22×C7#52911yescharacteristic
658C22×C7#52911yescharacteristic
659C22×C7#52911yescharacteristic
660C22×C7#52911yescharacteristic
661C22×C7#52911yescharacteristic
662C22×C7#52911yescharacteristic
663C22×C7#53211yescharacteristic
664C22×C7#53211yescharacteristic
665C22×C7#53211yescharacteristic
666C22×C7#53411yescharacteristic
667C22×C7#53411yescharacteristic
668C22×C7#53811yescharacteristic
669C22×C7#53811yescharacteristic
670C22×C7#53811yescharacteristic
671C22×C7#53811yescharacteristic
672C22×C7#54611yescharacteristic
673C22×C7#54611yescharacteristic
674C22×C7#54611yescharacteristic
675C22×C7#54611yescharacteristic
676C22×C7#55111yescharacteristic
677C22×C7#55111yescharacteristic
678C22×C7#55111yescharacteristic
679C22×C7#55111yescharacteristic
680C22×C7#55311yescharacteristic
681C22×C7#55311yescharacteristic
682C22×C7#55311yescharacteristic
683C22×C7#55311yescharacteristic
684C22×C7#55311yescharacteristic
685C22×C7#55311yescharacteristic
686C22×C7#55911yescharacteristic
687C22×C7#55911yescharacteristic
688C4×C7—24no—
689C4×C7—42no—
690C4×C7—42no—
691C4×C7—42no—
692C4×C7—42no—
693C4×C7—42no—
694C4×C7—42no—
695C4×C7—42no—
696C4×C7—42no—
697C4×C7—81no—
698C4×C7—81no—
699C4×C7—81no—
700C4×C7—81no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24C2×C7×D412yes—
728C24C2×C7×D412yes—
729C24C7×#4112yes—
730C24C7×#4112yes—
731C24C24×C711yescharacteristic
732C2×D4—28no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
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—28no—
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—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4C2×C7×D412yes—
827C22×C4C2×C7×D412yes—
828C22×C4C2×C7×D412yes—
829C22×C4C2×C7×D412yes—
830C22×C4C7×#4112yes—
831C22×C4C7×#4112yes—
832C22×C4C7×#4112yes—
833C22×C4C7×#4112yes—
834C22×C4C7×#4112yes—
835C22×C4C7×#4112yes—
836C22×C4C7×#4112yes—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C22⋊C4—28no—
840C22⋊C4—28no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C42—44no—
851C42—44no—
852C2×C7—44no—
853C2×C7—82no—
854C2×C7#239511yescharacteristic
855C2×C7#253411yescharacteristic
856C2×C7#254311yescharacteristic
857C2×C7#255711yescharacteristic
858C2×C7#255711yescharacteristic
859C2×C7#255911yescharacteristic
860C2×C7#255911yescharacteristic
861C2×C7#257611yescharacteristic
862C2×C7#257811yescharacteristic
863C2×C7#259511yescharacteristic
864C2×C7#259711yescharacteristic
865C2×C7#260011yescharacteristic
866C2×C7#260211yescharacteristic
867C2×C7#262211yescharacteristic
868C2×C7#285411yescharacteristic
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23C7×#12114yes—
939C23C22×C7×D411yescharacteristic
940C23C22×C7×D411yescharacteristic
941C23C2×C7×#4111yescharacteristic
942C23C2×C7×#4111yescharacteristic
943C23C2×C7×#4111yescharacteristic
944C23C2×C7×#4111yescharacteristic
945C23C2×C7×#4111yescharacteristic
946C23C2×C7×#4111yescharacteristic
947C23C2×C7×#4111yescharacteristic
948C23C2×C7×#4111yescharacteristic
949C23C2×C7×#4111yescharacteristic
950C23C7×H(5,𝔽2)11yescharacteristic
951C23C7×H(5,𝔽2)11yescharacteristic
952C23C7×H(5,𝔽2)11yescharacteristic
953C23C7×H(5,𝔽2)11yescharacteristic
954D4—416no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—416no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
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×C4C7×#12314yes—
1047C7#1516211yescharacteristic, direct product factor, Sylow
1048C22—24no—
1049C22—24no—
1050C22—24no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22C2×C7×#12111yescharacteristic
1079C22C2×C7×#12311yescharacteristic
1080C22C7×#52511yescharacteristic
1081C22C7×#52511yescharacteristic
1082C22C7×#52911yescharacteristic
1083C22C7×#52911yescharacteristic
1084C22C7×#52911yescharacteristic
1085C22C7×#52911yescharacteristic
1086C22C7×#52911yescharacteristic
1087C22C7×#52911yescharacteristic
1088C22C7×#53211yescharacteristic
1089C22C7×#53211yescharacteristic
1090C22C7×#53211yescharacteristic
1091C22C7×#53411yescharacteristic
1092C22C7×#53411yescharacteristic
1093C22C7×#53811yescharacteristic
1094C22C7×#53811yescharacteristic
1095C22C7×#53811yescharacteristic
1096C22C7×#53811yescharacteristic
1097C22C7×#54611yescharacteristic
1098C22C7×#54611yescharacteristic
1099C22C7×#54611yescharacteristic
1100C22C7×#54611yescharacteristic
1101C22C7×#55111yescharacteristic
1102C22C7×#55111yescharacteristic
1103C22C7×#55111yescharacteristic
1104C22C7×#55111yescharacteristic
1105C22C7×#55311yescharacteristic
1106C22C7×#55311yescharacteristic
1107C22C7×#55311yescharacteristic
1108C22C7×#55311yescharacteristic
1109C22C7×#55311yescharacteristic
1110C22C7×#55311yescharacteristic
1111C22C7×#55911yescharacteristic
1112C22C7×#55911yescharacteristic
1113C4—24no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C2—44no—
1127C2—82no—
1128C2C7×#239511yescharacteristic
1129C2C7×#253411yescharacteristic
1130C2C7×#254311yescharacteristic
1131C2C7×#255711yescharacteristic
1132C2C7×#255711yescharacteristic
1133C2C7×#255911yescharacteristic
1134C2C7×#255911yescharacteristic
1135C2C7×#257611yescharacteristic
1136C2C7×#257811yescharacteristic
1137C2C7×#259511yescharacteristic
1138C2C7×#259711yescharacteristic
1139C2C7×#260011yescharacteristic
1140C2C7×#260211yescharacteristic
1141C2C7×#262211yescharacteristic
1142C2C7×#285411yescharacteristic
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
4. C2×C4×C7×C22⋊C4C2semidirect
5. C7×#1443C2semidirect
6. C7×#1442C2semidirect
7. C7×#1440C2semidirect
8. C7×#1440C2semidirect
9. C7×#1439C2semidirect
11. C7×#1437C2semidirect
12. C7×#1437C2semidirect
13. C7×#1436C2semidirect
14. C7×#1436C2semidirect
15. C7×C22⋊#95C2semidirect
55. #15162C7direct (N × H)
148. C2×#397C2×C7semidirect
151. C2×C4×C22⋊C4C2×C7semidirect
152. #1443C2×C7semidirect
153. #1442C2×C7semidirect
154. #1440C2×C7semidirect
155. #1440C2×C7semidirect
156. #1439C2×C7semidirect
158. #1437C2×C7semidirect
159. #1437C2×C7semidirect
160. #1436C2×C7semidirect
161. #1436C2×C7semidirect
162. C22⋊#95C2×C7semidirect
1047. C7#15162direct (N × H)

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×#3942
C2×C7×#3862
C2×C4×C7×C22⋊C42
C7×#14432
C7×#14422
C7×#14402
C7×#14392
C7×#14382
C7×#14372
C7×#14362
C7×C22⋊#952
#151627