Finite Group Databasebeta

← #13275239

Subgroups — #13275239

Order 1792.

1662 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic7C211yesmaximal, characteristic
2C2×C4×Dic7⋊C4C211yesmaximal, characteristic
3C2×#89422C211yesmaximal, characteristic
4C2×#89421C211yesmaximal, characteristic
5C2×#89421C211yesmaximal, characteristic
6C7×#1436C211yesmaximal, characteristic
7#11729318C211yesmaximal, characteristic
8C4×C7⋊#95C211yesmaximal, characteristic
9#11727161C211yesmaximal, characteristic
10#11727161C211yesmaximal, characteristic
11Dic7⋊#95C211yesmaximal, characteristic
12Dic7⋊#95C211yesmaximal, characteristic
13#11727157C211yesmaximal, characteristic
14#11727156C211yesmaximal, characteristic
15Dic7×#95C211yesmaximal, characteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C22×C4⋊Dic7C2211yescharacteristic
19C22×Dic7⋊C4C2211yescharacteristic
20C22×Dic7⋊C4C2211yescharacteristic
21C22×Dic7⋊C4C2211yescharacteristic
22C22×Dic7⋊C4C2211yescharacteristic
23C22×C4×Dic7C2211yescharacteristic
24C22×C4×Dic7C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
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
51C4⋊C4×Dic7C418yescomplemented
52C4×Dic7⋊C4—24no—
53#89422C418yescomplemented
54#89421—24no—
55#89421C418yescomplemented
56#13804—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⋊C4C2×C414yes—
75C2×C42×C7—22no—
76C2×C42×C7—22no—
77C2×C42×C7—41no—
78C2×C4⋊Dic7—22no—
79C2×C4⋊Dic7—22no—
80C2×C4⋊Dic7C2×C414yes—
81C2×Dic7⋊C4—22no—
82C2×Dic7⋊C4—22no—
83C2×Dic7⋊C4—22no—
84C2×Dic7⋊C4—22no—
85C2×Dic7⋊C4—22no—
86C2×Dic7⋊C4—22no—
87C2×Dic7⋊C4C2×C414yes—
88C2×Dic7⋊C4C2×C414yes—
89C2×Dic7⋊C4C2×C414yes—
90C2×Dic7⋊C4C2×C414yes—
91C2×Dic7⋊C4D414yes—
92C2×Dic7⋊C4Q814yes—
93C2×C4×Dic7—22no—
94C2×C4×Dic7—22no—
95C2×C4×Dic7—22no—
96C2×C4×Dic7—22no—
97C2×C4×Dic7—22no—
98C2×C4×Dic7—22no—
99C2×C4×Dic7—22no—
100C2×C4×Dic7—22no—
101C2×C4×Dic7—22no—
102C2×C4×Dic7—22no—
103C2×C4×Dic7—41no—
104C2×C4×Dic7—41no—
105C2×C4×Dic7—41no—
106C2×C4×Dic7—41no—
107C2×C4×Dic7—41no—
108C2×C4×Dic7—41no—
109C2×C4×Dic7—41no—
110C2×C4×Dic7C2×C414yes—
111C2×C4×Dic7C2×C414yes—
112C2×C4×Dic7C2×C414yes—
113C2×C4×Dic7C2×C414yes—
114C2×C4×Dic7C2×C414yes—
115C2×C4×Dic7C2×C414yes—
116C2×C4×Dic7C2×C414yes—
117C7×#95—22no—
118C7×#95—22no—
119C7×#95—41no—
120C7×#95C2×C414yes—
121C7×#95C2×C414yes—
122C7⋊#95—22no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—22no—
128C7⋊#95—41no—
129C7⋊#95—41no—
130C7⋊#95—41no—
131C7⋊#95C2×C414yes—
132C7⋊#95C2×C414yes—
133C7⋊#95C2×C414yes—
134C7⋊#95C2×C414yes—
135C7⋊#95C2×C414yes—
136C7⋊#95C2×C414yes—
137C2×#382—71no—
138C2×C4×C4⋊C4—71no—
139C2×C4×C4⋊C4—71no—
140C2×C4×C4⋊C4—71no—
141C2×C4×C4⋊C4—71no—
142#1436—71no—
143#1436—71no—
144#1436—71no—
145#1436D711yescharacteristic
146C4⋊#95—71no—
147C4⋊#95—71no—
148#1434—71no—
149#1434—71no—
150C4×#95—71no—
151C4×#95—71no—
152C24×C7C2411yescharacteristic
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
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×C7C22×C412yes—
190C22×C4×C7C22×C412yes—
191C22×C4×C7C22×C412yes—
192C22×C4×C7C22×C412yes—
193C22×C4×C7C22×C412yes—
194C22×C4×C7C22×C412yes—
195C22×C4×C7C22×C412yes—
196C22×C4×C7C22×C412yes—
197C22×C4×C7C22×C412yes—
198C22×C4×C7C2×D412yes—
199C22×C4×C7C2×Q812yes—
200C22×C4×C7#4112yes—
201C22×C4×C7#4112yes—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—21no—
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×Dic7C22×C412yes—
239C22×Dic7C22×C412yes—
240C22×Dic7C22×C412yes—
241C22×Dic7C22×C412yes—
242C22×Dic7C22×C412yes—
243C22×Dic7C22×C412yes—
244C22×Dic7C22×C412yes—
245C22×Dic7C22×C412yes—
246C22×Dic7C22×C412yes—
247C22×Dic7C22×C412yes—
248C22×Dic7C22×C412yes—
249C22×Dic7C22×C412yes—
250C22×Dic7C2×D412yes—
251C22×Dic7C2×D412yes—
252C22×Dic7C2×Q812yes—
253C22×Dic7C2×Q812yes—
254C22×Dic7#4112yes—
255C22×Dic7#4112yes—
256C22×Dic7#4112yes—
257C22×Dic7#4112yes—
258C7×C4⋊C4—28no—
259C42×C7—44no—
260C4⋊Dic7—28no—
261Dic7⋊C4—28no—
262Dic7⋊C4—28no—
263Dic7⋊C4—28no—
264Dic7⋊C4C4⋊C4116yescomplemented
265C4×Dic7—28no—
266C4×Dic7—28no—
267C4×Dic7—44no—
268C4×Dic7—44no—
269C4×Dic7—44no—
270C4×Dic7—44no—
271C4×Dic7—44no—
272C4×Dic7C42116yescomplemented
273C22×C4⋊C4—71no—
274C22×C4⋊C4—71no—
275C22×C4⋊C4—71no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4C2×D711yescharacteristic
279C22×C42—71no—
280C22×C42—71no—
281C22×C42—71no—
282C22×C42—71no—
283C22×C42—71no—
284C22×C42—71no—
285C22×C42—71no—
286C22×C42—71no—
287C22×C42C2×D711yescharacteristic
288#382—78no—
289C4×C4⋊C4—78no—
290C4×C4⋊C4—78no—
291C4×C4⋊C4—144no—
292C4×C4⋊C4—144no—
293C2×#95—71no—
294C2×#95—71no—
295C2×#95—71no—
296C2×#95—71no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95—71no—
308C2×#95C2×D711yescharacteristic
309C2×#95C2×D711yescharacteristic
310C2×#95C2×D711yescharacteristic
311C2×#95C2×D711yescharacteristic
312C2×#95C2×D711yescharacteristic
313C23×C7C23×C411yescharacteristic
314C23×C7C23×C411yescharacteristic
315C23×C7C23×C411yescharacteristic
316C23×C7C22×D411yescharacteristic
317C23×C7C22×Q811yescharacteristic
318C23×C7C2×#4111yescharacteristic
319C23×C7C2×#4111yescharacteristic
320C23×C7C2×#4111yescharacteristic
321C23×C7C2×#4111yescharacteristic
322C23×C7C2×#4111yescharacteristic
323C23×C7C2×#4111yescharacteristic
324C23×C7H(5,𝔽2)11yescharacteristic
325C23×C7H(5,𝔽2)11yescharacteristic
326C23×C72−1+411yescharacteristic
327C23×C72−1+411yescharacteristic
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
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×C7C2×C4214yes—
375C2×C4×C7C2×C4⋊C414yes—
376C2×C4×C7#11714yes—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
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×Dic7C2×C4214yes—
424C2×Dic7C2×C4214yes—
425C2×Dic7C2×C4⋊C414yes—
426C2×Dic7C2×C4⋊C414yes—
427C2×Dic7#11714yes—
428C2×Dic7#11714yes—
429C2×Dic7C4×D414yes—
430C2×Dic7C4×D414yes—
431C2×Dic7C4×Q814yes—
432C2×Dic7C4×Q814yes—
433C23×C4—71no—
434C23×C4—71no—
435C23×C4—71no—
436C23×C4—71no—
437C23×C4—71no—
438C23×C4—71no—
439C23×C4—71no—
440C23×C4—71no—
441C23×C4C22×D711yescharacteristic
442C23×C4C22×D711yescharacteristic
443C23×C4C22×D711yescharacteristic
444C23×C4C22×D711yescharacteristic
445C23×C4C22×D711yescharacteristic
446C23×C4C22×D711yescharacteristic
447C23×C4C22×D711yescharacteristic
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—74no—
451C2×C4⋊C4—74no—
452C2×C4⋊C4—74no—
453C2×C4⋊C4—74no—
454C2×C4⋊C4—74no—
455C2×C4⋊C4—74no—
456C2×C4⋊C4—74no—
457C2×C4⋊C4—142no—
458C2×C4⋊C4—142no—
459C2×C4⋊C4—142no—
460C2×C4⋊C4—142no—
461C2×C4⋊C4—142no—
462C2×C4⋊C4—142no—
463C2×C4⋊C4—142no—
464C2×C4⋊C4—142no—
465C2×C4⋊C4C4×D714yes—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—41no—
469C2×C42—74no—
470C2×C42—74no—
471C2×C42—74no—
472C2×C42—74no—
473C2×C42—74no—
474C2×C42—74no—
475C2×C42—74no—
476C2×C42—142no—
477C2×C42—142no—
478C2×C42—142no—
479C2×C42—142no—
480C2×C42—142no—
481C2×C42—142no—
482C2×C42—142no—
483C2×C42—142no—
484C2×C42—142no—
485C2×C42—142no—
486C2×C42—281no—
487C2×C42—281no—
488C2×C42—281no—
489C2×C42—281no—
490C2×C42—281no—
491C2×C42—281no—
492C2×C42—281no—
493#95—22no—
494#95—22no—
495#95—41no—
496#95—74no—
497#95—74no—
498#95—74no—
499#95—74no—
500#95—74no—
501#95—74no—
502#95—142no—
503#95—142no—
504#95—142no—
505#95—142no—
506#95—142no—
507#95—142no—
508#95—281no—
509#95—281no—
510#95—281no—
511#95C4×D714yes—
512#95C4×D714yes—
513C22×C7C22×C4211yescharacteristic
514C22×C7C22×C4⋊C411yescharacteristic
515C22×C7C2×#11711yescharacteristic
516C22×C7C2×#11711yescharacteristic
517C22×C7C2×#11711yescharacteristic
518C22×C7C2×C4×D411yescharacteristic
519C22×C7C2×C4×D411yescharacteristic
520C22×C7C2×C4×Q811yescharacteristic
521C22×C7C2×C4×Q811yescharacteristic
522C22×C7C4×#4111yescharacteristic
523C22×C7C4×#4111yescharacteristic
524C22×C7C4×#4111yescharacteristic
525C22×C7C4×#4111yescharacteristic
526C22×C7#51811yescharacteristic
527C22×C7#51911yescharacteristic
528C22×C7#52011yescharacteristic
529C22×C7#52011yescharacteristic
530C22×C7#52011yescharacteristic
531C22×C7#52011yescharacteristic
532C22×C7#54611yescharacteristic
533C22×C7#54611yescharacteristic
534C22×C7#54811yescharacteristic
535C22×C7#54811yescharacteristic
536C22×C7#55211yescharacteristic
537C22×C7#55211yescharacteristic
538C22×C7#55311yescharacteristic
539C22×C7#55311yescharacteristic
540C22×C7#55411yescharacteristic
541C22×C7#55411yescharacteristic
542C22×C7#55611yescharacteristic
543C22×C7#55611yescharacteristic
544C22×C7#55711yescharacteristic
545C22×C7#55711yescharacteristic
546C22×C7#55911yescharacteristic
547C22×C7#55911yescharacteristic
548C4×C7—24no—
549C4×C7—24no—
550C4×C7—24no—
551C4×C7—42no—
552C4×C7—42no—
553C4×C7—42no—
554C4×C7—42no—
555Dic7—24no—
556Dic7—24no—
557Dic7—24no—
558Dic7—42no—
559Dic7—42no—
560Dic7—42no—
561Dic7—42no—
562Dic7C4×C4⋊C418yes—
563C24C23×D711yescharacteristic
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
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—72no—
601C22×C4—72no—
602C22×C4—72no—
603C22×C4—72no—
604C22×C4—72no—
605C22×C4—72no—
606C22×C4—72no—
607C22×C4—72no—
608C22×C4—72no—
609C22×C4—72no—
610C22×C4—72no—
611C22×C4—72no—
612C22×C4—72no—
613C22×C4—72no—
614C22×C4—72no—
615C22×C4—72no—
616C22×C4—72no—
617C22×C4—72no—
618C22×C4—72no—
619C22×C4—72no—
620C22×C4—141no—
621C22×C4—141no—
622C22×C4—141no—
623C22×C4—141no—
624C22×C4—141no—
625C22×C4—141no—
626C22×C4—141no—
627C22×C4—141no—
628C22×C4—141no—
629C22×C4—141no—
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×C4C2×C4×D712yes—
657C22×C4C2×C4×D712yes—
658C22×C4C2×C4×D712yes—
659C22×C4C2×C4×D712yes—
660C22×C4C2×C4×D712yes—
661C22×C4C2×C4×D712yes—
662C22×C4C2×C4×D712yes—
663C22×C4C2×C4×D712yes—
664C22×C4C2×C4×D712yes—
665C22×C4D4×D712yes—
666C22×C4#115912yes—
667C22×C4#115912yes—
668C22×C4Q8×D712yes—
669C4⋊C4—28no—
670C4⋊C4—716no—
671C4⋊C4—148no—
672C4⋊C4—148no—
673C4⋊C4—148no—
674C4⋊C4—148no—
675C42—44no—
676C42—716no—
677C42—148no—
678C42—148no—
679C42—284no—
680C42—284no—
681C42—284no—
682C42—284no—
683C42—284no—
684C2×C7C2×C4×C4⋊C411yescharacteristic
685C2×C7C4×#11711yescharacteristic
686C2×C7#227411yescharacteristic
687C2×C7#234911yescharacteristic
688C2×C7#235111yescharacteristic
689C2×C7#235211yescharacteristic
690C2×C7#235211yescharacteristic
691C2×C7#235511yescharacteristic
692C2×C7#235511yescharacteristic
693C2×C7#235611yescharacteristic
694C2×C7#235711yescharacteristic
695C2×C7#236711yescharacteristic
696C2×C7#236711yescharacteristic
697C2×C7#237011yescharacteristic
698C2×C7#237011yescharacteristic
699C23C22×C4×D711yescharacteristic
700C23C22×C4×D711yescharacteristic
701C23C22×C4×D711yescharacteristic
702C23C2×D4×D711yescharacteristic
703C23C2×#115911yescharacteristic
704C23C2×#115911yescharacteristic
705C23#654811yescharacteristic
706C23C2×Q8×D711yescharacteristic
707C23#655111yescharacteristic
708C23D7×#4111yescharacteristic
709C23D7×#4111yescharacteristic
710C23D7×#4111yescharacteristic
711C23D7×#4111yescharacteristic
712C23#655311yescharacteristic
713C23#655411yescharacteristic
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
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—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
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—74no—
761C2×C4—74no—
762C2×C4—74no—
763C2×C4—74no—
764C2×C4—74no—
765C2×C4—74no—
766C2×C4—74no—
767C2×C4—74no—
768C2×C4—74no—
769C2×C4—74no—
770C2×C4—142no—
771C2×C4—142no—
772C2×C4—142no—
773C2×C4—142no—
774C2×C4—142no—
775C2×C4—142no—
776C2×C4—142no—
777C2×C4—142no—
778C2×C4—142no—
779C2×C4—142no—
780C2×C4—142no—
781C2×C4—142no—
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—281no—
801C2×C4—281no—
802C2×C4—281no—
803C2×C4—281no—
804C2×C4—281no—
805C2×C4—281no—
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×C4C42×D714yes—
817C2×C4#644014yes—
818C2×C4D7×C4⋊C414yes—
819C7#1380411yescharacteristic, complemented, Sylow
820C22C2×C42×D711yescharacteristic
821C22C2×#644011yescharacteristic
822C22C2×D7×C4⋊C411yescharacteristic
823C22#9019511yescharacteristic
824C22D7×#11711yescharacteristic
825C22D7×#11711yescharacteristic
826C22#9021411yescharacteristic
827C22C4×#115911yescharacteristic
828C22C4×#115911yescharacteristic
829C22C4×#115911yescharacteristic
830C22C4×#115911yescharacteristic
831C22C4×D4×D711yescharacteristic
832C22C4×D4×D711yescharacteristic
833C22#9023611yescharacteristic
834C22#9023711yescharacteristic
835C22C4×Q8×D711yescharacteristic
836C22C4×Q8×D711yescharacteristic
837C22#9026311yescharacteristic
838C22#9026511yescharacteristic
839C22#9028211yescharacteristic
840C22#9028911yescharacteristic
841C22#9029211yescharacteristic
842C22#9032411yescharacteristic
843C22#9032611yescharacteristic
844C22#9032711yescharacteristic
845C22#9033211yescharacteristic
846C22#9034111yescharacteristic
847C22#9034511yescharacteristic
848C22#9035511yescharacteristic
849C22#9037211yescharacteristic
850C22#9037611yescharacteristic
851C22#9038411yescharacteristic
852C22#9039311yescharacteristic
853C22#9040011yescharacteristic
854C22#9041211yescharacteristic
855C4—24no—
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—78no—
863C4—144no—
864C4—144no—
865C4—144no—
866C4—282no—
867C4—282no—
868C4—282no—
869C4—282no—
870C2C4×#644011yescharacteristic
871C2C4×D7×C4⋊C411yescharacteristic
872C2#1173119511yescharacteristic
873C2#1173183911yescharacteristic
874C2#1173184311yescharacteristic
875C2#1173211811yescharacteristic
876C2#1173240811yescharacteristic
877C2#1173240911yescharacteristic
878C2#1173241411yescharacteristic
879C2#1173275011yescharacteristic
880C2#1173292111yescharacteristic
881C2#1173292711yescharacteristic
882C2#1173342711yescharacteristic
883C2#1173343511yescharacteristic
884C2#1173393411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC22×C7C22×C42
FittingC7×#1436C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1436D7
hypocenterC7#13804
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
51. C4⋊C4×Dic7C4semidirect
53. #89422C4semidirect
55. #89421C4semidirect
264. Dic7⋊C4C4⋊C4semidirect
272. C4×Dic7C42semidirect
819. C7#13804semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic72
C2×C4×Dic7⋊C42
C2×#894222
C2×#894212
C7×#14362
#117293182
C4×C7⋊#952
#117271612
Dic7⋊#952
#117271572
#117271562
Dic7×#952
#138047