Finite Group Databasebeta

← #13282288

Subgroups — #13282288

Order 1792.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6460C211yesmaximal, characteristic
2C2×C7×#387C211yesmaximal, characteristic, complemented
3C2×#89753C211yesmaximal, characteristic, complemented
4#11729324C211yesmaximal, characteristic
5#11729317C211yesmaximal, characteristic, complemented
6#11729291C211yesmaximal, characteristic
7#11729289C211yesmaximal, characteristic, complemented
8#11727181C211yesmaximal, characteristic
9(C2×D7)⋊#95C211yesmaximal, characteristic
10(C2×D7)⋊#95C211yesmaximal, characteristic
11#11727178C211yesmaximal, characteristic, complemented
12#11727178C211yesmaximal, characteristic, complemented
13#11727177C211yesmaximal, characteristic, complemented
14#11727176C211yesmaximal, characteristic, complemented
15#11727162C211yesmaximal, characteristic
16C23×C4×D7C2211yescharacteristic
17C23×Dic14C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C2×#6460—24no—
32C2×#6460—24no—
33C2×#6460C418yescomplemented
34C7×#387—24no—
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
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#89753—24no—
56#14448—71nomaximal, Sylow
57C24×D7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C22×C4×D7—22no—
73C22×C4×D7—22no—
74C22×C4×D7—41no—
75C22×C4×D7—41no—
76C22×C4×D7—41no—
77C22×C4×D7—41no—
78C22×C4×D7C2×C414yes—
79C22×Dic14—22no—
80C22×Dic14—22no—
81C22×Dic14—41no—
82C22×Dic14—41no—
83C22×Dic14—41no—
84C22×Dic14—41no—
85C22×Dic14C2×C414yes—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—41no—
89C2×C7×C4⋊C4C2×C414yes—
90C2×C7×C4⋊C4D414yes—
91C2×C7×C4⋊C4D414yes—
92C2×C42×C7—22no—
93C2×C42×C7—22no—
94C2×C42×C7—41no—
95C2×(C2×D7)⋊C4—22no—
96C2×(C2×D7)⋊C4—22no—
97C2×(C2×D7)⋊C4—22no—
98C2×(C2×D7)⋊C4—22no—
99C2×(C2×D7)⋊C4—22no—
100C2×(C2×D7)⋊C4—22no—
101C2×(C2×D7)⋊C4—22no—
102C2×(C2×D7)⋊C4—22no—
103C2×(C2×D7)⋊C4—22no—
104C2×(C2×D7)⋊C4—41no—
105C2×(C2×D7)⋊C4—41no—
106C2×(C2×D7)⋊C4—41no—
107C2×(C2×D7)⋊C4—41no—
108C2×(C2×D7)⋊C4—41no—
109C2×(C2×D7)⋊C4—41no—
110C2×(C2×D7)⋊C4C2×C414yes—
111C2×(C2×D7)⋊C4C2×C414yes—
112C2×(C2×D7)⋊C4Q814yescomplemented
113C2×C4⋊Dic7—22no—
114C2×C4⋊Dic7—22no—
115C2×C4⋊Dic7—22no—
116C2×C4⋊Dic7—22no—
117C2×C4⋊Dic7—22no—
118C2×C4⋊Dic7—22no—
119C2×C4⋊Dic7—41no—
120C2×C4⋊Dic7C2×C414yes—
121C2×C4⋊Dic7C2×C414yes—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—22no—
124C2×C4×Dic7—41no—
125#6460—232no—
126C7×#95—22no—
127C7×#95—22no—
128C7×#95—22no—
129C7×#95—22no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—41no—
135C7⋊#95—41no—
136C7⋊#95—41no—
137C7⋊#95—41no—
138C7⋊#95—41no—
139C7⋊#95—41no—
140C7⋊#95—41no—
141C7⋊#95—41no—
142C7⋊#95—41no—
143C7⋊#95—41no—
144C7⋊#95—41no—
145C7⋊#95—41no—
146C22×C22⋊Q8—71no—
147C2×#387—71no—
148C2×#387D711yescharacteristic, complemented
149#1446—71no—
150#1446—71no—
151#1445—71no—
152#1445—71no—
153#1439—71no—
154#1439—71no—
155#1437—71no—
156#1437—71no—
157C4⋊#95—71no—
158C4⋊#95—71no—
159C22⋊#95—71no—
160C22⋊#95—71no—
161C24×C7C2411yescharacteristic
162C23×D7—21no—
163C23×D7—21no—
164C23×D7—21no—
165C23×D7—21no—
166C23×D7—21no—
167C23×D7—21no—
168C23×D7—21no—
169C23×D7—21no—
170C23×D7—21no—
171C23×D7—21no—
172C23×D7—21no—
173C23×D7—21no—
174C23×D7C22×C412yes—
175C23×D7C2×Q812yes—
176C23×D7#4112yes—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
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×C7C22×C412yes—
216C22×C4×C7C22×C412yes—
217C22×C4×C7C22×C412yes—
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2×D412yes—
222C22×C4×C7C2×D412yes—
223C22×C4×C7C2×D412yes—
224C22×C4×C7C2×Q812yes—
225C22×C4×C7#4112yes—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—21no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
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×Dic7C22×C412yes—
271C22×Dic7C22×C412yes—
272C22×Dic7C22×C412yes—
273C22×Dic7C2×Q812yes—
274C22×Dic7#4112yes—
275C2×C4×D7—28no—
276C2×C4×D7—44no—
277C2×C4×D7—44no—
278C2×C4×D7—44no—
279C2×C4×D7—44no—
280C2×C4×D7—44no—
281C2×C4×D7—44no—
282C2×Dic14—28no—
283C2×Dic14—44no—
284C2×Dic14—44no—
285C2×Dic14—44no—
286C2×Dic14—44no—
287C2×Dic14—44no—
288C2×Dic14—44no—
289C7×C4⋊C4—44no—
290C7×C4⋊C4C22⋊C4116yescomplemented
291C42×C7—44no—
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4—28no—
294(C2×D7)⋊C4—44no—
295(C2×D7)⋊C4—44no—
296(C2×D7)⋊C4—44no—
297(C2×D7)⋊C4—44no—
298C4⋊Dic7—28no—
299C4⋊Dic7—28no—
300C4⋊Dic7—44no—
301C4×Dic7—44no—
302C23×Q8—71no—
303C24×C4—71no—
304C2×C22⋊Q8—78no—
305C2×C22⋊Q8—144no—
306C2×C22⋊Q8—144no—
307C22×C4⋊C4—71no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4—71no—
310C22×C4⋊C4C2×D711yescharacteristic
311C22×C4⋊C4C2×D711yescharacteristic
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4—71no—
317C22×C22⋊C4—71no—
318C22×C42—71no—
319C22×C42C2×D711yescharacteristic
320#387—24no—
321#387—144no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95—71no—
328C2×#95—71no—
329C2×#95—71no—
330C2×#95—71no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95C2×D711yescharacteristic
339C2×#95C2×D711yescharacteristic
340C2×#95C2×D711yescharacteristic
341C2×#95C2×D711yescharacteristic
342C23×C7C23×C411yescharacteristic
343C23×C7C22×D411yescharacteristic
344C23×C7C22×D411yescharacteristic
345C23×C7C22×Q811yescharacteristic
346C23×C7C2×#4111yescharacteristic
347C23×C7C2×#4111yescharacteristic
348C23×C7C2×#4111yescharacteristic
349C23×C7H(5,𝔽2)11yescharacteristic
350C23×C7H(5,𝔽2)11yescharacteristic
351C23×C7H(5,𝔽2)11yescharacteristic
352C23×C7H(5,𝔽2)11yescharacteristic
353C23×C7H(5,𝔽2)11yescharacteristic
354C23×C72−1+411yescharacteristic
355C23×C72−1+411yescharacteristic
356C23×C72−1+411yescharacteristic
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—41no—
376C22×D7—41no—
377C22×D7—41no—
378C22×D7—41no—
379C22×D7—41no—
380C22×D7—41no—
381C22×D7—41no—
382C22×D7—41no—
383C22×D7—41no—
384C22×D7—41no—
385C22×D7—41no—
386C22×D7—41no—
387C22×D7—41no—
388C22×D7—41no—
389C22×D7—41no—
390C22×D7—41no—
391C22×D7C4×Q814yes—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7C2×C22⋊C414yes—
439C2×C4×C7C2×C22⋊C414yes—
440C2×C4×C7C2×C22⋊C414yes—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—41no—
457C2×Dic7—41no—
458C2×Dic7—41no—
459C2×Dic7—41no—
460C2×Dic7—41no—
461C2×Dic7—41no—
462C2×Dic7—41no—
463C2×Dic7—41no—
464C2×Dic7—41no—
465C2×Dic7—41no—
466C2×Dic7—41no—
467C2×Dic7—41no—
468C2×Dic7—41no—
469C2×Dic7—41no—
470C2×Dic7—41no—
471C2×Dic7—41no—
472C2×Dic7—41no—
473C2×Dic7—41no—
474C2×Dic7—41no—
475C2×Dic7—41no—
476C2×Dic7—41no—
477C2×Dic7—41no—
478C2×Dic7—41no—
479C2×Dic7—41no—
480C2×Dic7—41no—
481C2×Dic7—41no—
482C2×Dic7—41no—
483C2×Dic7—41no—
484C2×Dic7—41no—
485C2×Dic7—41no—
486C2×Dic7—41no—
487C2×Dic7—41no—
488C2×Dic7—41no—
489C2×Dic7—41no—
490C4×D7—416no—
491Dic14—416no—
492C25—71no—
493C22×Q8—74no—
494C22×Q8—142no—
495C22×Q8—142no—
496C22×Q8—281no—
497C22×Q8—281no—
498C22×Q8—281no—
499C22×Q8—281no—
500C23×C4—71no—
501C23×C4—71no—
502C23×C4—71no—
503C23×C4—71no—
504C23×C4—71no—
505C23×C4—74no—
506C23×C4—71no—
507C23×C4—71no—
508C23×C4—142no—
509C23×C4—142no—
510C23×C4—281no—
511C23×C4—281no—
512C23×C4—281no—
513C23×C4—281no—
514C23×C4C22×D711yescharacteristic
515C23×C4C22×D711yescharacteristic
516C23×C4C22×D711yescharacteristic
517C23×C4C22×D711yescharacteristic
518C23×C4C22×D711yescharacteristic
519C23×C4C22×D711yescharacteristic
520C23×C4C22×D711yescharacteristic
521C22⋊Q8—1432no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4—74no—
526C2×C4⋊C4—74no—
527C2×C4⋊C4—142no—
528C2×C4⋊C4—142no—
529C2×C4⋊C4—142no—
530C2×C4⋊C4—142no—
531C2×C4⋊C4—142no—
532C2×C4⋊C4—142no—
533C2×C4⋊C4—281no—
534C2×C4⋊C4C4×D714yes—
535C2×C4⋊C4D2814yes—
536C2×C4⋊C4C22⋊D714yes—
537C2×C22⋊C4—74no—
538C2×C22⋊C4—74no—
539C2×C22⋊C4—74no—
540C2×C22⋊C4—142no—
541C2×C22⋊C4—142no—
542C2×C22⋊C4—142no—
543C2×C22⋊C4—142no—
544C2×C22⋊C4—142no—
545C2×C22⋊C4—142no—
546C2×C22⋊C4—142no—
547C2×C22⋊C4—142no—
548C2×C22⋊C4—142no—
549C2×C22⋊C4—281no—
550C2×C22⋊C4—281no—
551C2×C22⋊C4—281no—
552C2×C22⋊C4—281no—
553C2×C22⋊C4—281no—
554C2×C22⋊C4—281no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—41no—
558C2×C42—142no—
559C2×C42—142no—
560C2×C42—281no—
561#95—22no—
562#95—22no—
563#95—22no—
564#95—22no—
565#95—142no—
566#95—142no—
567#95—142no—
568#95—142no—
569#95—281no—
570#95—281no—
571#95—281no—
572#95—281no—
573#95—281no—
574#95—281no—
575#95—281no—
576#95—281no—
577#95—281no—
578#95—281no—
579#95—281no—
580#95—281no—
581C22×C7C22×C22⋊C411yescharacteristic
582C22×C7C2×C4×Q811yescharacteristic
583C22×C7C4×#4111yescharacteristic
584C22×C7#51811yescharacteristic
585C22×C7#51811yescharacteristic
586C22×C7#51911yescharacteristic
587C22×C7#52011yescharacteristic
588C22×C7#53511yescharacteristic
589C22×C7#53511yescharacteristic
590C22×C7#53511yescharacteristic
591C22×C7#53511yescharacteristic
592C22×C7#53811yescharacteristic
593C22×C7#53911yescharacteristic
594C22×C7#53911yescharacteristic
595C22×C7#53911yescharacteristic
596C22×C7#54211yescharacteristic
597C22×C7#54211yescharacteristic
598C22×C7#54311yescharacteristic
599C22×C7#54411yescharacteristic
600C22×C7#54611yescharacteristic
601C22×C7#54611yescharacteristic
602C22×C7#54711yescharacteristic
603C22×C7#54711yescharacteristic
604C22×C7#54811yescharacteristic
605C22×C7#54811yescharacteristic
606C22×C7D4×Q811yescharacteristic
607C22×C7D4×Q811yescharacteristic
608C22×C7#55111yescharacteristic
609C22×C7#55111yescharacteristic
610C22×C7#55411yescharacteristic
611C22×C7#55411yescharacteristic
612C22×C7#56211yescharacteristic
613C22×C7#56211yescharacteristic
614C22×C7#56311yescharacteristic
615C22×C7#56311yescharacteristic
616C2×D7—24no—
617C2×D7—24no—
618C2×D7—24no—
619C2×D7—42no—
620C2×D7—42no—
621C2×D7—42no—
622C2×D7—42no—
623C2×D7—42no—
624C2×D7—42no—
625C2×D7—42no—
626C2×D7—42no—
627C2×D7—42no—
628C2×D7—42no—
629C2×D7—42no—
630C2×D7—42no—
631C4×C7—24no—
632C4×C7—24no—
633C4×C7—24no—
634C4×C7—42no—
635C4×C7—42no—
636C4×C7—81no—
637C4×C7—81no—
638Dic7—42no—
639Dic7—42no—
640Dic7—42no—
641Dic7—42no—
642Dic7—42no—
643Dic7—81no—
644Dic7—81no—
645C24—72no—
646C24—72no—
647C24—72no—
648C24—141no—
649C24—141no—
650C24—141no—
651C24—141no—
652C24—141no—
653C24—141no—
654C24—141no—
655C24—141no—
656C24—141no—
657C24—141no—
658C24—141no—
659C24—141no—
660C24C23×D711yescharacteristic
661C2×Q8—148no—
662C2×Q8—284no—
663C2×Q8—284no—
664C2×Q8—284no—
665C2×Q8—284no—
666C2×Q8—284no—
667C2×Q8—284no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—72no—
707C22×C4—72no—
708C22×C4—72no—
709C22×C4—72no—
710C22×C4—72no—
711C22×C4—141no—
712C22×C4—141no—
713C22×C4—141no—
714C22×C4—141no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4—141no—
718C22×C4—141no—
719C22×C4—141no—
720C22×C4—141no—
721C22×C4—141no—
722C22×C4—141no—
723C22×C4—141no—
724C22×C4—141no—
725C22×C4—141no—
726C22×C4—141no—
727C22×C4—141no—
728C22×C4—141no—
729C22×C4—141no—
730C22×C4—141no—
731C22×C4—141no—
732C22×C4—141no—
733C22×C4—141no—
734C22×C4—141no—
735C22×C4—141no—
736C22×C4—141no—
737C22×C4—141no—
738C22×C4—141no—
739C22×C4—141no—
740C22×C4—141no—
741C22×C4—148no—
742C22×C4—141no—
743C22×C4—141no—
744C22×C4—141no—
745C22×C4—141no—
746C22×C4—141no—
747C22×C4—141no—
748C22×C4—141no—
749C22×C4—141no—
750C22×C4—141no—
751C22×C4—141no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—141no—
755C22×C4—141no—
756C22×C4—284no—
757C22×C4—284no—
758C22×C4—284no—
759C22×C4—284no—
760C22×C4—284no—
761C22×C4—284no—
762C22×C4C2×C4×D712yes—
763C22×C4C2×C4×D712yes—
764C22×C4C2×C4×D712yes—
765C22×C4C2×D2812yes—
766C22×C4C2×D2812yes—
767C22×C4C2×D2812yes—
768C22×C4#115912yes—
769C22×C4Q8×D712yes—
770C22×C4C2×C22⋊D712yes—
771C22×C4C2×C22⋊D712yes—
772C22×C4C2×C22⋊D712yes—
773C4⋊C4—44no—
774C4⋊C4—148no—
775C4⋊C4—148no—
776C4⋊C4—284no—
777C4⋊C4(C2×D7)⋊C4116yescomplemented
778C22⋊C4—148no—
779C22⋊C4—148no—
780C22⋊C4—284no—
781C22⋊C4—284no—
782C22⋊C4—284no—
783C22⋊C4—284no—
784C42—44no—
785C42—284no—
786C2×C7#230911yescharacteristic
787C2×C7#232911yescharacteristic
788C2×C7#233211yescharacteristic
789C2×C7#233911yescharacteristic
790C2×C7Q8×C22⋊C411yescharacteristic
791C2×C7#236811yescharacteristic
792C2×C7#237811yescharacteristic
793C2×C7#269211yescharacteristic
794C2×C7#269211yescharacteristic
795C2×C7#269611yescharacteristic
796C2×C7#269611yescharacteristic
797C2×C7#272011yescharacteristic
798C2×C7#272011yescharacteristic
799C2×C7#272311yescharacteristic
800C2×C7#272311yescharacteristic
801D7—44no—
802C23—74no—
803C23—142no—
804C23—142no—
805C23—142no—
806C23—142no—
807C23—142no—
808C23—142no—
809C23—142no—
810C23—142no—
811C23—142no—
812C23—142no—
813C23—142no—
814C23—142no—
815C23—142no—
816C23—142no—
817C23—142no—
818C23—142no—
819C23—142no—
820C23—142no—
821C23—281no—
822C23—281no—
823C23—281no—
824C23—281no—
825C23—281no—
826C23—281no—
827C23—281no—
828C23—281no—
829C23—281no—
830C23—281no—
831C23—281no—
832C23—281no—
833C23—281no—
834C23—281no—
835C23—281no—
836C23—281no—
837C23C22×C4×D711yescharacteristic
838C23C22×D2811yescharacteristic
839C23C2×#115911yescharacteristic
840C23#654811yescharacteristic
841C23C2×Q8×D711yescharacteristic
842C23#655111yescharacteristic
843C23D7×#4111yescharacteristic
844C23D7×#4111yescharacteristic
845C23#655311yescharacteristic
846C23#655311yescharacteristic
847C23#655311yescharacteristic
848C23#655311yescharacteristic
849C23#655411yescharacteristic
850C23#655411yescharacteristic
851C23C22×C22⋊D711yescharacteristic
852Q8—2816no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—142no—
900C2×C4—142no—
901C2×C4—142no—
902C2×C4—142no—
903C2×C4—142no—
904C2×C4—142no—
905C2×C4—142no—
906C2×C4—142no—
907C2×C4—142no—
908C2×C4—142no—
909C2×C4—142no—
910C2×C4—142no—
911C2×C4—142no—
912C2×C4—142no—
913C2×C4—142no—
914C2×C4—2816no—
915C2×C4—281no—
916C2×C4—281no—
917C2×C4—281no—
918C2×C4—281no—
919C2×C4—281no—
920C2×C4—281no—
921C2×C4—281no—
922C2×C4—281no—
923C2×C4—281no—
924C2×C4—281no—
925C2×C4—281no—
926C2×C4—281no—
927C2×C4—281no—
928C2×C4—281no—
929C2×C4—281no—
930C2×C4—281no—
931C2×C4—281no—
932C2×C4—281no—
933C2×C4—281no—
934C2×C4—281no—
935C2×C4—281no—
936C2×C4—281no—
937C2×C4—281no—
938C2×C4—281no—
939C2×C4—281no—
940C2×C4—281no—
941C2×C4—281no—
942C2×C4—281no—
943C2×C4—281no—
944C2×C4—281no—
945C2×C4—281no—
946C2×C4—281no—
947C2×C4—281no—
948C2×C4—281no—
949C2×C4C2×(C2×D7)⋊C414yes—
950C2×C4C2×(C2×D7)⋊C414yes—
951C2×C4C2×(C2×D7)⋊C414yes—
952C7#1444811yescharacteristic, complemented, Sylow
953C22—144no—
954C22—144no—
955C22—144no—
956C22—282no—
957C22—282no—
958C22—282no—
959C22—282no—
960C22—282no—
961C22—282no—
962C22—282no—
963C22—282no—
964C22—282no—
965C22—282no—
966C22—282no—
967C22—282no—
968C22#9021211yescharacteristic
969C22#9021211yescharacteristic
970C22#9021611yescharacteristic
971C22#9021611yescharacteristic
972C22C4×#115911yescharacteristic
973C22#9023711yescharacteristic
974C22#9024511yescharacteristic
975C22#9024611yescharacteristic
976C22C4×Q8×D711yescharacteristic
977C22#9026311yescharacteristic
978C22Q8×D2811yescharacteristic
979C22#9026711yescharacteristic
980C22#9032511yescharacteristic
981C22#9032611yescharacteristic
982C22#9033411yescharacteristic
983C22#9033811yescharacteristic
984C22#9034811yescharacteristic
985C22#9034911yescharacteristic
986C22#9035611yescharacteristic
987C22#9035811yescharacteristic
988C22#9038011yescharacteristic
989C22#9038111yescharacteristic
990C22#9038311yescharacteristic
991C22#9039011yescharacteristic
992C22#9039611yescharacteristic
993C22#9039811yescharacteristic
994C22#9040111yescharacteristic
995C22#9040311yescharacteristic
996C22C22×(C2×D7)⋊C411yescharacteristic
997C22#9049711yescharacteristic
998C22Q8×C22⋊D711yescharacteristic
999C22#9051511yescharacteristic
1000C22#9052111yescharacteristic
1001C22#9052111yescharacteristic
1002C22#9052211yescharacteristic
1003C4—24no—
1004C4—24no—
1005C4—24no—
1006C4—42no—
1007C4—42no—
1008C4—81no—
1009C4—81no—
1010C4—282no—
1011C4—282no—
1012C4—282no—
1013C4—282no—
1014C4—282no—
1015C4—561no—
1016C4—561no—
1017C2—284no—
1018C2#1173239611yescharacteristic
1019C2#1173259711yescharacteristic
1020C2#1173261411yescharacteristic
1021C2#1173261911yescharacteristic
1022C2#1173274511yescharacteristic
1023C2#1173275611yescharacteristic
1024C2#1173275911yescharacteristic
1025C2#1173283911yescharacteristic
1026C2#1173971411yescharacteristic
1027C2#1173977511yescharacteristic
1028C2Q8×(C2×D7)⋊C411yescharacteristic
1029C2#1174024211yescharacteristic
1030C2#1174032311yescharacteristic
1031C2#1174049611yescharacteristic
1032C2#1174054511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#387C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#387D7
hypocenterC7#14448
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C2×C7×#387C2semidirect
3. C2×#89753C2semidirect
5. #11729317C2semidirect
7. #11729289C2semidirect
11. #11727178C2semidirect
12. #11727178C2semidirect
13. #11727177C2semidirect
14. #11727176C2semidirect
33. C2×#6460C4semidirect
112. C2×(C2×D7)⋊C4Q8semidirect
148. C2×#387D7semidirect
290. C7×C4⋊C4C22⋊C4semidirect
777. C4⋊C4(C2×D7)⋊C4semidirect
952. C7#14448semidirect

Maximal subgroups

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

subgroupindex
C22×#64602
C2×C7×#3872
C2×#897532
#117293242
#117293172
#117292912
#117292892
#117271812
(C2×D7)⋊#952
#117271782
#117271772
#117271762
#117271622
#144487