Finite Group Databasebeta

← #13277521

Subgroups — #13277521

Order 1792.

1530 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89744C211yesmaximal, characteristic
2C2×#89744C211yesmaximal, characteristic
3C2×C4×Dic7⋊C4C211yesmaximal, characteristic
4C2×#89419C211yesmaximal, characteristic
5C2×#89421C211yesmaximal, characteristic
6C7×C4⋊#95C211yesmaximal, characteristic
7#11729322C211yesmaximal, characteristic
8#11729319C211yesmaximal, characteristic
9#11729290C211yesmaximal, characteristic
10#11727174C211yesmaximal, characteristic
11#11727163C211yesmaximal, characteristic
12#11727159C211yesmaximal, characteristic
13Dic7⋊#95C211yesmaximal, characteristic
14Dic7⋊#95C211yesmaximal, characteristic
15Dic7⋊#95C211yesmaximal, characteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×C4⋊Dic7C2211yescharacteristic
20C22×Dic7⋊C4C2211yescharacteristic
21C22×Dic7⋊C4C2211yescharacteristic
22C22×Dic7⋊C4C2211yescharacteristic
23C22×Dic7⋊C4C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
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
51#89744—24no—
52#89744C418yescomplemented
53C4×Dic7⋊C4—24no—
54#89421—24no—
55#89419—24no—
56#14045—71nomaximal, Sylow
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—41no—
75C2×C7×C4⋊C4—41no—
76C2×C7×C4⋊C4—41no—
77C2×C7×C4⋊C4C2×C414yes—
78C2×C42×C7—22no—
79C2×C42×C7—22no—
80C2×C42×C7—41no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—41no—
83C2×C4⋊Dic7—41no—
84C2×Dic7⋊C4—22no—
85C2×Dic7⋊C4—22no—
86C2×Dic7⋊C4—22no—
87C2×Dic7⋊C4—22no—
88C2×Dic7⋊C4—22no—
89C2×Dic7⋊C4—22no—
90C2×Dic7⋊C4—22no—
91C2×Dic7⋊C4—22no—
92C2×Dic7⋊C4—22no—
93C2×Dic7⋊C4—22no—
94C2×Dic7⋊C4—22no—
95C2×Dic7⋊C4—22no—
96C2×Dic7⋊C4—22no—
97C2×Dic7⋊C4—22no—
98C2×Dic7⋊C4—22no—
99C2×Dic7⋊C4—41no—
100C2×Dic7⋊C4—41no—
101C2×Dic7⋊C4—41no—
102C2×Dic7⋊C4—41no—
103C2×Dic7⋊C4—41no—
104C2×Dic7⋊C4C2×C414yes—
105C2×Dic7⋊C4C2×C414yes—
106C2×Dic7⋊C4C2×C414yes—
107C2×Dic7⋊C4D414yes—
108C2×Dic7⋊C4Q814yes—
109C2×Dic7⋊C4Q814yes—
110C2×Dic7⋊C4Q814yes—
111C2×C4×Dic7—22no—
112C2×C4×Dic7—22no—
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—22no—
120C2×C4×Dic7—41no—
121C2×C4×Dic7C2×C414yes—
122C2×C4×Dic7D414yes—
123C7×#95—22no—
124C7×#95—22no—
125C7×#95—41no—
126C7×#95—41no—
127C7⋊#95—22no—
128C7⋊#95—22no—
129C7⋊#95—22no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—41no—
136C7⋊#95—41no—
137C7⋊#95—41no—
138C7⋊#95—41no—
139C7⋊#95C2×C414yes—
140C7⋊#95C2×C414yes—
141C2×#389—71no—
142C2×#389—71no—
143C2×#389—71no—
144C2×C4×C4⋊C4—71no—
145C2×C4×C4⋊C4—71no—
146#1444—71no—
147#1444—71no—
148#1441—71no—
149#1441—71no—
150#1436—71no—
151#1436—71no—
152C4⋊#95—71no—
153C4⋊#95—71no—
154C4⋊#95—71no—
155C4⋊#95D711yescharacteristic
156C24×C7C2411yescharacteristic
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
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×C7C22×C412yes—
197C22×C4×C7C22×C412yes—
198C22×C4×C7C22×C412yes—
199C22×C4×C7C2×D412yes—
200C22×C4×C7C2×D412yes—
201C22×C4×C7C2×Q812yes—
202C22×C4×C7C2×Q812yes—
203C22×C4×C7C2×Q812yes—
204C22×C4×C7#4112yes—
205C22×C4×C7#4112yes—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
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×Dic7C22×C412yes—
246C22×Dic7C22×C412yes—
247C22×Dic7C22×C412yes—
248C22×Dic7C22×C412yes—
249C22×Dic7C2×D412yes—
250C22×Dic7C2×D412yes—
251C22×Dic7C2×D412yes—
252C22×Dic7C2×D412yes—
253C22×Dic7C2×Q812yes—
254C22×Dic7C2×Q812yes—
255C22×Dic7C2×Q812yes—
256C22×Dic7C2×Q812yes—
257C22×Dic7C2×Q812yes—
258C22×Dic7C2×Q812yes—
259C22×Dic7#4112yes—
260C22×Dic7#4112yes—
261C22×Dic7#4112yes—
262C7×C4⋊C4—44no—
263C7×C4⋊C4—44no—
264C42×C7—44no—
265C4⋊Dic7—44no—
266Dic7⋊C4—28no—
267Dic7⋊C4—28no—
268Dic7⋊C4—28no—
269Dic7⋊C4—28no—
270Dic7⋊C4—44no—
271Dic7⋊C4—44no—
272Dic7⋊C4—44no—
273Dic7⋊C4—44no—
274Dic7⋊C4C4⋊C4116yescomplemented
275C4×Dic7—28no—
276C4×Dic7—28no—
277C4×Dic7—44no—
278C4×Dic7—44no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4—71no—
287C22×C4⋊C4—71no—
288C22×C4⋊C4—71no—
289C22×C4⋊C4C2×D711yescharacteristic
290C22×C4⋊C4C2×D711yescharacteristic
291C22×C42—71no—
292C22×C42—71no—
293C22×C42—71no—
294C22×C42—71no—
295C22×C42C2×D711yescharacteristic
296#389—78no—
297#389—144no—
298#389—144no—
299C4×C4⋊C4—144no—
300C4×C4⋊C4—144no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95C2×D711yescharacteristic
316C2×#95C2×D711yescharacteristic
317C2×#95C2×D711yescharacteristic
318C2×#95C2×D711yescharacteristic
319C23×C7C23×C411yescharacteristic
320C23×C7C22×D411yescharacteristic
321C23×C7C22×D411yescharacteristic
322C23×C7C22×Q811yescharacteristic
323C23×C7C22×Q811yescharacteristic
324C23×C7C22×Q811yescharacteristic
325C23×C7C2×#4111yescharacteristic
326C23×C7C2×#4111yescharacteristic
327C23×C7C2×#4111yescharacteristic
328C23×C7C2×#4111yescharacteristic
329C23×C7C2×#4111yescharacteristic
330C23×C7H(5,𝔽2)11yescharacteristic
331C23×C7H(5,𝔽2)11yescharacteristic
332C23×C7H(5,𝔽2)11yescharacteristic
333C23×C72−1+411yescharacteristic
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—41no—
370C2×C4×C7—41no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—41no—
377C2×C4×C7—41no—
378C2×C4×C7—41no—
379C2×C4×C7—41no—
380C2×C4×C7—41no—
381C2×C4×C7C2×C4⋊C414yes—
382C2×C4×C7C22⋊Q814yes—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—41no—
408C2×Dic7—41no—
409C2×Dic7—41no—
410C2×Dic7—41no—
411C2×Dic7—41no—
412C2×Dic7—41no—
413C2×Dic7—41no—
414C2×Dic7—41no—
415C2×Dic7—41no—
416C2×Dic7—41no—
417C2×Dic7—41no—
418C2×Dic7—41no—
419C2×Dic7—41no—
420C2×Dic7—41no—
421C2×Dic7—41no—
422C2×Dic7—41no—
423C2×Dic7—41no—
424C2×Dic7—41no—
425C2×Dic7—41no—
426C2×Dic7—41no—
427C2×Dic7—41no—
428C2×Dic7—41no—
429C2×Dic7—41no—
430C2×Dic7C2×C4⋊C414yes—
431C2×Dic7C2×C4⋊C414yes—
432C2×Dic7C4×D414yes—
433C2×Dic7C4×Q814yes—
434C2×Dic7C4×Q814yes—
435C2×Dic7#12114yes—
436C2×Dic7C22⋊Q814yes—
437C2×Dic7#12514yes—
438C2×Dic7C4⋊Q814yes—
439C23×C4—71no—
440C23×C4—71no—
441C23×C4—71no—
442C23×C4—71no—
443C23×C4—71no—
444C23×C4—71no—
445C23×C4—71no—
446C23×C4—71no—
447C23×C4C22×D711yescharacteristic
448C23×C4C22×D711yescharacteristic
449C23×C4C22×D711yescharacteristic
450C23×C4C22×D711yescharacteristic
451C23×C4C22×D711yescharacteristic
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D711yescharacteristic
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4—41no—
459C2×C4⋊C4—74no—
460C2×C4⋊C4—74no—
461C2×C4⋊C4—74no—
462C2×C4⋊C4—74no—
463C2×C4⋊C4—74no—
464C2×C4⋊C4—74no—
465C2×C4⋊C4—74no—
466C2×C4⋊C4—142no—
467C2×C4⋊C4—142no—
468C2×C4⋊C4—142no—
469C2×C4⋊C4—142no—
470C2×C4⋊C4—142no—
471C2×C4⋊C4—142no—
472C2×C4⋊C4—142no—
473C2×C4⋊C4—142no—
474C2×C4⋊C4—142no—
475C2×C4⋊C4—142no—
476C2×C4⋊C4—142no—
477C2×C4⋊C4—142no—
478C2×C4⋊C4—142no—
479C2×C4⋊C4—142no—
480C2×C4⋊C4—142no—
481C2×C4⋊C4—142no—
482C2×C4⋊C4—281no—
483C2×C4⋊C4—281no—
484C2×C4⋊C4—281no—
485C2×C4⋊C4—281no—
486C2×C4⋊C4—281no—
487C2×C4⋊C4—281no—
488C2×C4⋊C4—281no—
489C2×C4⋊C4C4×D714yes—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42—41no—
493C2×C42—74no—
494C2×C42—74no—
495C2×C42—142no—
496C2×C42—142no—
497C2×C42—142no—
498C2×C42—142no—
499C2×C42—142no—
500C2×C42—142no—
501C2×C42—142no—
502C2×C42—142no—
503C2×C42—142no—
504C2×C42—281no—
505#95—22no—
506#95—22no—
507#95—41no—
508#95—41no—
509#95—74no—
510#95—74no—
511#95—142no—
512#95—142no—
513#95—142no—
514#95—142no—
515#95—142no—
516#95—142no—
517#95—142no—
518#95—142no—
519#95—281no—
520#95—281no—
521#95—281no—
522#95—281no—
523C22×C7C22×C4⋊C411yescharacteristic
524C22×C7C2×C4×D411yescharacteristic
525C22×C7C2×C4×Q811yescharacteristic
526C22×C7C2×C4×Q811yescharacteristic
527C22×C7C4×#4111yescharacteristic
528C22×C7#51811yescharacteristic
529C22×C7#52011yescharacteristic
530C22×C7C2×#12111yescharacteristic
531C22×C7C2×C22⋊Q811yescharacteristic
532C22×C7C2×C22⋊Q811yescharacteristic
533C22×C7#52511yescharacteristic
534C22×C7C2×#12511yescharacteristic
535C22×C7#52911yescharacteristic
536C22×C7C2×C4⋊Q811yescharacteristic
537C22×C7#53311yescharacteristic
538C22×C7#53511yescharacteristic
539C22×C7#53711yescharacteristic
540C22×C7#54011yescharacteristic
541C22×C7#54211yescharacteristic
542C22×C7#54611yescharacteristic
543C22×C7#54611yescharacteristic
544C22×C7D4×Q811yescharacteristic
545C22×C7#55011yescharacteristic
546C22×C7#55211yescharacteristic
547C22×C7#55311yescharacteristic
548C22×C7#55411yescharacteristic
549C22×C7#55411yescharacteristic
550C22×C7#55411yescharacteristic
551C22×C7#55411yescharacteristic
552C22×C7#55411yescharacteristic
553C22×C7#55511yescharacteristic
554C22×C7#55711yescharacteristic
555C22×C7#55711yescharacteristic
556C22×C7Q8211yescharacteristic
557C22×C7Q8211yescharacteristic
558C4×C7—24no—
559C4×C7—24no—
560C4×C7—42no—
561C4×C7—42no—
562C4×C7—42no—
563C4×C7—42no—
564C4×C7—81no—
565Dic7—24no—
566Dic7—24no—
567Dic7—42no—
568Dic7—42no—
569Dic7—42no—
570Dic7—42no—
571Dic7—81no—
572Dic7#38918yes—
573C24C23×D711yescharacteristic
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—72no—
614C22×C4—72no—
615C22×C4—72no—
616C22×C4—72no—
617C22×C4—72no—
618C22×C4—72no—
619C22×C4—72no—
620C22×C4—72no—
621C22×C4—72no—
622C22×C4—72no—
623C22×C4—72no—
624C22×C4—72no—
625C22×C4—72no—
626C22×C4—72no—
627C22×C4—72no—
628C22×C4—72no—
629C22×C4—72no—
630C22×C4—141no—
631C22×C4—141no—
632C22×C4—141no—
633C22×C4—141no—
634C22×C4—141no—
635C22×C4—141no—
636C22×C4—141no—
637C22×C4—141no—
638C22×C4—141no—
639C22×C4—141no—
640C22×C4—141no—
641C22×C4—141no—
642C22×C4—141no—
643C22×C4—141no—
644C22×C4—141no—
645C22×C4—141no—
646C22×C4—141no—
647C22×C4—141no—
648C22×C4—141no—
649C22×C4—141no—
650C22×C4—141no—
651C22×C4—141no—
652C22×C4—141no—
653C22×C4—141no—
654C22×C4—141no—
655C22×C4—141no—
656C22×C4—141no—
657C22×C4—141no—
658C22×C4—141no—
659C22×C4—141no—
660C22×C4—141no—
661C22×C4—141no—
662C22×C4—141no—
663C22×C4—141no—
664C22×C4—141no—
665C22×C4—141no—
666C22×C4—141no—
667C22×C4—141no—
668C22×C4—141no—
669C22×C4C2×C4×D712yes—
670C22×C4C2×C4×D712yes—
671C22×C4C2×C4×D712yes—
672C22×C4#115712yes—
673C22×C4#115712yes—
674C22×C4D4×D712yes—
675C22×C4D4×D712yes—
676C22×C4Q8×D712yes—
677C22×C4Q8×D712yes—
678C22×C4Q8×D712yes—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—716no—
682C4⋊C4—148no—
683C4⋊C4—148no—
684C4⋊C4—148no—
685C4⋊C4—148no—
686C4⋊C4—284no—
687C4⋊C4—284no—
688C4⋊C4—284no—
689C4⋊C4—284no—
690C4⋊C4—284no—
691C42—44no—
692C42—148no—
693C42—148no—
694C42—284no—
695C42—284no—
696C2×C7C2×#38911yescharacteristic
697C2×C7C4×C22⋊Q811yescharacteristic
698C2×C7#232411yescharacteristic
699C2×C7#234911yescharacteristic
700C2×C7Q8×C4⋊C411yescharacteristic
701C2×C7#236911yescharacteristic
702C2×C7#237011yescharacteristic
703C2×C7#241411yescharacteristic
704C2×C7#241711yescharacteristic
705C2×C7#245111yescharacteristic
706C2×C7#245411yescharacteristic
707C2×C7#250711yescharacteristic
708C2×C7#250811yescharacteristic
709C2×C7#256711yescharacteristic
710C2×C7#258411yescharacteristic
711C23C22×C4×D711yescharacteristic
712C23C2×#115711yescharacteristic
713C23C2×#115711yescharacteristic
714C23C2×D4×D711yescharacteristic
715C23C2×D4×D711yescharacteristic
716C23#654811yescharacteristic
717C23#654811yescharacteristic
718C23#654811yescharacteristic
719C23C2×Q8×D711yescharacteristic
720C23C2×Q8×D711yescharacteristic
721C23C2×Q8×D711yescharacteristic
722C23D7×#4111yescharacteristic
723C23D7×#4111yescharacteristic
724C23D7×#4111yescharacteristic
725C23#655411yescharacteristic
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—74no—
774C2×C4—74no—
775C2×C4—74no—
776C2×C4—74no—
777C2×C4—74no—
778C2×C4—74no—
779C2×C4—74no—
780C2×C4—74no—
781C2×C4—74no—
782C2×C4—142no—
783C2×C4—142no—
784C2×C4—142no—
785C2×C4—142no—
786C2×C4—142no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—142no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—142no—
803C2×C4—142no—
804C2×C4—142no—
805C2×C4—142no—
806C2×C4—281no—
807C2×C4—281no—
808C2×C4—281no—
809C2×C4—281no—
810C2×C4—281no—
811C2×C4—281no—
812C2×C4—281no—
813C2×C4—281no—
814C2×C4—281no—
815C2×C4—281no—
816C2×C4—281no—
817C2×C4—281no—
818C2×C4—281no—
819C2×C4—281no—
820C2×C4—281no—
821C2×C4—281no—
822C2×C4—281no—
823C2×C4—281no—
824C2×C4—281no—
825C2×C4—281no—
826C2×C4—281no—
827C2×C4—281no—
828C2×C4—281no—
829C2×C4D7×C4⋊C414yes—
830C2×C4#645914yes—
831C7#1404511yescharacteristic, complemented, Sylow
832C22C4×#115711yescharacteristic
833C22#9017711yescharacteristic
834C22#9018111yescharacteristic
835C22#9018111yescharacteristic
836C22C2×D7×C4⋊C411yescharacteristic
837C22C2×#645911yescharacteristic
838C22#9020211yescharacteristic
839C22#9020211yescharacteristic
840C22#9020211yescharacteristic
841C22#9021911yescharacteristic
842C22#9022211yescharacteristic
843C22#9023111yescharacteristic
844C22C4×D4×D711yescharacteristic
845C22#9023711yescharacteristic
846C22#9023811yescharacteristic
847C22#9025811yescharacteristic
848C22C4×Q8×D711yescharacteristic
849C22C4×Q8×D711yescharacteristic
850C22#9026911yescharacteristic
851C22#9028811yescharacteristic
852C22#9029011yescharacteristic
853C22D7×#12111yescharacteristic
854C22#9030611yescharacteristic
855C22D7×C22⋊Q811yescharacteristic
856C22#9032311yescharacteristic
857C22#9032711yescharacteristic
858C22#9032711yescharacteristic
859C22#9036011yescharacteristic
860C22#9036111yescharacteristic
861C22#9037611yescharacteristic
862C22D7×#12511yescharacteristic
863C22#9040611yescharacteristic
864C22#9041311yescharacteristic
865C22#9041311yescharacteristic
866C22D7×C4⋊Q811yescharacteristic
867C4—24no—
868C4—24no—
869C4—42no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—78no—
874C4—81no—
875C4—144no—
876C4—144no—
877C4—282no—
878C4—282no—
879C4—282no—
880C4—282no—
881C4—561no—
882C2#1173081411yescharacteristic
883C2#1173110711yescharacteristic
884C2C4×#645911yescharacteristic
885C2#1173133411yescharacteristic
886C2#1173134811yescharacteristic
887C2#1173161511yescharacteristic
888C2#1173178511yescharacteristic
889C2#1173342611yescharacteristic
890C2#1173348111yescharacteristic
891C2#1173352511yescharacteristic
892C2D7×#38911yescharacteristic
893C2#1173374111yescharacteristic
894C2#1173375611yescharacteristic
895C2#1173393911yescharacteristic
896C2#1173395511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, prime radical, cosocleC24×C7C24
hypercenterC4⋊#95D7
hypocenterC7#14045
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
52. #89744C4semidirect
274. Dic7⋊C4C4⋊C4semidirect
831. C7#14045semidirect

Maximal subgroups

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

subgroupindex
C2×#897442
C2×C4×Dic7⋊C42
C2×#894192
C2×#894212
C7×C4⋊#952
#117293222
#117293192
#117292902
#117271742
#117271632
#117271592
Dic7⋊#952
#140457