Finite Group Databasebeta

← #13277497

Subgroups — #13277497

Order 1792.

2366 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D7×C4⋊C4C211yesmaximal, characteristic
2C2×C7×#389C211yesmaximal, characteristic, complemented
3C2×#89761C211yesmaximal, characteristic
4C2×#89761C211yesmaximal, characteristic
5C2×#89761C211yesmaximal, characteristic
6C2×#89744C211yesmaximal, characteristic, complemented
7C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
8#11729322C211yesmaximal, characteristic, complemented
9#11729319C211yesmaximal, characteristic, complemented
10#11729318C211yesmaximal, characteristic, complemented
11#11729290C211yesmaximal, characteristic, complemented
12(C2×D7)⋊#95C211yesmaximal, characteristic
13(C2×D7)⋊#95C211yesmaximal, characteristic
14#11727174C211yesmaximal, characteristic, complemented
15#11727163C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C2×D7×C4⋊C4—24no—
36C2×D7×C4⋊C4—24no—
37C2×D7×C4⋊C4—24no—
38C7×#389—24no—
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#89761—24no—
56#89761—24no—
57#89761C418yescomplemented
58#89744—24no—
59C4×(C2×D7)⋊C4—24no—
60#14043—71nomaximal, Sylow
61C24×D7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C22×C4×D7—22no—
77C22×C4×D7—22no—
78C22×C4×D7—22no—
79C22×C4×D7—22no—
80C22×C4×D7—22no—
81C22×C4×D7—22no—
82C22×C4×D7—22no—
83C22×C4×D7—22no—
84C22×C4×D7—22no—
85C22×C4×D7—22no—
86C22×C4×D7—22no—
87C22×C4×D7—22no—
88C22×C4×D7—22no—
89C22×C4×D7—22no—
90C22×C4×D7—22no—
91C22×C4×D7—41no—
92C22×C4×D7—41no—
93C22×C4×D7—41no—
94C22×C4×D7—41no—
95C22×C4×D7C2×C414yes—
96C22×C4×D7D414yes—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4—22no—
99C2×C7×C4⋊C4—22no—
100C2×C7×C4⋊C4—22no—
101C2×C7×C4⋊C4—22no—
102C2×C7×C4⋊C4—22no—
103C2×C7×C4⋊C4—22no—
104C2×C7×C4⋊C4—22no—
105C2×C7×C4⋊C4—22no—
106C2×C7×C4⋊C4—41no—
107C2×C7×C4⋊C4C2×C414yescomplemented
108C2×C7×C4⋊C4D414yes—
109C2×C42×C7—22no—
110C2×C42×C7—22no—
111C2×C42×C7—41no—
112C2×(C2×D7)⋊C4—22no—
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)⋊C4C2×C414yes—
120C2×(C2×D7)⋊C4C2×C414yes—
121C2×(C2×D7)⋊C4D414yes—
122C2×(C2×D7)⋊C4Q814yes—
123C2×(C2×D7)⋊C4Q814yes—
124C2×C4⋊Dic7—22no—
125C2×C4⋊Dic7—22no—
126C2×C4⋊Dic7—22no—
127C2×Dic7⋊C4—22no—
128C2×Dic7⋊C4—22no—
129C2×Dic7⋊C4—22no—
130C2×Dic7⋊C4—22no—
131C2×Dic7⋊C4—22no—
132C2×Dic7⋊C4—22no—
133C2×Dic7⋊C4—22no—
134C2×Dic7⋊C4—22no—
135C2×Dic7⋊C4—22no—
136C2×Dic7⋊C4—22no—
137C2×Dic7⋊C4—41no—
138C2×Dic7⋊C4—41no—
139C2×Dic7⋊C4—41no—
140C2×Dic7⋊C4C2×C414yescomplemented
141C2×Dic7⋊C4D414yes—
142C2×C4×Dic7—22no—
143C2×C4×Dic7—22no—
144C2×C4×Dic7—41no—
145D7×C4⋊C4—232no—
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—22no—
157C7⋊#95—22no—
158C7⋊#95—41no—
159C7⋊#95—41no—
160C7⋊#95C2×C414yescomplemented
161C7⋊#95C2×C414yescomplemented
162C23×C4⋊C4—71no—
163C2×#389—71no—
164C2×#389D711yescharacteristic, complemented
165C2×#385—71no—
166C2×#385—71no—
167C2×#385—71no—
168C2×C4×C22⋊C4—71no—
169#1444—71no—
170#1444—71no—
171#1441—71no—
172#1441—71no—
173#1436—71no—
174#1436—71no—
175C22⋊#95—71no—
176C22⋊#95—71no—
177C24×C7C2411yescharacteristic
178C23×D7—21no—
179C23×D7—21no—
180C23×D7—21no—
181C23×D7—21no—
182C23×D7—21no—
183C23×D7—21no—
184C23×D7—21no—
185C23×D7—21no—
186C23×D7C22×C412yes—
187C23×D7C2×D412yes—
188C23×D7C2×D412yes—
189C23×D7C2×Q812yes—
190C23×D7C2×Q812yes—
191C23×D7#4112yes—
192C23×D7#4112yes—
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×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×C7C22×C412yes—
231C22×C4×C7C22×C412yes—
232C22×C4×C7C22×C412yes—
233C22×C4×C7C2×D412yes—
234C22×C4×C7C2×D412yes—
235C22×C4×C7C2×D412yes—
236C22×C4×C7C2×D412yes—
237C22×C4×C7C2×D412yes—
238C22×C4×C7C2×D412yes—
239C22×C4×C7C2×Q812yes—
240C22×C4×C7C2×Q812yes—
241C22×C4×C7#4112yes—
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×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×Dic7C22×C412yes—
282C22×Dic7C22×C412yes—
283C22×Dic7C22×C412yes—
284C22×Dic7C2×D412yes—
285C22×Dic7C2×D412yes—
286C22×Dic7C2×D412yes—
287C22×Dic7C2×D412yes—
288C22×Dic7C2×Q812yes—
289C22×Dic7C2×Q812yes—
290C22×Dic7#4112yes—
291C2×C4×D7—28no—
292C2×C4×D7—28no—
293C2×C4×D7—28no—
294C2×C4×D7—28no—
295C2×C4×D7—28no—
296C2×C4×D7—28no—
297C2×C4×D7—28no—
298C2×C4×D7—28no—
299C2×C4×D7—28no—
300C2×C4×D7—28no—
301C2×C4×D7—44no—
302C2×C4×D7—44no—
303C2×C4×D7—44no—
304C2×C4×D7—44no—
305C2×C4×D7—44no—
306C2×C4×D7—44no—
307C2×C4×D7—44no—
308C2×C4×D7—44no—
309C2×C4×D7—44no—
310C2×C4×D7—44no—
311C2×C4×D7—44no—
312C7×C4⋊C4—28no—
313C7×C4⋊C4—28no—
314C7×C4⋊C4—44no—
315C7×C4⋊C4—44no—
316C42×C7—44no—
317(C2×D7)⋊C4—28no—
318(C2×D7)⋊C4—28no—
319(C2×D7)⋊C4—44no—
320(C2×D7)⋊C4C4⋊C4116yescomplemented
321C4⋊Dic7—28no—
322Dic7⋊C4—28no—
323Dic7⋊C4—28no—
324Dic7⋊C4—28no—
325Dic7⋊C4—44no—
326Dic7⋊C4—44no—
327C4×Dic7—44no—
328C24×C4—71no—
329C24×C4—71no—
330C24×C4—71no—
331C22×C4⋊C4—71no—
332C22×C4⋊C4—71no—
333C22×C4⋊C4—71no—
334C22×C4⋊C4—71no—
335C22×C4⋊C4—71no—
336C22×C4⋊C4—71no—
337C22×C4⋊C4—144no—
338C22×C4⋊C4—144no—
339C22×C4⋊C4—144no—
340C22×C4⋊C4C2×D711yescharacteristic
341C22×C4⋊C4C2×D711yescharacteristic
342C22×C4⋊C4C2×D711yescharacteristic
343C22×C4⋊C4C2×D711yescharacteristic
344C22×C22⋊C4—71no—
345C22×C22⋊C4—71no—
346C22×C22⋊C4—71no—
347C22×C22⋊C4—71no—
348C22×C42—71no—
349C22×C42C2×D711yescharacteristic
350#389—24no—
351#389—144no—
352#385—78no—
353#385—144no—
354#385—144no—
355C4×C22⋊C4—144no—
356C2×#95—71no—
357C2×#95—71no—
358C2×#95—71no—
359C2×#95—71no—
360C2×#95—71no—
361C2×#95—71no—
362C2×#95—71no—
363C2×#95—71no—
364C2×#95—71no—
365C2×#95—71no—
366C2×#95—71no—
367C2×#95—71no—
368C2×#95—71no—
369C2×#95—71no—
370C2×#95C2×D711yescharacteristic
371C2×#95C2×D711yescharacteristic
372C23×C7C23×C411yescharacteristic
373C23×C7C22×D411yescharacteristic
374C23×C7C22×D411yescharacteristic
375C23×C7C22×D411yescharacteristic
376C23×C7C22×D411yescharacteristic
377C23×C7C22×Q811yescharacteristic
378C23×C7C22×Q811yescharacteristic
379C23×C7C2×#4111yescharacteristic
380C23×C7C2×#4111yescharacteristic
381C23×C7C2×#4111yescharacteristic
382C23×C7C2×#4111yescharacteristic
383C23×C7H(5,𝔽2)11yescharacteristic
384C23×C7H(5,𝔽2)11yescharacteristic
385C23×C72−1+411yescharacteristic
386C23×C72−1+411yescharacteristic
387C22×D7—22no—
388C22×D7—22no—
389C22×D7—22no—
390C22×D7—22no—
391C22×D7—22no—
392C22×D7—22no—
393C22×D7—22no—
394C22×D7—22no—
395C22×D7—22no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—22no—
401C22×D7—22no—
402C22×D7—22no—
403C22×D7—22no—
404C22×D7—22no—
405C22×D7—22no—
406C22×D7—22no—
407C22×D7—22no—
408C22×D7—22no—
409C22×D7—22no—
410C22×D7—22no—
411C22×D7—22no—
412C22×D7—22no—
413C22×D7—22no—
414C22×D7—22no—
415C22×D7C2×C4⋊C414yes—
416C22×D7C4×D414yes—
417C22×D7C4×Q814yes—
418C22×D7#12114yes—
419C22×D7C22⋊Q814yes—
420C22×D7#12514yes—
421C22×D7C4⋊Q814yes—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—22no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
435C2×C4×C7—22no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—22no—
440C2×C4×C7—22no—
441C2×C4×C7—22no—
442C2×C4×C7—22no—
443C2×C4×C7—22no—
444C2×C4×C7—22no—
445C2×C4×C7—22no—
446C2×C4×C7—22no—
447C2×C4×C7—22no—
448C2×C4×C7—22no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7—41no—
459C2×C4×C7—41no—
460C2×C4×C7—41no—
461C2×C4×C7—41no—
462C2×C4×C7—41no—
463C2×C4×C7—41no—
464C2×C4×C7—41no—
465C2×C4×C7—41no—
466C2×C4×C7—41no—
467C2×C4×C7—41no—
468C2×C4×C7C2×C4⋊C414yescomplemented
469C2×C4×C7C4×D414yes—
470C2×C4×C7#12014yes—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—22no—
476C2×Dic7—22no—
477C2×Dic7—22no—
478C2×Dic7—22no—
479C2×Dic7—22no—
480C2×Dic7—22no—
481C2×Dic7—22no—
482C2×Dic7—22no—
483C2×Dic7—22no—
484C2×Dic7—22no—
485C2×Dic7—22no—
486C2×Dic7—22no—
487C2×Dic7—22no—
488C2×Dic7—22no—
489C2×Dic7—22no—
490C2×Dic7—22no—
491C2×Dic7—22no—
492C2×Dic7—22no—
493C2×Dic7—22no—
494C2×Dic7—22no—
495C2×Dic7—41no—
496C2×Dic7—41no—
497C2×Dic7—41no—
498C2×Dic7—41no—
499C2×Dic7—41no—
500C2×Dic7—41no—
501C2×Dic7—41no—
502C2×Dic7—41no—
503C2×Dic7—41no—
504C2×Dic7—41no—
505C2×Dic7—41no—
506C2×Dic7—41no—
507C2×Dic7—41no—
508C2×Dic7—41no—
509C2×Dic7—41no—
510C2×Dic7—41no—
511C2×Dic7—41no—
512C2×Dic7—41no—
513C2×Dic7—41no—
514C2×Dic7—41no—
515C2×Dic7—41no—
516C2×Dic7—41no—
517C2×Dic7—41no—
518C2×Dic7C2×C4⋊C414yescomplemented
519C2×Dic7C4×D414yes—
520C4×D7—232no—
521C4×D7—416no—
522C4×D7—416no—
523C25—71no—
524C23×C4—71no—
525C23×C4—71no—
526C23×C4—71no—
527C23×C4—71no—
528C23×C4—71no—
529C23×C4—71no—
530C23×C4—74no—
531C23×C4—74no—
532C23×C4—71no—
533C23×C4—142no—
534C23×C4—142no—
535C23×C4—142no—
536C23×C4—142no—
537C23×C4—142no—
538C23×C4—142no—
539C23×C4—142no—
540C23×C4—142no—
541C23×C4—142no—
542C23×C4—142no—
543C23×C4—142no—
544C23×C4—142no—
545C23×C4—142no—
546C23×C4—142no—
547C23×C4—142no—
548C23×C4—281no—
549C23×C4—281no—
550C23×C4—281no—
551C23×C4—281no—
552C23×C4C22×D711yescharacteristic
553C23×C4C22×D711yescharacteristic
554C23×C4C22×D711yescharacteristic
555C23×C4C22×D711yescharacteristic
556C23×C4C22×D711yescharacteristic
557C23×C4C22×D711yescharacteristic
558C23×C4C22×D711yescharacteristic
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—74no—
570C2×C4⋊C4—74no—
571C2×C4⋊C4—1432no—
572C2×C4⋊C4—142no—
573C2×C4⋊C4—142no—
574C2×C4⋊C4—142no—
575C2×C4⋊C4—142no—
576C2×C4⋊C4—142no—
577C2×C4⋊C4—142no—
578C2×C4⋊C4—142no—
579C2×C4⋊C4—142no—
580C2×C4⋊C4—142no—
581C2×C4⋊C4—142no—
582C2×C4⋊C4—142no—
583C2×C4⋊C4—142no—
584C2×C4⋊C4—142no—
585C2×C4⋊C4—281no—
586C2×C4⋊C4—281no—
587C2×C4⋊C4—281no—
588C2×C4⋊C4C4×D714yescomplemented
589C2×C4⋊C4C22⋊D714yes—
590C2×C22⋊C4—74no—
591C2×C22⋊C4—74no—
592C2×C22⋊C4—74no—
593C2×C22⋊C4—74no—
594C2×C22⋊C4—74no—
595C2×C22⋊C4—142no—
596C2×C22⋊C4—142no—
597C2×C22⋊C4—142no—
598C2×C22⋊C4—142no—
599C2×C22⋊C4—142no—
600C2×C22⋊C4—142no—
601C2×C22⋊C4—142no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—41no—
605C2×C42—142no—
606C2×C42—142no—
607C2×C42—281no—
608#95—22no—
609#95—22no—
610#95—74no—
611#95—74no—
612#95—142no—
613#95—142no—
614#95—142no—
615#95—142no—
616#95—142no—
617#95—142no—
618#95—142no—
619#95—142no—
620#95—142no—
621#95—142no—
622#95—281no—
623#95—281no—
624C22×C7C22×C4⋊C411yescharacteristic
625C22×C7C2×C4×D411yescharacteristic
626C22×C7C2×C4×D411yescharacteristic
627C22×C7C2×C4×D411yescharacteristic
628C22×C7C2×C4×Q811yescharacteristic
629C22×C7#52011yescharacteristic
630C22×C7#52011yescharacteristic
631C22×C7C2×#12011yescharacteristic
632C22×C7C2×#12111yescharacteristic
633C22×C7C2×C22⋊Q811yescharacteristic
634C22×C7#52511yescharacteristic
635C22×C7#52511yescharacteristic
636C22×C7#52511yescharacteristic
637C22×C7C2×#12511yescharacteristic
638C22×C7C2×C4⋊Q811yescharacteristic
639C22×C7#53411yescharacteristic
640C22×C7#53611yescharacteristic
641C22×C7#53911yescharacteristic
642C22×C7#53911yescharacteristic
643C22×C7D4211yescharacteristic
644C22×C7D4211yescharacteristic
645C22×C7#54611yescharacteristic
646C22×C7#54611yescharacteristic
647C22×C7#54711yescharacteristic
648C22×C7#54711yescharacteristic
649C22×C7D4×Q811yescharacteristic
650C22×C7D4×Q811yescharacteristic
651C22×C7D4×Q811yescharacteristic
652C22×C7D4×Q811yescharacteristic
653C22×C7#55211yescharacteristic
654C22×C7#55211yescharacteristic
655C22×C7#55411yescharacteristic
656C22×C7#55411yescharacteristic
657C22×C7#55411yescharacteristic
658C22×C7#55411yescharacteristic
659C2×D7—24no—
660C2×D7—24no—
661C2×D7—24no—
662C2×D7—24no—
663C2×D7—24no—
664C2×D7—24no—
665C2×D7—24no—
666C2×D7—24no—
667C2×D7—24no—
668C2×D7—24no—
669C2×D7—24no—
670C2×D7—24no—
671C2×D7—24no—
672C2×D7—24no—
673C2×D7#38918yescomplemented
674C4×C7—24no—
675C4×C7—24no—
676C4×C7—24no—
677C4×C7—42no—
678C4×C7—42no—
679C4×C7—42no—
680C4×C7—81no—
681Dic7—24no—
682Dic7—24no—
683Dic7—42no—
684Dic7—42no—
685Dic7—42no—
686Dic7—42no—
687Dic7—81no—
688C24—72no—
689C24—72no—
690C24—72no—
691C24—72no—
692C24—72no—
693C24—72no—
694C24—72no—
695C24—141no—
696C24—141no—
697C24—141no—
698C24—141no—
699C24—141no—
700C24—141no—
701C24—141no—
702C24—141no—
703C24C23×D711yescharacteristic
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—72no—
742C22×C4—72no—
743C22×C4—72no—
744C22×C4—72no—
745C22×C4—72no—
746C22×C4—72no—
747C22×C4—72no—
748C22×C4—72no—
749C22×C4—72no—
750C22×C4—72no—
751C22×C4—148no—
752C22×C4—148no—
753C22×C4—148no—
754C22×C4—148no—
755C22×C4—148no—
756C22×C4—148no—
757C22×C4—148no—
758C22×C4—148no—
759C22×C4—141no—
760C22×C4—141no—
761C22×C4—141no—
762C22×C4—141no—
763C22×C4—141no—
764C22×C4—141no—
765C22×C4—141no—
766C22×C4—141no—
767C22×C4—148no—
768C22×C4—141no—
769C22×C4—141no—
770C22×C4—141no—
771C22×C4—141no—
772C22×C4—141no—
773C22×C4—141no—
774C22×C4—141no—
775C22×C4—141no—
776C22×C4—141no—
777C22×C4—141no—
778C22×C4—141no—
779C22×C4—141no—
780C22×C4—141no—
781C22×C4—141no—
782C22×C4—141no—
783C22×C4—141no—
784C22×C4—141no—
785C22×C4—141no—
786C22×C4—141no—
787C22×C4—141no—
788C22×C4—141no—
789C22×C4—141no—
790C22×C4—141no—
791C22×C4—141no—
792C22×C4—148no—
793C22×C4—141no—
794C22×C4—141no—
795C22×C4—141no—
796C22×C4—141no—
797C22×C4—141no—
798C22×C4—141no—
799C22×C4—141no—
800C22×C4—284no—
801C22×C4—284no—
802C22×C4—284no—
803C22×C4—284no—
804C22×C4—284no—
805C22×C4—284no—
806C22×C4—284no—
807C22×C4—284no—
808C22×C4—284no—
809C22×C4—284no—
810C22×C4—284no—
811C22×C4C2×C4×D712yes—
812C22×C4C2×C4×D712yes—
813C22×C4C2×C4×D712yes—
814C22×C4#115712yes—
815C22×C4D4×D712yes—
816C22×C4D4×D712yes—
817C22×C4D4×D712yes—
818C22×C4Q8×D712yes—
819C22×C4Q8×D712yes—
820C22×C4C2×C22⋊D712yes—
821C22×C4C2×C22⋊D712yes—
822C22×C4C2×C22⋊D712yes—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—148no—
828C4⋊C4—148no—
829C4⋊C4—148no—
830C4⋊C4—148no—
831C4⋊C4—284no—
832C4⋊C4—284no—
833C22⋊C4—716no—
834C22⋊C4—148no—
835C22⋊C4—148no—
836C22⋊C4—284no—
837C42—44no—
838C42—284no—
839C2×C7C2×#38911yescharacteristic
840C2×C7C4×#12011yescharacteristic
841C2×C7#232211yescharacteristic
842C2×C7D4×C4⋊C411yescharacteristic
843C2×C7D4×C4⋊C411yescharacteristic
844C2×C7#236011yescharacteristic
845C2×C7#236011yescharacteristic
846C2×C7#241011yescharacteristic
847C2×C7#241311yescharacteristic
848C2×C7#243411yescharacteristic
849C2×C7#244911yescharacteristic
850C2×C7#244911yescharacteristic
851C2×C7#247311yescharacteristic
852C2×C7#247311yescharacteristic
853C2×C7#258311yescharacteristic
854D7—28no—
855C23—74no—
856C23—74no—
857C23—74no—
858C23—74no—
859C23—74no—
860C23—74no—
861C23—74no—
862C23—142no—
863C23—142no—
864C23—142no—
865C23—142no—
866C23—142no—
867C23—142no—
868C23—142no—
869C23—142no—
870C23—142no—
871C23—142no—
872C23—142no—
873C23—142no—
874C23—142no—
875C23—142no—
876C23—142no—
877C23—142no—
878C23—142no—
879C23—142no—
880C23—142no—
881C23—142no—
882C23—142no—
883C23—142no—
884C23—142no—
885C23—142no—
886C23—142no—
887C23—142no—
888C23—142no—
889C23—142no—
890C23C22×C4×D711yescharacteristic
891C23C2×#115711yescharacteristic
892C23C2×D4×D711yescharacteristic
893C23C2×D4×D711yescharacteristic
894C23C2×D4×D711yescharacteristic
895C23#654811yescharacteristic
896C23C2×Q8×D711yescharacteristic
897C23C2×Q8×D711yescharacteristic
898C23#655111yescharacteristic
899C23#655111yescharacteristic
900C23D7×#4111yescharacteristic
901C23D7×#4111yescharacteristic
902C23D7×#4111yescharacteristic
903C23#655311yescharacteristic
904C23C22×C22⋊D711yescharacteristic
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—74no—
952C2×C4—74no—
953C2×C4—1432no—
954C2×C4—142no—
955C2×C4—142no—
956C2×C4—142no—
957C2×C4—142no—
958C2×C4—142no—
959C2×C4—142no—
960C2×C4—142no—
961C2×C4—142no—
962C2×C4—142no—
963C2×C4—142no—
964C2×C4—142no—
965C2×C4—142no—
966C2×C4—142no—
967C2×C4—142no—
968C2×C4—142no—
969C2×C4—142no—
970C2×C4—142no—
971C2×C4—142no—
972C2×C4—142no—
973C2×C4—142no—
974C2×C4—142no—
975C2×C4—142no—
976C2×C4—142no—
977C2×C4—142no—
978C2×C4—2816no—
979C2×C4—2816no—
980C2×C4—281no—
981C2×C4—281no—
982C2×C4—281no—
983C2×C4—281no—
984C2×C4—281no—
985C2×C4—281no—
986C2×C4—281no—
987C2×C4—281no—
988C2×C4—281no—
989C2×C4—281no—
990C2×C4—281no—
991C2×C4—281no—
992C2×C4—281no—
993C2×C4—281no—
994C2×C4—281no—
995C2×C4—281no—
996C2×C4—281no—
997C2×C4—281no—
998C2×C4—281no—
999C2×C4—281no—
1000C2×C4—281no—
1001C2×C4—281no—
1002C2×C4—281no—
1003C2×C4D7×C4⋊C414yescomplemented
1004C2×C4C4×C22⋊D714yes—
1005C2×C4#650014yes—
1006C7#1404311yescharacteristic, complemented, Sylow
1007C22—78no—
1008C22—144no—
1009C22—144no—
1010C22—144no—
1011C22—144no—
1012C22—144no—
1013C22—144no—
1014C22—144no—
1015C22—144no—
1016C22—144no—
1017C22—144no—
1018C22—144no—
1019C22—144no—
1020C22—144no—
1021C22—144no—
1022C22C2×D7×C4⋊C411yescharacteristic
1023C22#9019511yescharacteristic
1024C22#9019811yescharacteristic
1025C22#9020211yescharacteristic
1026C22C4×D4×D711yescharacteristic
1027C22C4×D4×D711yescharacteristic
1028C22#9023811yescharacteristic
1029C22#9023811yescharacteristic
1030C22C4×Q8×D711yescharacteristic
1031C22#9026511yescharacteristic
1032C22#9027011yescharacteristic
1033C22#9027211yescharacteristic
1034C22D7×#12111yescharacteristic
1035C22#9029611yescharacteristic
1036C22#9030011yescharacteristic
1037C22#9030111yescharacteristic
1038C22D7×C22⋊Q811yescharacteristic
1039C22#9032211yescharacteristic
1040C22#9032711yescharacteristic
1041C22#9032911yescharacteristic
1042C22D7×#12511yescharacteristic
1043C22#9038111yescharacteristic
1044C22#9038311yescharacteristic
1045C22#9038411yescharacteristic
1046C22D7×C4⋊Q811yescharacteristic
1047C22#9041511yescharacteristic
1048C22#9041811yescharacteristic
1049C22#9041811yescharacteristic
1050C22C2×C4×C22⋊D711yescharacteristic
1051C22C2×#650011yescharacteristic
1052C22D4×C22⋊D711yescharacteristic
1053C22Q8×C22⋊D711yescharacteristic
1054C22Q8×C22⋊D711yescharacteristic
1055C22#9051911yescharacteristic
1056C22#9052011yescharacteristic
1057C4—24no—
1058C4—24no—
1059C4—24no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—81no—
1064C4—144no—
1065C4—144no—
1066C4—282no—
1067C4—282no—
1068C4—282no—
1069C4—282no—
1070C4—561no—
1071C2—148no—
1072C2#1173342811yescharacteristic
1073C2#1173346811yescharacteristic
1074C2D7×#38911yescharacteristic
1075C2#1173364111yescharacteristic
1076C2#1173364711yescharacteristic
1077C2#1173365311yescharacteristic
1078C2#1173367011yescharacteristic
1079C2#1173369211yescharacteristic
1080C2C4⋊C4×C22⋊D711yescharacteristic
1081C2C4×#650011yescharacteristic
1082C2#1173993511yescharacteristic
1083C2#1174014711yescharacteristic
1084C2#1174026211yescharacteristic
1085C2#1174047711yescharacteristic
1086C2#1174067711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#389C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#389D7
hypocenterC7#14043
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×C7×#389C2semidirect
6. C2×#89744C2semidirect
8. #11729322C2semidirect
9. #11729319C2semidirect
10. #11729318C2semidirect
11. #11729290C2semidirect
14. #11727174C2semidirect
15. #11727163C2semidirect
57. #89761C4semidirect
107. C2×C7×C4⋊C4C2×C4semidirect
140. C2×Dic7⋊C4C2×C4semidirect
160. C7⋊#95C2×C4semidirect
161. C7⋊#95C2×C4semidirect
164. C2×#389D7semidirect
320. (C2×D7)⋊C4C4⋊C4semidirect
468. C2×C4×C7C2×C4⋊C4semidirect
518. C2×Dic7C2×C4⋊C4semidirect
588. C2×C4⋊C4C4×D7semidirect
673. C2×D7#389semidirect
1003. C2×C4D7×C4⋊C4semidirect
1006. C7#14043semidirect

Maximal subgroups

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

subgroupindex
C22×D7×C4⋊C42
C2×C7×#3892
C2×#897612
C2×#897442
C2×C4×(C2×D7)⋊C42
#117293222
#117293192
#117293182
#117292902
(C2×D7)⋊#952
#117271742
#117271632
#140437