Finite Group Databasebeta

← C7×#16535 #13193751

Subgroups — C7×#16535 #13193751

Order 1792.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1292 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, complemented
3C2×C7×#392C211yesmaximal, characteristic
4C2×C7×#388C211yesmaximal, characteristic, complemented
5C7×#1443C211yesmaximal, characteristic, complemented
6C7×#1442C211yesmaximal, characteristic, complemented
7C7×#1439C211yesmaximal, characteristic, complemented
8C7×#1439C211yesmaximal, characteristic, complemented
9C7×#1438C211yesmaximal, characteristic, complemented
10C7×#1438C211yesmaximal, characteristic, complemented
11C7×#1438C211yesmaximal, characteristic, complemented
12C7×#1438C211yesmaximal, characteristic, complemented
13C7×#1438C211yesmaximal, characteristic, complemented
14C7×#1437C211yesmaximal, characteristic, complemented
15C7×#1437C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C23×C7×D4C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊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×C7×C22⋊C4C2211yescharacteristic
32C22×C7×C22⋊C4C2211yescharacteristic
33C22×C7×C22⋊C4C2211yescharacteristic
34C22×C7×C22⋊C4C2211yescharacteristic
35C22×C7×C22⋊C4C2211yescharacteristic
36C22×C42×C7C2211yescharacteristic
37C7×#397—24no—
38C7×#394—24no—
39C7×#392—24no—
40C7×#388—24no—
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#16535C711yesmaximal, characteristic, direct product factor, Sylow
56C25×C7C2311yescharacteristic
57C25×C7C2311yescharacteristic
58C25×C7C2311yescharacteristic
59C22×C7×D4—22no—
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×D4—22no—
67C22×C7×D4—22no—
68C22×C7×D4—41no—
69C22×C7×D4—41no—
70C22×C7×D4—41no—
71C22×C7×D4—41no—
72C22×C7×D4—41no—
73C22×C7×D4—41no—
74C22×C7×D4—41no—
75C22×C7×D4—41no—
76C22×C7×D4—41no—
77C22×C7×D4—41no—
78C22×C7×D4—41no—
79C22×C7×D4—41no—
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
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
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4—41no—
96C2×C7×C4⋊C4—41no—
97C2×C7×C4⋊C4—41no—
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—22no—
116C2×C7×C22⋊C4—22no—
117C2×C7×C22⋊C4—22no—
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⋊C4—41no—
124C2×C7×C22⋊C4—41no—
125C2×C7×C22⋊C4—41no—
126C2×C7×C22⋊C4—41no—
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⋊C4—41no—
134C2×C7×C22⋊C4—41no—
135C2×C7×C22⋊C4—41no—
136C2×C7×C22⋊C4—41no—
137C2×C7×C22⋊C4—41no—
138C2×C7×C22⋊C4—41no—
139C2×C7×C22⋊C4—41no—
140C2×C7×C22⋊C4—41no—
141C2×C7×C22⋊C4—41no—
142C2×C7×C22⋊C4D414yes—
143C2×C42×C7—22no—
144C2×C42×C7—41no—
145C2×C42×C7—41no—
146C7×#95—22no—
147C7×#95—22no—
148C7×#95—22no—
149C7×#95—22no—
150C7×#95—22no—
151C7×#95—22no—
152C7×#95—41no—
153C7×#95—41no—
154C7×#95—41no—
155C7×#95—41no—
156C7×#95—41no—
157C7×#95—41no—
158C7×#95—41no—
159C7×#95D414yescomplemented
160C2×#397C2×C711yescharacteristic, complemented
161C2×#394C2×C711yescharacteristic, complemented
162C2×#392C2×C711yescharacteristic
163C2×#388C2×C711yescharacteristic, complemented
164#1443C2×C711yescharacteristic, complemented
165#1442C2×C711yescharacteristic, complemented
166#1439C2×C711yescharacteristic, complemented
167#1439C2×C711yescharacteristic, complemented
168#1438C2×C711yescharacteristic, complemented
169#1438C2×C711yescharacteristic, complemented
170#1438C2×C711yescharacteristic, complemented
171#1438C2×C711yescharacteristic, complemented
172#1438C2×C711yescharacteristic, complemented
173#1437C2×C711yescharacteristic, complemented
174#1437C2×C711yescharacteristic, complemented
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×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×C7—21no—
206C24×C7—21no—
207C24×C7—21no—
208C24×C7—21no—
209C24×C7—21no—
210C24×C7—21no—
211C24×C7—21no—
212C24×C7—21no—
213C24×C7—21no—
214C24×C7—21no—
215C24×C7—21no—
216C24×C7—21no—
217C24×C7C2×D412yes—
218C24×C7#4112yes—
219C24×C7#4112yes—
220C24×C7C2411yescharacteristic
221C2×C7×D4—44no—
222C2×C7×D4—44no—
223C2×C7×D4—44no—
224C2×C7×D4—44no—
225C2×C7×D4—44no—
226C2×C7×D4—44no—
227C2×C7×D4—44no—
228C2×C7×D4—44no—
229C2×C7×D4—44no—
230C2×C7×D4—44no—
231C2×C7×D4—44no—
232C2×C7×D4—44no—
233C2×C7×D4—44no—
234C2×C7×D4—44no—
235C2×C7×D4—44no—
236C2×C7×D4—44no—
237C2×C7×D4—44no—
238C2×C7×D4—44no—
239C2×C7×D4—44no—
240C2×C7×D4—44no—
241C2×C7×D4—44no—
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—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—21no—
304C22×C4×C7—21no—
305C22×C4×C7—21no—
306C22×C4×C7—21no—
307C22×C4×C7—21no—
308C22×C4×C7—21no—
309C22×C4×C7—21no—
310C22×C4×C7—21no—
311C22×C4×C7—21no—
312C22×C4×C7—21no—
313C22×C4×C7—21no—
314C22×C4×C7—21no—
315C22×C4×C7—21no—
316C22×C4×C7—21no—
317C22×C4×C7—21no—
318C22×C4×C7C2×D412yes—
319C22×C4×C7C2×D412yes—
320C22×C4×C7C2×D412yes—
321C22×C4×C7C2×D412yes—
322C22×C4×C7C2×D412yes—
323C22×C4×C7#4112yes—
324C22×C4×C7#4112yes—
325C22×C4×C7#4112yes—
326C7×C4⋊C4—44no—
327C7×C4⋊C4—44no—
328C7×C22⋊C4—28no—
329C7×C22⋊C4—44no—
330C7×C22⋊C4—44no—
331C7×C22⋊C4—44no—
332C7×C22⋊C4—44no—
333C7×C22⋊C4—44no—
334C7×C22⋊C4—44no—
335C7×C22⋊C4—44no—
336C7×C22⋊C4—44no—
337C7×C22⋊C4—44no—
338C7×C22⋊C4—44no—
339C7×C22⋊C4—44no—
340C7×C22⋊C4—44no—
341C7×C22⋊C4—44no—
342C7×C22⋊C4—44no—
343C42×C7—44no—
344C23×D4C22×C711yescharacteristic
345C23×D4C22×C711yescharacteristic
346C23×D4C22×C711yescharacteristic
347C22×C4⋊C4C22×C711yescharacteristic
348C22×C4⋊C4C22×C711yescharacteristic
349C22×C22⋊C4C22×C711yescharacteristic
350C22×C22⋊C4C22×C711yescharacteristic
351C22×C22⋊C4C22×C711yescharacteristic
352C22×C22⋊C4C22×C711yescharacteristic
353C22×C22⋊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#397—24no—
366#394—24no—
367#392—24no—
368#388—24no—
369C2×#95C22×C711yescharacteristic
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
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—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—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×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×C7—41no—
463C23×C7—41no—
464C23×C7—41no—
465C23×C7—41no—
466C23×C7—41no—
467C23×C7—41no—
468C23×C7—41no—
469C23×C7—41no—
470C23×C7—41no—
471C23×C7—41no—
472C23×C7—41no—
473C23×C7—41no—
474C23×C7—41no—
475C23×C7—41no—
476C23×C7—41no—
477C23×C7—41no—
478C23×C7—41no—
479C23×C7—41no—
480C23×C7—41no—
481C23×C7—41no—
482C23×C7—41no—
483C23×C7—41no—
484C23×C7—41no—
485C23×C7—41no—
486C23×C7—41no—
487C23×C7—41no—
488C23×C7C22×D411yescharacteristic
489C23×C7C22×D411yescharacteristic
490C23×C7C2×#4111yescharacteristic
491C23×C7C2×#4111yescharacteristic
492C23×C7C2×#4111yescharacteristic
493C23×C7C2×#4111yescharacteristic
494C23×C7C2×#4111yescharacteristic
495C23×C7H(5,𝔽2)11yescharacteristic
496C23×C7H(5,𝔽2)11yescharacteristic
497C23×C7H(5,𝔽2)11yescharacteristic
498C23×C7H(5,𝔽2)11yescharacteristic
499C23×C7H(5,𝔽2)11yescharacteristic
500C23×C7H(5,𝔽2)11yescharacteristic
501C23×C7H(5,𝔽2)11yescharacteristic
502C23×C7H(5,𝔽2)11yescharacteristic
503C7×D4—416no—
504C7×D4—416no—
505C7×D4—416no—
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—22no—
529C2×C4×C7—22no—
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—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×C7—41no—
579C2×C4×C7—41no—
580C2×C4×C7—41no—
581C2×C4×C7—41no—
582C2×C4×C7—41no—
583C2×C4×C7—41no—
584C2×C4×C7—41no—
585C2×C4×C7—41no—
586C2×C4×C7—41no—
587C2×C4×C7—41no—
588C2×C4×C7—41no—
589C2×C4×C7—41no—
590C25C23×C711yescharacteristic
591C25C23×C711yescharacteristic
592C25C23×C711yescharacteristic
593C22×D4—22no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—22no—
597C22×D4—22no—
598C22×D4—22no—
599C22×D4—22no—
600C22×D4—22no—
601C22×D4—22no—
602C22×D4—41no—
603C22×D4—41no—
604C22×D4—41no—
605C22×D4—41no—
606C22×D4—41no—
607C22×D4—41no—
608C22×D4—41no—
609C22×D4—41no—
610C22×D4—41no—
611C22×D4—41no—
612C22×D4—41no—
613C22×D4—41no—
614C23×C4C23×C711yescharacteristic
615C23×C4C23×C711yescharacteristic
616C23×C4C23×C711yescharacteristic
617C23×C4C23×C711yescharacteristic
618C23×C4C23×C711yescharacteristic
619C23×C4C23×C711yescharacteristic
620C23×C4C23×C711yescharacteristic
621C23×C4C23×C711yescharacteristic
622C23×C4C23×C711yescharacteristic
623C23×C4C23×C711yescharacteristic
624C23×C4C23×C711yescharacteristic
625C23×C4C23×C711yescharacteristic
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
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—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—41no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4—41no—
656C2×C22⋊C4—41no—
657C2×C22⋊C4—41no—
658C2×C22⋊C4—41no—
659C2×C22⋊C4—41no—
660C2×C22⋊C4—41no—
661C2×C22⋊C4—41no—
662C2×C22⋊C4—41no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—41no—
669C2×C22⋊C4—41no—
670C2×C22⋊C4—41no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4C7×D414yes—
677C2×C42—22no—
678C2×C42—41no—
679C2×C42—41no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—22no—
685#95—22no—
686#95—41no—
687#95—41no—
688#95—41no—
689#95—41no—
690#95—41no—
691#95—41no—
692#95—41no—
693#95C7×D414yescomplemented
694C22×C7—42no—
695C22×C7—42no—
696C22×C7—42no—
697C22×C7—42no—
698C22×C7—42no—
699C22×C7—42no—
700C22×C7—42no—
701C22×C7—42no—
702C22×C7—42no—
703C22×C7—42no—
704C22×C7—42no—
705C22×C7—42no—
706C22×C7—42no—
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—81no—
716C22×C7—81no—
717C22×C7—81no—
718C22×C7—81no—
719C22×C7—81no—
720C22×C7—81no—
721C22×C7—81no—
722C22×C7—81no—
723C22×C7—81no—
724C22×C7—81no—
725C22×C7—81no—
726C22×C7—81no—
727C22×C7—81no—
728C22×C7—81no—
729C22×C7—81no—
730C22×C7—81no—
731C22×C7—81no—
732C22×C7—81no—
733C22×C7—81no—
734C22×C7—81no—
735C22×C7—81no—
736C22×C7—81no—
737C22×C7—81no—
738C22×C7—81no—
739C22×C7#52511yescharacteristic
740C22×C7#52911yescharacteristic
741C22×C7#53211yescharacteristic
742C22×C7#53411yescharacteristic
743C22×C7#53511yescharacteristic
744C22×C7#53511yescharacteristic
745C22×C7#53511yescharacteristic
746C22×C7#53811yescharacteristic
747C22×C7#53811yescharacteristic
748C22×C7#53811yescharacteristic
749C22×C7#53811yescharacteristic
750C22×C7#53811yescharacteristic
751C22×C7#53811yescharacteristic
752C22×C7#53811yescharacteristic
753C22×C7#53811yescharacteristic
754C22×C7#54011yescharacteristic
755C22×C7#54011yescharacteristic
756C22×C7#54011yescharacteristic
757C22×C7#54011yescharacteristic
758C22×C7D4211yescharacteristic
759C22×C7#54611yescharacteristic
760C22×C7#54611yescharacteristic
761C22×C7#54611yescharacteristic
762C22×C7#54611yescharacteristic
763C22×C7#54611yescharacteristic
764C22×C7#55011yescharacteristic
765C22×C7#55111yescharacteristic
766C22×C7#55111yescharacteristic
767C22×C7#55311yescharacteristic
768C22×C7#55311yescharacteristic
769C22×C7#55311yescharacteristic
770C22×C7#56011yescharacteristic
771C22×C7#56011yescharacteristic
772C22×C7#56011yescharacteristic
773C22×C7H(3,𝔽4)11yescharacteristic
774C4×C7—42no—
775C4×C7—42no—
776C4×C7—42no—
777C4×C7—42no—
778C4×C7—42no—
779C4×C7—42no—
780C4×C7—42no—
781C4×C7—42no—
782C4×C7—81no—
783C4×C7—81no—
784C4×C7—81no—
785C4×C7—81no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24C2×C7×D412yes—
829C24C7×#4112yes—
830C24C7×#4112yes—
831C24C24×C711yescharacteristic
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—44no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—44no—
846C2×D4—44no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—44no—
850C2×D4—44no—
851C2×D4—44no—
852C2×D4—44no—
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—21no—
871C22×C4—21no—
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—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4C2×C7×D412yes—
930C22×C4C2×C7×D412yes—
931C22×C4C2×C7×D412yes—
932C22×C4C2×C7×D412yes—
933C22×C4C2×C7×D412yes—
934C22×C4C7×#4112yes—
935C22×C4C7×#4112yes—
936C22×C4C7×#4112yes—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C22⋊C4—28no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C42—44no—
955C2×C7—82no—
956C2×C7—82no—
957C2×C7—82no—
958C2×C7#246411yescharacteristic
959C2×C7#247111yescharacteristic
960C2×C7#255911yescharacteristic
961C2×C7#263111yescharacteristic
962C2×C7#264811yescharacteristic
963C2×C7#266111yescharacteristic
964C2×C7#267011yescharacteristic
965C2×C7#267311yescharacteristic
966C2×C7#268511yescharacteristic
967C2×C7#269711yescharacteristic
968C2×C7#270311yescharacteristic
969C2×C7#271411yescharacteristic
970C2×C7#275311yescharacteristic
971C2×C7#277811yescharacteristic
972C2×C7#282811yescharacteristic
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—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
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—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23C22×C7×D411yescharacteristic
1079C23C22×C7×D411yescharacteristic
1080C23C2×C7×#4111yescharacteristic
1081C23C2×C7×#4111yescharacteristic
1082C23C2×C7×#4111yescharacteristic
1083C23C2×C7×#4111yescharacteristic
1084C23C2×C7×#4111yescharacteristic
1085C23C7×H(5,𝔽2)11yescharacteristic
1086C23C7×H(5,𝔽2)11yescharacteristic
1087C23C7×H(5,𝔽2)11yescharacteristic
1088C23C7×H(5,𝔽2)11yescharacteristic
1089C23C7×H(5,𝔽2)11yescharacteristic
1090C23C7×H(5,𝔽2)11yescharacteristic
1091C23C7×H(5,𝔽2)11yescharacteristic
1092C23C7×H(5,𝔽2)11yescharacteristic
1093D4—416no—
1094D4—416no—
1095D4—416no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
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×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C7#1653511yescharacteristic, direct product factor, Sylow
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22C7×#52511yescharacteristic
1227C22C7×#52911yescharacteristic
1228C22C7×#53211yescharacteristic
1229C22C7×#53411yescharacteristic
1230C22C7×#53511yescharacteristic
1231C22C7×#53511yescharacteristic
1232C22C7×#53511yescharacteristic
1233C22C7×#53811yescharacteristic
1234C22C7×#53811yescharacteristic
1235C22C7×#53811yescharacteristic
1236C22C7×#53811yescharacteristic
1237C22C7×#53811yescharacteristic
1238C22C7×#53811yescharacteristic
1239C22C7×#53811yescharacteristic
1240C22C7×#53811yescharacteristic
1241C22C7×#54011yescharacteristic
1242C22C7×#54011yescharacteristic
1243C22C7×#54011yescharacteristic
1244C22C7×#54011yescharacteristic
1245C22C7×D4211yescharacteristic
1246C22C7×#54611yescharacteristic
1247C22C7×#54611yescharacteristic
1248C22C7×#54611yescharacteristic
1249C22C7×#54611yescharacteristic
1250C22C7×#54611yescharacteristic
1251C22C7×#55011yescharacteristic
1252C22C7×#55111yescharacteristic
1253C22C7×#55111yescharacteristic
1254C22C7×#55311yescharacteristic
1255C22C7×#55311yescharacteristic
1256C22C7×#55311yescharacteristic
1257C22C7×#56011yescharacteristic
1258C22C7×#56011yescharacteristic
1259C22C7×#56011yescharacteristic
1260C22C7×H(3,𝔽4)11yescharacteristic
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—42no—
1268C4—42no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C2—82no—
1274C2—82no—
1275C2—82no—
1276C2C7×#246411yescharacteristic
1277C2C7×#247111yescharacteristic
1278C2C7×#255911yescharacteristic
1279C2C7×#263111yescharacteristic
1280C2C7×#264811yescharacteristic
1281C2C7×#266111yescharacteristic
1282C2C7×#267011yescharacteristic
1283C2C7×#267311yescharacteristic
1284C2C7×#268511yescharacteristic
1285C2C7×#269711yescharacteristic
1286C2C7×#270311yescharacteristic
1287C2C7×#271411yescharacteristic
1288C2C7×#275311yescharacteristic
1289C2C7×#277811yescharacteristic
1290C2C7×#282811yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC2×C7×#392C2
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
2. C2×C7×#394C2semidirect
4. C2×C7×#388C2semidirect
5. C7×#1443C2semidirect
6. C7×#1442C2semidirect
7. C7×#1439C2semidirect
8. C7×#1439C2semidirect
9. C7×#1438C2semidirect
10. C7×#1438C2semidirect
11. C7×#1438C2semidirect
12. C7×#1438C2semidirect
13. C7×#1438C2semidirect
14. C7×#1437C2semidirect
15. C7×#1437C2semidirect
55. #16535C7direct (N × H)
159. C7×#95D4semidirect
160. C2×#397C2×C7semidirect
161. C2×#394C2×C7semidirect
163. C2×#388C2×C7semidirect
164. #1443C2×C7semidirect
165. #1442C2×C7semidirect
166. #1439C2×C7semidirect
167. #1439C2×C7semidirect
168. #1438C2×C7semidirect
169. #1438C2×C7semidirect
170. #1438C2×C7semidirect
171. #1438C2×C7semidirect
172. #1438C2×C7semidirect
173. #1437C2×C7semidirect
174. #1437C2×C7semidirect
693. #95C7×D4semidirect
1180. C7#16535direct (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×#3922
C2×C7×#3882
C7×#14432
C7×#14422
C7×#14392
C7×#14382
C7×#14372
#165357