Finite Group Databasebeta

← C7×#14095 #13191311

Subgroups — C7×#14095 #13191311

Order 1792.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#123C211yesmaximal, characteristic
2C2×C7×#390C211yesmaximal, characteristic
3C2×C7×#387C211yesmaximal, characteristic, complemented
4C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
6C7×#1441C211yesmaximal, characteristic, complemented
7C7×#1439C211yesmaximal, characteristic, complemented
8C7×#1439C211yesmaximal, characteristic, complemented
9C7×#1438C211yesmaximal, characteristic
10C7×#1437C211yesmaximal, characteristic, complemented
11C7×#1437C211yesmaximal, characteristic, complemented
12C7×#1437C211yesmaximal, characteristic, complemented
13C7×#1437C211yesmaximal, characteristic, complemented
14C7×#1436C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic
18C2×C7×#123—24no—
19C2×C7×#123—24no—
20C2×C7×#123C418yescomplemented
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊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
37C22×C42×C7C2211yescharacteristic
38C22×C42×C7C2211yescharacteristic
39C22×C42×C7C2211yescharacteristic
40C7×#390—24no—
41C7×#387—24no—
42C4×C7×C4⋊C4—24no—
43C4×C7×C22⋊C4—24no—
44C2×C7×#95C2211yescharacteristic
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47C2×C7×#95C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56C2×C7×#95C2211yescharacteristic
57C2×C7×#95C2211yescharacteristic
58#14095C711yesmaximal, characteristic, direct product factor, Sylow
59C25×C7C2311yescharacteristic
60C25×C7C2311yescharacteristic
61C22×C7×D4—22no—
62C22×C7×D4—22no—
63C22×C7×D4—22no—
64C22×C7×D4—22no—
65C22×C7×D4—41no—
66C22×C7×D4—41no—
67C22×C7×D4C2×C414yes—
68C23×C4×C7—22no—
69C23×C4×C7—22no—
70C23×C4×C7—22no—
71C23×C4×C7—22no—
72C23×C4×C7—41no—
73C23×C4×C7—41no—
74C23×C4×C7C2×C414yes—
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
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C7×#123—232no—
89C2×C7×C4⋊C4—22no—
90C2×C7×C4⋊C4—22no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4—41no—
97C2×C7×C4⋊C4C2×C414yes—
98C2×C7×C4⋊C4C2×C414yes—
99C2×C7×C4⋊C4D414yes—
100C2×C7×C4⋊C4D414yes—
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—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—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⋊C4C2×C414yes—
131C2×C7×C22⋊C4C2×C414yes—
132C2×C7×C22⋊C4C2×C414yes—
133C2×C7×C22⋊C4D414yes—
134C2×C42×C7—22no—
135C2×C42×C7—22no—
136C2×C42×C7—22no—
137C2×C42×C7—22no—
138C2×C42×C7—22no—
139C2×C42×C7—22no—
140C2×C42×C7—22no—
141C2×C42×C7—22no—
142C2×C42×C7—22no—
143C2×C42×C7—41no—
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—22no—
153C7×#95—22no—
154C7×#95—22no—
155C7×#95—22no—
156C7×#95—41no—
157C7×#95—41no—
158C7×#95—41no—
159C7×#95—41no—
160C22×#123C2×C711yescharacteristic
161C2×#390C2×C711yescharacteristic
162C2×#387C2×C711yescharacteristic, complemented
163C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
164C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
165#1441C2×C711yescharacteristic, complemented
166#1439C2×C711yescharacteristic, complemented
167#1439C2×C711yescharacteristic, complemented
168#1438C2×C711yescharacteristic
169#1437C2×C711yescharacteristic, complemented
170#1437C2×C711yescharacteristic, complemented
171#1437C2×C711yescharacteristic, complemented
172#1437C2×C711yescharacteristic, complemented
173#1436C2×C711yescharacteristic, complemented
174C22⋊#95C2×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×C7C22×C412yes—
202C24×C7C22×C412yes—
203C24×C7C2×D412yes—
204C24×C7#4112yes—
205C24×C7C2411yescharacteristic
206C2×C7×D4—28no—
207C2×C7×D4—28no—
208C2×C7×D4—44no—
209C2×C7×D4—44no—
210C2×C7×D4—44no—
211C2×C7×D4—44no—
212C2×C7×D4—44no—
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—28no—
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—28no—
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—44no—
288C22×C4×C7—44no—
289C22×C4×C7—44no—
290C22×C4×C7—44no—
291C22×C4×C7—44no—
292C22×C4×C7C22×C412yes—
293C22×C4×C7C22×C412yes—
294C22×C4×C7C22×C412yes—
295C22×C4×C7C22×C412yes—
296C22×C4×C7C22×C412yes—
297C22×C4×C7C2×D412yes—
298C22×C4×C7C2×D412yes—
299C22×C4×C7C2×D412yes—
300C22×C4×C7C2×D412yes—
301C22×C4×C7C2×D412yes—
302C22×C4×C7C2×D412yes—
303C22×C4×C7C2×D412yes—
304C22×C4×C7C2×D412yes—
305C22×C4×C7#4112yes—
306C22×C4×C7#4112yes—
307C22×C4×C7#4112yes—
308C22×C4×C7#4112yes—
309C22×C4×C7#4112yes—
310C22×C4×C7#4112yes—
311C7×C4⋊C4—28no—
312C7×C4⋊C4—28no—
313C7×C4⋊C4—44no—
314C7×C4⋊C4C22⋊C4116yescomplemented
315C7×C22⋊C4—28no—
316C7×C22⋊C4—28no—
317C7×C22⋊C4—28no—
318C7×C22⋊C4—28no—
319C7×C22⋊C4—28no—
320C7×C22⋊C4—44no—
321C7×C22⋊C4—44no—
322C7×C22⋊C4—44no—
323C7×C22⋊C4—44no—
324C7×C22⋊C4—44no—
325C7×C22⋊C4—44no—
326C42×C7—28no—
327C42×C7—44no—
328C42×C7—44no—
329C42×C7—44no—
330C23×D4C22×C711yescharacteristic
331C24×C4C22×C711yescharacteristic
332C2×#123—24no—
333C2×#123—24no—
334C2×#123C4×C718yescomplemented
335C22×C4⋊C4C22×C711yescharacteristic
336C22×C4⋊C4C22×C711yescharacteristic
337C22×C4⋊C4C22×C711yescharacteristic
338C22×C4⋊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
345C22×C22⋊C4C22×C711yescharacteristic
346C22×C22⋊C4C22×C711yescharacteristic
347C22×C22⋊C4C22×C711yescharacteristic
348C22×C22⋊C4C22×C711yescharacteristic
349C22×C22⋊C4C22×C711yescharacteristic
350C22×C42C22×C711yescharacteristic
351C22×C42C22×C711yescharacteristic
352C22×C42C22×C711yescharacteristic
353C22×C42C22×C711yescharacteristic
354#390—24no—
355#387—24no—
356C4×C4⋊C4—24no—
357C4×C22⋊C4—24no—
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
371C2×#95C22×C711yescharacteristic
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—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—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×C7C4×D414yes—
442C23×C7C23×C411yescharacteristic
443C23×C7C22×D411yescharacteristic
444C23×C7C22×D411yescharacteristic
445C23×C7C22×D411yescharacteristic
446C23×C7C2×#4111yescharacteristic
447C23×C7C2×#4111yescharacteristic
448C23×C7C2×#4111yescharacteristic
449C23×C7C2×#4111yescharacteristic
450C23×C7C2×#4111yescharacteristic
451C23×C7C2×#4111yescharacteristic
452C23×C7C2×#4111yescharacteristic
453C23×C7H(5,𝔽2)11yescharacteristic
454C23×C7H(5,𝔽2)11yescharacteristic
455C23×C7H(5,𝔽2)11yescharacteristic
456C23×C72−1+411yescharacteristic
457C7×D4—416no—
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—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—416no—
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×C7C2×C22⋊C414yes—
547C2×C4×C7C2×C22⋊C414yes—
548C2×C4×C7C2×C22⋊C414yes—
549C2×C4×C7#12314yescomplemented
550C25C23×C711yescharacteristic
551C25C23×C711yescharacteristic
552C22×D4—22no—
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—41no—
557C22×D4—41no—
558C22×D4C2×C4×C714yes—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—41no—
564C23×C4—41no—
565C23×C4C2×C4×C714yes—
566C23×C4C23×C711yescharacteristic
567C23×C4C23×C711yescharacteristic
568C23×C4C23×C711yescharacteristic
569C23×C4C23×C711yescharacteristic
570C23×C4C23×C711yescharacteristic
571C23×C4C23×C711yescharacteristic
572C23×C4C23×C711yescharacteristic
573C23×C4C23×C711yescharacteristic
574C23×C4C23×C711yescharacteristic
575C23×C4C23×C711yescharacteristic
576C23×C4C23×C711yescharacteristic
577C23×C4C23×C711yescharacteristic
578C23×C4C23×C711yescharacteristic
579#123—232no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4C2×C4×C714yes—
589C2×C4⋊C4C2×C4×C714yes—
590C2×C4⋊C4C7×D414yes—
591C2×C4⋊C4C7×D414yes—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
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—41no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4C2×C4×C714yes—
622C2×C22⋊C4C2×C4×C714yes—
623C2×C22⋊C4C2×C4×C714yes—
624C2×C22⋊C4C7×D414yes—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—41no—
635C2×C42—41no—
636C2×C42—41no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651C22×C7—24no—
652C22×C7—24no—
653C22×C7—24no—
654C22×C7—42no—
655C22×C7—42no—
656C22×C7—42no—
657C22×C7—42no—
658C22×C7—42no—
659C22×C7—42no—
660C22×C7—42no—
661C22×C7—42no—
662C22×C7—42no—
663C22×C7—42no—
664C22×C7—42no—
665C22×C7—42no—
666C22×C7—42no—
667C22×C7—42no—
668C22×C7—42no—
669C22×C7—42no—
670C22×C7—42no—
671C22×C7—42no—
672C22×C7—42no—
673C22×C7—81no—
674C22×C7—81no—
675C22×C7—81no—
676C22×C7—81no—
677C22×C7—81no—
678C22×C7—81no—
679C22×C7—81no—
680C22×C7—81no—
681C22×C7C22×C22⋊C411yescharacteristic
682C22×C7C2×C4×D411yescharacteristic
683C22×C7C4×#4111yescharacteristic
684C22×C7C4×#4111yescharacteristic
685C22×C7C4×#4111yescharacteristic
686C22×C7#51811yescharacteristic
687C22×C7#52011yescharacteristic
688C22×C7C2×#12311yescharacteristic
689C22×C7#52511yescharacteristic
690C22×C7#52511yescharacteristic
691C22×C7#52511yescharacteristic
692C22×C7#52911yescharacteristic
693C22×C7#52911yescharacteristic
694C22×C7#53211yescharacteristic
695C22×C7#53211yescharacteristic
696C22×C7#53811yescharacteristic
697C22×C7#53911yescharacteristic
698C22×C7#54011yescharacteristic
699C22×C7#54211yescharacteristic
700C22×C7D4211yescharacteristic
701C22×C7D4211yescharacteristic
702C22×C7#54611yescharacteristic
703C22×C7#54611yescharacteristic
704C22×C7#54611yescharacteristic
705C22×C7#54711yescharacteristic
706C22×C7#54811yescharacteristic
707C22×C7#54811yescharacteristic
708C22×C7#55011yescharacteristic
709C22×C7#55011yescharacteristic
710C22×C7#55111yescharacteristic
711C22×C7#55111yescharacteristic
712C22×C7#55211yescharacteristic
713C22×C7#55311yescharacteristic
714C22×C7#55311yescharacteristic
715C22×C7#55911yescharacteristic
716C4×C7—24no—
717C4×C7—24no—
718C4×C7—24no—
719C4×C7—24no—
720C4×C7—42no—
721C4×C7—42no—
722C4×C7—42no—
723C4×C7—42no—
724C4×C7—42no—
725C4×C7—42no—
726C4×C7—42no—
727C4×C7—81no—
728C4×C7—81no—
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—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24C22×C4×C712yes—
756C24C22×C4×C712yes—
757C24C2×C7×D412yes—
758C24C7×#4112yes—
759C24C24×C711yescharacteristic
760C2×D4—28no—
761C2×D4—28no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
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—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—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—28no—
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—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4C22×C4×C712yes—
847C22×C4C22×C4×C712yes—
848C22×C4C22×C4×C712yes—
849C22×C4C22×C4×C712yes—
850C22×C4C22×C4×C712yes—
851C22×C4C2×C7×D412yes—
852C22×C4C2×C7×D412yes—
853C22×C4C2×C7×D412yes—
854C22×C4C2×C7×D412yes—
855C22×C4C2×C7×D412yes—
856C22×C4C2×C7×D412yes—
857C22×C4C2×C7×D412yes—
858C22×C4C2×C7×D412yes—
859C22×C4C7×#4112yes—
860C22×C4C7×#4112yes—
861C22×C4C7×#4112yes—
862C22×C4C7×#4112yes—
863C22×C4C7×#4112yes—
864C22×C4C7×#4112yes—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—44no—
868C4⋊C4C7×C22⋊C4116yescomplemented
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C42—28no—
881C42—44no—
882C42—44no—
883C42—44no—
884C2×C7—44no—
885C2×C7—82no—
886C2×C7#229711yescharacteristic
887C2×C7C4×#12311yescharacteristic
888C2×C7#233511yescharacteristic
889C2×C7D4×C22⋊C411yescharacteristic
890C2×C7#234111yescharacteristic
891C2×C7#235911yescharacteristic
892C2×C7#237411yescharacteristic
893C2×C7#244311yescharacteristic
894C2×C7#244511yescharacteristic
895C2×C7#245611yescharacteristic
896C2×C7#245811yescharacteristic
897C2×C7#246111yescharacteristic
898C2×C7#247111yescharacteristic
899C2×C7#255411yescharacteristic
900C2×C7#255811yescharacteristic
901C23—22no—
902C23—22no—
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—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
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—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23C4×C7×D414yes—
971C23C23×C4×C711yescharacteristic
972C23C22×C7×D411yescharacteristic
973C23C22×C7×D411yescharacteristic
974C23C22×C7×D411yescharacteristic
975C23C2×C7×#4111yescharacteristic
976C23C2×C7×#4111yescharacteristic
977C23C2×C7×#4111yescharacteristic
978C23C2×C7×#4111yescharacteristic
979C23C2×C7×#4111yescharacteristic
980C23C2×C7×#4111yescharacteristic
981C23C2×C7×#4111yescharacteristic
982C23C7×H(5,𝔽2)11yescharacteristic
983C23C7×H(5,𝔽2)11yescharacteristic
984C23C7×H(5,𝔽2)11yescharacteristic
985C23C7×2−1+411yescharacteristic
986D4—416no—
987C2×C4—22no—
988C2×C4—22no—
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—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—416no—
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×C4C2×C7×C22⋊C414yes—
1076C2×C4C2×C7×C22⋊C414yes—
1077C2×C4C2×C7×C22⋊C414yes—
1078C2×C4C7×#12314yescomplemented
1079C7#1409511yescharacteristic, direct product factor, Sylow
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C22×C7×C22⋊C411yescharacteristic
1111C22C2×C4×C7×D411yescharacteristic
1112C22C4×C7×#4111yescharacteristic
1113C22C4×C7×#4111yescharacteristic
1114C22C4×C7×#4111yescharacteristic
1115C22C7×#51811yescharacteristic
1116C22C7×#52011yescharacteristic
1117C22C2×C7×#12311yescharacteristic
1118C22C7×#52511yescharacteristic
1119C22C7×#52511yescharacteristic
1120C22C7×#52511yescharacteristic
1121C22C7×#52911yescharacteristic
1122C22C7×#52911yescharacteristic
1123C22C7×#53211yescharacteristic
1124C22C7×#53211yescharacteristic
1125C22C7×#53811yescharacteristic
1126C22C7×#53911yescharacteristic
1127C22C7×#54011yescharacteristic
1128C22C7×#54211yescharacteristic
1129C22C7×D4211yescharacteristic
1130C22C7×D4211yescharacteristic
1131C22C7×#54611yescharacteristic
1132C22C7×#54611yescharacteristic
1133C22C7×#54611yescharacteristic
1134C22C7×#54711yescharacteristic
1135C22C7×#54811yescharacteristic
1136C22C7×#54811yescharacteristic
1137C22C7×#55011yescharacteristic
1138C22C7×#55011yescharacteristic
1139C22C7×#55111yescharacteristic
1140C22C7×#55111yescharacteristic
1141C22C7×#55211yescharacteristic
1142C22C7×#55311yescharacteristic
1143C22C7×#55311yescharacteristic
1144C22C7×#55911yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—81no—
1157C4—81no—
1158C2—44no—
1159C2—82no—
1160C2C7×#229711yescharacteristic
1161C2C4×C7×#12311yescharacteristic
1162C2C7×#233511yescharacteristic
1163C2C7×D4×C22⋊C411yescharacteristic
1164C2C7×#234111yescharacteristic
1165C2C7×#235911yescharacteristic
1166C2C7×#237411yescharacteristic
1167C2C7×#244311yescharacteristic
1168C2C7×#244511yescharacteristic
1169C2C7×#245611yescharacteristic
1170C2C7×#245811yescharacteristic
1171C2C7×#246111yescharacteristic
1172C2C7×#247111yescharacteristic
1173C2C7×#255411yescharacteristic
1174C2C7×#255811yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C7×#387C2semidirect
4. C2×C4×C7×C4⋊C4C2semidirect
5. C2×C4×C7×C22⋊C4C2semidirect
6. C7×#1441C2semidirect
7. C7×#1439C2semidirect
8. C7×#1439C2semidirect
10. C7×#1437C2semidirect
11. C7×#1437C2semidirect
12. C7×#1437C2semidirect
13. C7×#1437C2semidirect
14. C7×#1436C2semidirect
15. C7×C22⋊#95C2semidirect
20. C2×C7×#123C4semidirect
58. #14095C7direct (N × H)
162. C2×#387C2×C7semidirect
163. C2×C4×C4⋊C4C2×C7semidirect
164. C2×C4×C22⋊C4C2×C7semidirect
165. #1441C2×C7semidirect
166. #1439C2×C7semidirect
167. #1439C2×C7semidirect
169. #1437C2×C7semidirect
170. #1437C2×C7semidirect
171. #1437C2×C7semidirect
172. #1437C2×C7semidirect
173. #1436C2×C7semidirect
174. C22⋊#95C2×C7semidirect
314. C7×C4⋊C4C22⋊C4semidirect
334. C2×#123C4×C7semidirect
549. C2×C4×C7#123semidirect
868. C4⋊C4C7×C22⋊C4semidirect
1078. C2×C4C7×#123semidirect
1079. C7#14095direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1232
C2×C7×#3902
C2×C7×#3872
C2×C4×C7×C4⋊C42
C2×C4×C7×C22⋊C42
C7×#14412
C7×#14392
C7×#14382
C7×#14372
C7×#14362
C7×C22⋊#952
#140957