Finite Group Databasebeta

← #13275397

Subgroups — #13275397

Order 1792.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89728C211yesmaximal, characteristic
2C2×#89729C211yesmaximal, characteristic
3C2×#89730C211yesmaximal, characteristic
4C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
7C2×#89438C211yesmaximal, characteristic, complemented
8C7×#1437C211yesmaximal, characteristic, complemented
9#11729299C211yesmaximal, characteristic, complemented
10C4×C7⋊#95C211yesmaximal, characteristic, complemented
11#11727162C211yesmaximal, characteristic, complemented
12#11727162C211yesmaximal, characteristic, complemented
13#11727160C211yesmaximal, characteristic, complemented
14#11727159C211yesmaximal, characteristic, complemented
15Dic7×#95C211yesmaximal, characteristic, complemented
16C23×C22⋊D7C2211yescharacteristic
17C24×Dic7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C22×C4×Dic7C2211yescharacteristic
36C22×C4×Dic7C2211yescharacteristic
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
51#89730C418yescomplemented
52#89729C418yescomplemented
53#89728C418yescomplemented
54C22⋊C4×Dic7—24no—
55C22⋊C4×Dic7—24no—
56C4×(C2×D7)⋊C4—24no—
57#89438—24no—
58#13824—71nomaximal, Sylow
59C25×C7C2311yescharacteristic
60C24×D7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C22×C22⋊D7—41no—
68C22×C22⋊D7—41no—
69C22×C22⋊D7—41no—
70C22×C22⋊D7—41no—
71C22×C22⋊D7C2×C414yes—
72C22×C22⋊D7C2×C414yes—
73C22×C22⋊D7C2×C414yes—
74C23×Dic7—22no—
75C23×Dic7—22no—
76C23×Dic7—22no—
77C23×Dic7—22no—
78C23×Dic7—41no—
79C23×Dic7—41no—
80C23×Dic7C2×C414yescomplemented
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C22×C4×D7—22no—
89C22×C4×D7—22no—
90C22×C4×D7—22no—
91C22×C4×D7—22no—
92C22×C4×D7—41no—
93C22×C4×D7—41no—
94C22×C4×D7C2×C414yescomplemented
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—22no—
98C2×C7×C22⋊C4—22no—
99C2×C7×C22⋊C4—41no—
100C2×C7×C22⋊C4—41no—
101C2×C7×C22⋊C4C2×C414yes—
102C2×C7×C22⋊C4C2×C414yescomplemented
103C2×C7×C22⋊C4C2×C414yescomplemented
104C2×C42×C7—22no—
105C2×C42×C7—22no—
106C2×C42×C7—41no—
107C2×C22⋊Dic7—22no—
108C2×C22⋊Dic7—22no—
109C2×C22⋊Dic7—22no—
110C2×C22⋊Dic7—22no—
111C2×C22⋊Dic7C2×C414yes—
112C2×C22⋊Dic7C2×C414yescomplemented
113C2×(C2×D7)⋊C4—22no—
114C2×(C2×D7)⋊C4—22no—
115C2×(C2×D7)⋊C4—22no—
116C2×(C2×D7)⋊C4—22no—
117C2×(C2×D7)⋊C4—22no—
118C2×(C2×D7)⋊C4—22no—
119C2×(C2×D7)⋊C4—22no—
120C2×(C2×D7)⋊C4—22no—
121C2×(C2×D7)⋊C4—41no—
122C2×(C2×D7)⋊C4—41no—
123C2×(C2×D7)⋊C4C2×C414yes—
124C2×(C2×D7)⋊C4C2×C414yes—
125C2×(C2×D7)⋊C4C2×C414yescomplemented
126C2×(C2×D7)⋊C4C2×C414yescomplemented
127C2×(C2×D7)⋊C4C2×C414yescomplemented
128C2×Dic7⋊C4—41no—
129C2×Dic7⋊C4—41no—
130C2×Dic7⋊C4C2×C414yescomplemented
131C2×C4×Dic7—22no—
132C2×C4×Dic7—22no—
133C2×C4×Dic7—22no—
134C2×C4×Dic7—22no—
135C2×C4×Dic7—22no—
136C2×C4×Dic7—22no—
137C2×C4×Dic7—22no—
138C2×C4×Dic7—22no—
139C2×C4×Dic7—22no—
140C2×C4×Dic7—22no—
141C2×C4×Dic7—41no—
142C2×C4×Dic7—41no—
143C2×C4×Dic7—41no—
144C2×C4×Dic7—41no—
145C2×C4×Dic7—41no—
146C2×C4×Dic7—41no—
147C2×C4×Dic7—41no—
148C2×C4×Dic7C2×C414yescomplemented
149C7×#95—22no—
150C7×#95—22no—
151C7×#95—41no—
152C7⋊#95—22no—
153C7⋊#95—22no—
154C7⋊#95—22no—
155C7⋊#95—22no—
156C7⋊#95—41no—
157C7⋊#95C2×C414yescomplemented
158C7⋊#95C2×C414yescomplemented
159C7⋊#95C2×C414yescomplemented
160C7⋊#95C2×C414yescomplemented
161C7⋊#95D414yescomplemented
162C7⋊#95D414yescomplemented
163C2×#390—71no—
164C2×#386—71no—
165C2×#386—71no—
166C2×C4×C22⋊C4—71no—
167C2×C4×C22⋊C4—71no—
168C2×C4×C22⋊C4—71no—
169C2×C4×C22⋊C4—71no—
170#1437—71no—
171#1437—71no—
172#1437—71no—
173#1437D711yescharacteristic, complemented
174#1436—71no—
175#1436—71no—
176C4×#95—71no—
177C4×#95—71no—
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×C7C22×C412yes—
191C24×C7C22×C412yes—
192C24×C7C22×C412yes—
193C24×C7C2411yescharacteristic
194C23×D7—21no—
195C23×D7—21no—
196C23×D7—21no—
197C23×D7—21no—
198C23×D7—21no—
199C23×D7—21no—
200C23×D7—21no—
201C23×D7—21no—
202C23×D7—21no—
203C23×D7—21no—
204C23×D7—21no—
205C23×D7—21no—
206C23×D7C22×C412yes—
207C23×D7C22×C412yes—
208C23×D7C22×C412yes—
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×C7C22×C412yes—
242C22×C4×C7C22×C412yes—
243C22×C4×C7C22×C412yes—
244C22×C4×C7C22×C412yes—
245C22×C4×C7C22×C412yes—
246C22×C4×C7C22×C412yes—
247C22×C4×C7C2×D412yes—
248C22×C4×C7C2×D412yes—
249C22×C4×C7#4112yes—
250C22×C4×C7#4112yes—
251C2×C22⋊D7—44no—
252C2×C22⋊D7—44no—
253C2×C22⋊D7—44no—
254C2×C22⋊D7—44no—
255C2×C22⋊D7—44no—
256C2×C22⋊D7—44no—
257C2×C22⋊D7C42116yescomplemented
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7—21no—
265C22×Dic7—21no—
266C22×Dic7—21no—
267C22×Dic7—21no—
268C22×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7—21no—
271C22×Dic7—21no—
272C22×Dic7—21no—
273C22×Dic7—21no—
274C22×Dic7—21no—
275C22×Dic7—21no—
276C22×Dic7—21no—
277C22×Dic7—21no—
278C22×Dic7—21no—
279C22×Dic7—21no—
280C22×Dic7—21no—
281C22×Dic7—21no—
282C22×Dic7—21no—
283C22×Dic7—21no—
284C22×Dic7—21no—
285C22×Dic7—21no—
286C22×Dic7—21no—
287C22×Dic7—21no—
288C22×Dic7—21no—
289C22×Dic7—21no—
290C22×Dic7—28no—
291C22×Dic7—28no—
292C22×Dic7—44no—
293C22×Dic7—44no—
294C22×Dic7—44no—
295C22×Dic7—44no—
296C22×Dic7—44no—
297C22×Dic7C22×C412yes—
298C22×Dic7C22×C412yes—
299C22×Dic7C22×C412yes—
300C22×Dic7C22×C412yes—
301C22×Dic7C22×C412yes—
302C22×Dic7C22×C412yes—
303C22×Dic7C22×C412yes—
304C22×Dic7C22×C412yes—
305C22×Dic7C22×C412yes—
306C22×Dic7C2×D412yes—
307C22×Dic7C2×D412yes—
308C22×Dic7C2×D412yes—
309C22×Dic7C2×D412yes—
310C22×Dic7#4112yes—
311C22×Dic7#4112yes—
312C22×Dic7#4112yes—
313C22×Dic7#4112yes—
314C2×C4×D7—28no—
315C2×C4×D7—28no—
316C2×C4×D7—44no—
317C2×C4×D7—44no—
318C2×C4×D7—44no—
319C2×C4×D7—44no—
320C2×C4×D7—44no—
321C7×C22⋊C4—28no—
322C7×C22⋊C4—28no—
323C7×C22⋊C4—44no—
324C42×C7—44no—
325C22⋊Dic7—28no—
326C22⋊Dic7—28no—
327(C2×D7)⋊C4—28no—
328(C2×D7)⋊C4—28no—
329(C2×D7)⋊C4—28no—
330(C2×D7)⋊C4—28no—
331(C2×D7)⋊C4—44no—
332Dic7⋊C4—44no—
333C4×Dic7—44no—
334C4×Dic7—44no—
335C4×Dic7—44no—
336C4×Dic7—44no—
337C4×Dic7—44no—
338C4×Dic7—44no—
339C23×D4—71no—
340C24×C4—71no—
341C24×C4—71no—
342C22×C4⋊C4—71no—
343C22×C22⋊C4—71no—
344C22×C22⋊C4—71no—
345C22×C22⋊C4—71no—
346C22×C22⋊C4—71no—
347C22×C22⋊C4—71no—
348C22×C22⋊C4—71no—
349C22×C22⋊C4—71no—
350C22×C22⋊C4C2×D711yescharacteristic
351C22×C22⋊C4C2×D711yescharacteristic
352C22×C22⋊C4C2×D711yescharacteristic
353C22×C42—71no—
354C22×C42—71no—
355C22×C42—71no—
356C22×C42—71no—
357C22×C42—71no—
358C22×C42—71no—
359C22×C42C2×D711yescharacteristic
360#390—78no—
361#386—78no—
362#386—78no—
363C4×C22⋊C4—144no—
364C4×C22⋊C4—144no—
365C4×C22⋊C4—144no—
366C4×C22⋊C4—144no—
367C2×#95—71no—
368C2×#95—71no—
369C2×#95—71no—
370C2×#95—71no—
371C2×#95—71no—
372C2×#95—71no—
373C2×#95—71no—
374C2×#95—71no—
375C2×#95—71no—
376C2×#95—71no—
377C2×#95—71no—
378C2×#95C2×D711yescharacteristic
379C2×#95C2×D711yescharacteristic
380C2×#95C2×D711yescharacteristic
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—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×C7C2×C4214yes—
416C23×C7C23×C411yescharacteristic
417C23×C7C23×C411yescharacteristic
418C23×C7C23×C411yescharacteristic
419C23×C7C22×D411yescharacteristic
420C23×C7C22×D411yescharacteristic
421C23×C7C2×#4111yescharacteristic
422C23×C7C2×#4111yescharacteristic
423C23×C7C2×#4111yescharacteristic
424C23×C7C2×#4111yescharacteristic
425C23×C7C2×#4111yescharacteristic
426C23×C7C2×#4111yescharacteristic
427C23×C7H(5,𝔽2)11yescharacteristic
428C23×C7H(5,𝔽2)11yescharacteristic
429C23×C7H(5,𝔽2)11yescharacteristic
430C23×C7H(5,𝔽2)11yescharacteristic
431C22×D7—22no—
432C22×D7—22no—
433C22×D7—22no—
434C22×D7—22no—
435C22×D7—22no—
436C22×D7—22no—
437C22×D7—22no—
438C22×D7—22no—
439C22×D7—22no—
440C22×D7—22no—
441C22×D7—22no—
442C22×D7—22no—
443C22×D7—22no—
444C22×D7—22no—
445C22×D7—22no—
446C22×D7—22no—
447C22×D7—22no—
448C22×D7—22no—
449C22×D7—41no—
450C22×D7—41no—
451C22×D7—41no—
452C22×D7—41no—
453C22×D7—41no—
454C22×D7—41no—
455C22×D7—41no—
456C22×D7—41no—
457C22×D7—41no—
458C22×D7—41no—
459C22×D7—41no—
460C22×D7—41no—
461C22×D7—41no—
462C22×D7—41no—
463C22×D7—41no—
464C22×D7—41no—
465C22×D7C2×C4214yes—
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—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×C7C4×D414yes—
507C2×C4×C7C4×D414yes—
508C22⋊D7—416no—
509C2×Dic7—22no—
510C2×Dic7—22no—
511C2×Dic7—22no—
512C2×Dic7—22no—
513C2×Dic7—22no—
514C2×Dic7—22no—
515C2×Dic7—22no—
516C2×Dic7—22no—
517C2×Dic7—22no—
518C2×Dic7—22no—
519C2×Dic7—22no—
520C2×Dic7—22no—
521C2×Dic7—22no—
522C2×Dic7—22no—
523C2×Dic7—22no—
524C2×Dic7—22no—
525C2×Dic7—22no—
526C2×Dic7—22no—
527C2×Dic7—22no—
528C2×Dic7—22no—
529C2×Dic7—22no—
530C2×Dic7—22no—
531C2×Dic7—22no—
532C2×Dic7—22no—
533C2×Dic7—22no—
534C2×Dic7—22no—
535C2×Dic7—22no—
536C2×Dic7—22no—
537C2×Dic7—22no—
538C2×Dic7—22no—
539C2×Dic7—22no—
540C2×Dic7—22no—
541C2×Dic7—22no—
542C2×Dic7—22no—
543C2×Dic7—22no—
544C2×Dic7—22no—
545C2×Dic7—416no—
546C2×Dic7—41no—
547C2×Dic7—41no—
548C2×Dic7—41no—
549C2×Dic7—41no—
550C2×Dic7—41no—
551C2×Dic7—41no—
552C2×Dic7—41no—
553C2×Dic7—41no—
554C2×Dic7C2×C4214yes—
555C2×Dic7C4×D414yes—
556C2×Dic7C4×D414yes—
557C2×Dic7C4×D414yes—
558C2×Dic7C4×D414yes—
559C4×D7—416no—
560C25—71no—
561C25C22×D711yescharacteristic
562C22×D4—74no—
563C22×D4—74no—
564C22×D4—74no—
565C22×D4—281no—
566C22×D4—281no—
567C22×D4—281no—
568C22×D4—281no—
569C23×C4—71no—
570C23×C4—71no—
571C23×C4—71no—
572C23×C4—71no—
573C23×C4—71no—
574C23×C4—71no—
575C23×C4—71no—
576C23×C4—74no—
577C23×C4—74no—
578C23×C4—142no—
579C23×C4—142no—
580C23×C4—142no—
581C23×C4—142no—
582C23×C4—142no—
583C23×C4—142no—
584C23×C4—142no—
585C23×C4—142no—
586C23×C4—281no—
587C23×C4—281no—
588C23×C4—281no—
589C23×C4—281no—
590C23×C4C22×D711yescharacteristic
591C23×C4C22×D711yescharacteristic
592C23×C4C22×D711yescharacteristic
593C23×C4C22×D711yescharacteristic
594C23×C4C22×D711yescharacteristic
595C23×C4C22×D711yescharacteristic
596C2×C4⋊C4—74no—
597C2×C4⋊C4—281no—
598C2×C4⋊C4—281no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—74no—
606C2×C22⋊C4—74no—
607C2×C22⋊C4—74no—
608C2×C22⋊C4—74no—
609C2×C22⋊C4—74no—
610C2×C22⋊C4—74no—
611C2×C22⋊C4—74no—
612C2×C22⋊C4—142no—
613C2×C22⋊C4—142no—
614C2×C22⋊C4—142no—
615C2×C22⋊C4—142no—
616C2×C22⋊C4—142no—
617C2×C22⋊C4—142no—
618C2×C22⋊C4—142no—
619C2×C22⋊C4—142no—
620C2×C22⋊C4—142no—
621C2×C22⋊C4—142no—
622C2×C22⋊C4—142no—
623C2×C22⋊C4—142no—
624C2×C22⋊C4—281no—
625C2×C22⋊C4—281no—
626C2×C22⋊C4C4×D714yes—
627C2×C22⋊C4C4×D714yescomplemented
628C2×C22⋊C4C4×D714yescomplemented
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—41no—
632C2×C42—74no—
633C2×C42—142no—
634C2×C42—142no—
635C2×C42—142no—
636C2×C42—142no—
637C2×C42—142no—
638C2×C42—142no—
639C2×C42—142no—
640C2×C42—142no—
641C2×C42—142no—
642C2×C42—142no—
643C2×C42—281no—
644C2×C42—281no—
645C2×C42—281no—
646C2×C42—281no—
647C2×C42—281no—
648C2×C42—281no—
649C2×C42—281no—
650#95—22no—
651#95—22no—
652#95—41no—
653#95—74no—
654#95—74no—
655#95—74no—
656#95—74no—
657#95—74no—
658#95—74no—
659#95—142no—
660#95—142no—
661#95—142no—
662#95—142no—
663#95—281no—
664C22×C7—24no—
665C22×C7—24no—
666C22×C7—24no—
667C22×C7—42no—
668C22×C7—42no—
669C22×C7—42no—
670C22×C7—42no—
671C22×C7—42no—
672C22×C7—42no—
673C22×C7—42no—
674C22×C7—42no—
675C22×C7—42no—
676C22×C7—42no—
677C22×C7—42no—
678C22×C7—42no—
679C22×C7C22×C4211yescharacteristic
680C22×C7C2×C4×D411yescharacteristic
681C22×C7C2×C4×D411yescharacteristic
682C22×C7C2×C4×D411yescharacteristic
683C22×C7C2×C4×D411yescharacteristic
684C22×C7C2×C4×D411yescharacteristic
685C22×C7C2×C4×D411yescharacteristic
686C22×C7C4×#4111yescharacteristic
687C22×C7C4×#4111yescharacteristic
688C22×C7C4×#4111yescharacteristic
689C22×C7C4×#4111yescharacteristic
690C22×C7C4×#4111yescharacteristic
691C22×C7C4×#4111yescharacteristic
692C22×C7#51811yescharacteristic
693C22×C7#51811yescharacteristic
694C22×C7#51811yescharacteristic
695C22×C7#51811yescharacteristic
696C22×C7#51811yescharacteristic
697C22×C7#51811yescharacteristic
698C22×C7D4211yescharacteristic
699C22×C7#54611yescharacteristic
700C22×C7#54611yescharacteristic
701C22×C7#54611yescharacteristic
702C22×C7#54611yescharacteristic
703C22×C7#55011yescharacteristic
704C22×C7#55011yescharacteristic
705C22×C7#55111yescharacteristic
706C22×C7#55111yescharacteristic
707C22×C7#55311yescharacteristic
708C22×C7#55311yescharacteristic
709C22×C7#55311yescharacteristic
710C22×C7#55311yescharacteristic
711C22×C7#55511yescharacteristic
712C22×C7#55511yescharacteristic
713C22×C7#55911yescharacteristic
714C2×D7—24no—
715C2×D7—24no—
716C2×D7—24no—
717C2×D7—42no—
718C2×D7—42no—
719C2×D7—42no—
720C2×D7—42no—
721C2×D7—42no—
722C2×D7—42no—
723C2×D7—42no—
724C2×D7—42no—
725C2×D7—42no—
726C2×D7—42no—
727C2×D7—42no—
728C2×D7—42no—
729C4×C7—24no—
730C4×C7—24no—
731C4×C7—42no—
732C4×C7—42no—
733C4×C7—42no—
734C4×C7—42no—
735Dic7—24no—
736Dic7—24no—
737Dic7—24no—
738Dic7—24no—
739Dic7—24no—
740Dic7—42no—
741Dic7—42no—
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—72no—
755C24—72no—
756C24—72no—
757C24—141no—
758C24—141no—
759C24—141no—
760C24—141no—
761C24—141no—
762C24—141no—
763C24—141no—
764C24—141no—
765C24—141no—
766C24—141no—
767C24—141no—
768C24—141no—
769C24C2×C4×D712yes—
770C24C2×C4×D712yes—
771C24C2×C4×D712yes—
772C24C23×D711yescharacteristic
773C2×D4—716no—
774C2×D4—284no—
775C2×D4—284no—
776C2×D4—284no—
777C2×D4—284no—
778C2×D4—284no—
779C2×D4—284no—
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—72no—
813C22×C4—72no—
814C22×C4—72no—
815C22×C4—72no—
816C22×C4—72no—
817C22×C4—72no—
818C22×C4—72no—
819C22×C4—72no—
820C22×C4—72no—
821C22×C4—72no—
822C22×C4—72no—
823C22×C4—72no—
824C22×C4—72no—
825C22×C4—72no—
826C22×C4—72no—
827C22×C4—72no—
828C22×C4—72no—
829C22×C4—148no—
830C22×C4—148no—
831C22×C4—148no—
832C22×C4—141no—
833C22×C4—141no—
834C22×C4—141no—
835C22×C4—141no—
836C22×C4—141no—
837C22×C4—141no—
838C22×C4—141no—
839C22×C4—141no—
840C22×C4—141no—
841C22×C4—141no—
842C22×C4—141no—
843C22×C4—141no—
844C22×C4—141no—
845C22×C4—141no—
846C22×C4—141no—
847C22×C4—141no—
848C22×C4—141no—
849C22×C4—141no—
850C22×C4—141no—
851C22×C4—141no—
852C22×C4—141no—
853C22×C4—141no—
854C22×C4—141no—
855C22×C4—141no—
856C22×C4—141no—
857C22×C4—141no—
858C22×C4—141no—
859C22×C4—141no—
860C22×C4—141no—
861C22×C4—141no—
862C22×C4—141no—
863C22×C4—141no—
864C22×C4—148no—
865C22×C4—284no—
866C22×C4—284no—
867C22×C4—284no—
868C22×C4—284no—
869C22×C4—284no—
870C22×C4—284no—
871C22×C4—284no—
872C22×C4—284no—
873C22×C4—284no—
874C22×C4—284no—
875C22×C4C2×C4×D712yes—
876C22×C4C2×C4×D712yes—
877C22×C4C2×C4×D712yes—
878C22×C4C2×C4×D712yes—
879C22×C4C2×C4×D712yes—
880C22×C4C2×C4×D712yes—
881C22×C4D4×D712yes—
882C22×C4D4×D712yes—
883C22×C4#115912yes—
884C22×C4#115912yes—
885C4⋊C4—284no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—44no—
889C22⋊C4—148no—
890C22⋊C4—148no—
891C22⋊C4—148no—
892C22⋊C4—148no—
893C22⋊C4—148no—
894C22⋊C4—148no—
895C22⋊C4—284no—
896C42—44no—
897C42—284no—
898C42—284no—
899C42—284no—
900C42—284no—
901C42—284no—
902C42—284no—
903C2×C7—44no—
904C2×C7C42×D411yescharacteristic
905C2×C7C42×D411yescharacteristic
906C2×C7#227311yescharacteristic
907C2×C7#235811yescharacteristic
908C2×C7#235811yescharacteristic
909C2×C7#236311yescharacteristic
910C2×C7#236311yescharacteristic
911C2×C7#236311yescharacteristic
912C2×C7#236311yescharacteristic
913C2×C7#236411yescharacteristic
914C2×C7#236411yescharacteristic
915C2×C7#236611yescharacteristic
916C2×C7#237211yescharacteristic
917C2×C7#237411yescharacteristic
918C2×C7#237411yescharacteristic
919D7—44no—
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—74no—
955C23—142no—
956C23—142no—
957C23—142no—
958C23—142no—
959C23—142no—
960C23—142no—
961C23—142no—
962C23—142no—
963C23—142no—
964C23—142no—
965C23—142no—
966C23—142no—
967C23—142no—
968C23—142no—
969C23—142no—
970C23—142no—
971C23—142no—
972C23—142no—
973C23—281no—
974C23—281no—
975C23—281no—
976C23—281no—
977C23—281no—
978C23—281no—
979C23—281no—
980C23—281no—
981C23—281no—
982C23—281no—
983C23—281no—
984C23—281no—
985C23—281no—
986C23—281no—
987C23—281no—
988C23—281no—
989C23C42×D714yes—
990C23C22×C4×D711yescharacteristic
991C23C22×C4×D711yescharacteristic
992C23C22×C4×D711yescharacteristic
993C23C2×D4×D711yescharacteristic
994C23C2×D4×D711yescharacteristic
995C23C2×#115911yescharacteristic
996C23C2×#115911yescharacteristic
997C23#654811yescharacteristic
998C23#654811yescharacteristic
999C23D7×#4111yescharacteristic
1000C23D7×#4111yescharacteristic
1001C23D7×#4111yescharacteristic
1002C23D7×#4111yescharacteristic
1003C23#655311yescharacteristic
1004C23#655311yescharacteristic
1005D4—2816no—
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—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—74no—
1047C2×C4—74no—
1048C2×C4—74no—
1049C2×C4—74no—
1050C2×C4—74no—
1051C2×C4—142no—
1052C2×C4—142no—
1053C2×C4—142no—
1054C2×C4—142no—
1055C2×C4—142no—
1056C2×C4—142no—
1057C2×C4—142no—
1058C2×C4—142no—
1059C2×C4—142no—
1060C2×C4—142no—
1061C2×C4—142no—
1062C2×C4—142no—
1063C2×C4—142no—
1064C2×C4—142no—
1065C2×C4—142no—
1066C2×C4—142no—
1067C2×C4—142no—
1068C2×C4—142no—
1069C2×C4—142no—
1070C2×C4—142no—
1071C2×C4—142no—
1072C2×C4—142no—
1073C2×C4—142no—
1074C2×C4—142no—
1075C2×C4—142no—
1076C2×C4—142no—
1077C2×C4—142no—
1078C2×C4—142no—
1079C2×C4—142no—
1080C2×C4—142no—
1081C2×C4—142no—
1082C2×C4—142no—
1083C2×C4—142no—
1084C2×C4—142no—
1085C2×C4—142no—
1086C2×C4—142no—
1087C2×C4—2816no—
1088C2×C4—2816no—
1089C2×C4—281no—
1090C2×C4—281no—
1091C2×C4—281no—
1092C2×C4—281no—
1093C2×C4—281no—
1094C2×C4—281no—
1095C2×C4—281no—
1096C2×C4—281no—
1097C2×C4(C22⋊D7)⋊C414yes—
1098C2×C4(C22⋊D7)⋊C414yes—
1099C7#1382411yescharacteristic, complemented, Sylow
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—144no—
1116C22—144no—
1117C22—144no—
1118C22—282no—
1119C22—282no—
1120C22—282no—
1121C22—282no—
1122C22—282no—
1123C22—282no—
1124C22—282no—
1125C22—282no—
1126C22—282no—
1127C22—282no—
1128C22—282no—
1129C22—282no—
1130C22C2×C42×D711yescharacteristic
1131C22C2×(C22⋊D7)⋊C411yescharacteristic
1132C22C2×(C22⋊D7)⋊C411yescharacteristic
1133C22#9017711yescharacteristic
1134C22#9021211yescharacteristic
1135C22#9021311yescharacteristic
1136C22#9021311yescharacteristic
1137C22C4×#115911yescharacteristic
1138C22C4×#115911yescharacteristic
1139C22C4×#115911yescharacteristic
1140C22C4×#115911yescharacteristic
1141C22C4×D4×D711yescharacteristic
1142C22C4×D4×D711yescharacteristic
1143C22C4×D4×D711yescharacteristic
1144C22C4×D4×D711yescharacteristic
1145C22#9023611yescharacteristic
1146C22#9023611yescharacteristic
1147C22#9023611yescharacteristic
1148C22#9023611yescharacteristic
1149C22#9028211yescharacteristic
1150C22#9029011yescharacteristic
1151C22#9029211yescharacteristic
1152C22#9030011yescharacteristic
1153C22#9030111yescharacteristic
1154C22#9030711yescharacteristic
1155C22#9030911yescharacteristic
1156C22#9034511yescharacteristic
1157C22#9034911yescharacteristic
1158C22#9035211yescharacteristic
1159C22#9036111yescharacteristic
1160C22#9036711yescharacteristic
1161C22#9037211yescharacteristic
1162C22#9039611yescharacteristic
1163C22#9040011yescharacteristic
1164C22#9040911yescharacteristic
1165C4—24no—
1166C4—24no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—144no—
1172C4—144no—
1173C4—144no—
1174C4—144no—
1175C4—144no—
1176C4—282no—
1177C4—282no—
1178C2—44no—
1179C2—284no—
1180C2C4×(C22⋊D7)⋊C411yescharacteristic
1181C2C4×(C22⋊D7)⋊C411yescharacteristic
1182C2#1173100511yescharacteristic
1183C2#1173212211yescharacteristic
1184C2#1173212311yescharacteristic
1185C2#1173232411yescharacteristic
1186C2#1173292511yescharacteristic
1187C2#1173292811yescharacteristic
1188C2#1173293211yescharacteristic
1189C2#1173293311yescharacteristic
1190C2#1173328111yescharacteristic
1191C2#1173328411yescharacteristic
1192C2#1173374911yescharacteristic
1193C2#1173375011yescharacteristic
1194C2#1173375111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC22×C7C22×C42
FittingC7×#1437C2
socle, cosocleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenter#1437D7
hypocenterC7#13824
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic7C2semidirect
5. C2×C22⋊C4×Dic7C2semidirect
6. C2×C4×(C2×D7)⋊C4C2semidirect
7. C2×#89438C2semidirect
8. C7×#1437C2semidirect
9. #11729299C2semidirect
10. C4×C7⋊#95C2semidirect
11. #11727162C2semidirect
12. #11727162C2semidirect
13. #11727160C2semidirect
14. #11727159C2semidirect
15. Dic7×#95C2semidirect
51. #89730C4semidirect
52. #89729C4semidirect
53. #89728C4semidirect
80. C23×Dic7C2×C4semidirect
94. C22×C4×D7C2×C4semidirect
102. C2×C7×C22⋊C4C2×C4semidirect
103. C2×C7×C22⋊C4C2×C4semidirect
112. C2×C22⋊Dic7C2×C4semidirect
125. C2×(C2×D7)⋊C4C2×C4semidirect
126. C2×(C2×D7)⋊C4C2×C4semidirect
127. C2×(C2×D7)⋊C4C2×C4semidirect
130. C2×Dic7⋊C4C2×C4semidirect
148. C2×C4×Dic7C2×C4semidirect
157. C7⋊#95C2×C4semidirect
158. C7⋊#95C2×C4semidirect
159. C7⋊#95C2×C4semidirect
160. C7⋊#95C2×C4semidirect
161. C7⋊#95D4semidirect
162. C7⋊#95D4semidirect
173. #1437D7semidirect
257. C2×C22⋊D7C42semidirect
627. C2×C22⋊C4C4×D7semidirect
628. C2×C22⋊C4C4×D7semidirect
1099. C7#13824semidirect

Maximal subgroups

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

subgroupindex
C2×#897282
C2×#897292
C2×#897302
C2×C22⋊C4×Dic72
C2×C4×(C2×D7)⋊C42
C2×#894382
C7×#14372
#117292992
C4×C7⋊#952
#117271622
#117271602
#117271592
Dic7×#952
#138247