Finite Group Databasebeta

← #13281141

Subgroups — #13281141

Order 1792.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6509C211yesmaximal, characteristic
2C2×C7×#391C211yesmaximal, characteristic, complemented
3C2×#89744C211yesmaximal, characteristic, complemented
4C2×#89705C211yesmaximal, characteristic, complemented
5C2×#89439C211yesmaximal, characteristic
6#11729888C211yesmaximal, characteristic, complemented
7#11729324C211yesmaximal, characteristic
8#11729291C211yesmaximal, characteristic
9#11727182C211yesmaximal, characteristic
10(C2×D7)⋊#95C211yesmaximal, characteristic
11#11727165C211yesmaximal, characteristic, complemented
12#11727163C211yesmaximal, characteristic, complemented
13#11727163C211yesmaximal, characteristic, complemented
14#11727162C211yesmaximal, characteristic
15#11727161C211yesmaximal, characteristic, complemented
16C23×C7×Q8C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C2×#6509—24no—
21C2×#6509—24no—
22C2×#6509C418yescomplemented
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×C4×Dic7C2211yescharacteristic
36C7×#391—24no—
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#89744—24no—
56#89705—24no—
57#89439—24no—
58#14362—71nomaximal, Sylow
59C24×D7C2311yescharacteristic
60C22×C7×Q8—22no—
61C22×C7×Q8—22no—
62C22×C7×Q8—22no—
63C22×C7×Q8—22no—
64C22×C7×Q8—41no—
65C22×C7×Q8—41no—
66C22×C7×Q8C2×C414yes—
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C22×C4×D7—22no—
82C22×C4×D7—22no—
83C22×C4×D7—22no—
84C22×C4×D7—22no—
85C22×C4×D7—41no—
86C22×C4×D7—41no—
87C22×C4×D7C2×C414yes—
88C2×C7×C4⋊C4—22no—
89C2×C7×C4⋊C4—22no—
90C2×C7×C4⋊C4—41no—
91C2×C42×C7—22no—
92C2×C42×C7—22no—
93C2×C42×C7—41no—
94#6509—232no—
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⋊Dic7C2×C414yes—
116C2×Dic7⋊C4—22no—
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4—22no—
119C2×Dic7⋊C4—22no—
120C2×Dic7⋊C4—22no—
121C2×Dic7⋊C4—22no—
122C2×Dic7⋊C4—22no—
123C2×Dic7⋊C4—41no—
124C2×Dic7⋊C4—41no—
125C2×Dic7⋊C4—41no—
126C2×Dic7⋊C4—41no—
127C2×Dic7⋊C4C2×C414yes—
128C2×Dic7⋊C4C2×C414yes—
129C2×Dic7⋊C4D414yes—
130C2×Dic7⋊C4D414yes—
131C2×C4×Dic7—22no—
132C2×C4×Dic7—41no—
133C2×C4×Dic7—41no—
134C7×#95—22no—
135C7×#95—22no—
136C7×#95—22no—
137C7×#95D414yes—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—22no—
144C7⋊#95—22no—
145C7⋊#95—22no—
146C7⋊#95—41no—
147C7⋊#95—41no—
148C7⋊#95—41no—
149C7⋊#95—41no—
150C7⋊#95—41no—
151C7⋊#95—41no—
152C22×C22⋊Q8—71no—
153C2×#391D711yescharacteristic, complemented
154C2×#389—71no—
155C2×#387—71no—
156C2×#380—71no—
157#1446—71no—
158#1441—71no—
159#1441—71no—
160#1441—71no—
161#1439—71no—
162#1439—71no—
163#1437—71no—
164#1437—71no—
165#1436—71no—
166C22⋊#95—71no—
167C24×C7C2411yescharacteristic
168C23×D7—21no—
169C23×D7—21no—
170C23×D7—21no—
171C23×D7—21no—
172C23×D7—21no—
173C23×D7—21no—
174C23×D7—21no—
175C23×D7—21no—
176C23×D7—21no—
177C23×D7—21no—
178C23×D7—21no—
179C23×D7—21no—
180C23×D7C22×C412yes—
181C23×D7C2×Q812yes—
182C23×D7#4112yes—
183C2×C7×Q8—28no—
184C2×C7×Q8—28no—
185C2×C7×Q8—44no—
186C2×C7×Q8—44no—
187C2×C7×Q8—44no—
188C2×C7×Q8—44no—
189C2×C7×Q8—44no—
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×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×C7C22×C412yes—
230C22×C4×C7C22×C412yes—
231C22×C4×C7C22×C412yes—
232C22×C4×C7C2×D412yes—
233C22×C4×C7C2×D412yes—
234C22×C4×C7C2×D412yes—
235C22×C4×C7C2×D412yes—
236C22×C4×C7C2×D412yes—
237C22×C4×C7C2×Q812yes—
238C22×C4×C7#4112yes—
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×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×Dic7C22×C412yes—
281C22×Dic7C22×C412yes—
282C22×Dic7C22×C412yes—
283C22×Dic7C2×D412yes—
284C22×Dic7C2×D412yes—
285C22×Dic7C2×D412yes—
286C22×Dic7C2×D412yes—
287C22×Dic7C2×Q812yes—
288C2×C4×D7—28no—
289C2×C4×D7—28no—
290C2×C4×D7—44no—
291C2×C4×D7—44no—
292C2×C4×D7—44no—
293C2×C4×D7—44no—
294C2×C4×D7—44no—
295C7×C4⋊C4—44no—
296C42×C7—44no—
297(C2×D7)⋊C4—28no—
298(C2×D7)⋊C4—28no—
299(C2×D7)⋊C4—44no—
300(C2×D7)⋊C4—44no—
301(C2×D7)⋊C4—44no—
302(C2×D7)⋊C4—44no—
303C4⋊Dic7—28no—
304Dic7⋊C4—28no—
305Dic7⋊C4—44no—
306Dic7⋊C4—44no—
307Dic7⋊C4—44no—
308Dic7⋊C4C22⋊C4116yescomplemented
309C4×Dic7—44no—
310C23×Q8C2×D711yescharacteristic
311C24×C4—71no—
312C2×C22⋊Q8—78no—
313C2×C22⋊Q8—144no—
314C2×C22⋊Q8—144no—
315C22×C4⋊C4—71no—
316C22×C4⋊C4—71no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4C2×D711yescharacteristic
322C22×C22⋊C4—71no—
323C22×C22⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C22⋊C4—71no—
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C42—71no—
329C22×C42C2×D711yescharacteristic
330#391—24no—
331#389—144no—
332#387—144no—
333#380—144no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C2×#95—71no—
344C2×#95—71no—
345C2×#95—71no—
346C2×#95—71no—
347C2×#95—71no—
348C2×#95C2×D711yescharacteristic
349C2×#95C2×D711yescharacteristic
350C2×#95C2×D711yescharacteristic
351C2×#95C2×D711yescharacteristic
352C23×C7C23×C411yescharacteristic
353C23×C7C22×D411yescharacteristic
354C23×C7C22×D411yescharacteristic
355C23×C7C22×D411yescharacteristic
356C23×C7C22×Q811yescharacteristic
357C23×C7C2×#4111yescharacteristic
358C23×C7C2×#4111yescharacteristic
359C23×C7H(5,𝔽2)11yescharacteristic
360C23×C7H(5,𝔽2)11yescharacteristic
361C23×C7H(5,𝔽2)11yescharacteristic
362C23×C7H(5,𝔽2)11yescharacteristic
363C23×C72−1+411yescharacteristic
364C23×C72−1+411yescharacteristic
365C23×C72−1+411yescharacteristic
366C23×C72−1+411yescharacteristic
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—22no—
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—22no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—41no—
386C22×D7—41no—
387C22×D7—41no—
388C22×D7—41no—
389C22×D7—41no—
390C22×D7—41no—
391C22×D7—41no—
392C22×D7—41no—
393C22×D7—41no—
394C22×D7—41no—
395C22×D7—41no—
396C22×D7—41no—
397C22×D7—41no—
398C22×D7—41no—
399C22×D7—41no—
400C22×D7—41no—
401C22×D7C4×Q814yes—
402C7×Q8—416no—
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—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
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×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7C2×C22⋊C414yes—
451C2×C4×C7C4×D414yes—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—22no—
460C2×Dic7—22no—
461C2×Dic7—22no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—22no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467C2×Dic7—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
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—
490C2×Dic7—41no—
491C2×Dic7—41no—
492C2×Dic7—41no—
493C2×Dic7—41no—
494C2×Dic7—41no—
495C2×Dic7—41no—
496C2×Dic7—41no—
497C2×Dic7—41no—
498C2×Dic7—41no—
499C2×Dic7C2×C22⋊C414yes—
500C2×Dic7C2×C22⋊C414yes—
501C4×D7—416no—
502C25—71no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—22no—
506C22×Q8—22no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8C4×D714yes—
510C23×C4—71no—
511C23×C4—71no—
512C23×C4—71no—
513C23×C4—71no—
514C23×C4—74no—
515C23×C4—71no—
516C23×C4—71no—
517C23×C4—71no—
518C23×C4—142no—
519C23×C4—142no—
520C23×C4—142no—
521C23×C4—142no—
522C23×C4—281no—
523C23×C4—281no—
524C23×C4C22×D711yescharacteristic
525C23×C4C22×D711yescharacteristic
526C23×C4C22×D711yescharacteristic
527C23×C4C22×D711yescharacteristic
528C23×C4C22×D711yescharacteristic
529C23×C4C22×D711yescharacteristic
530C23×C4C22×D711yescharacteristic
531C22⋊Q8—1432no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4—74no—
536C2×C4⋊C4—74no—
537C2×C4⋊C4—74no—
538C2×C4⋊C4—74no—
539C2×C4⋊C4—74no—
540C2×C4⋊C4—142no—
541C2×C4⋊C4—142no—
542C2×C4⋊C4—142no—
543C2×C4⋊C4—142no—
544C2×C4⋊C4—142no—
545C2×C4⋊C4—142no—
546C2×C4⋊C4—142no—
547C2×C4⋊C4—142no—
548C2×C4⋊C4—142no—
549C2×C4⋊C4—281no—
550C2×C4⋊C4—281no—
551C2×C4⋊C4—281no—
552C2×C4⋊C4—281no—
553C2×C22⋊C4—74no—
554C2×C22⋊C4—74no—
555C2×C22⋊C4—74no—
556C2×C22⋊C4—142no—
557C2×C22⋊C4—142no—
558C2×C22⋊C4—142no—
559C2×C22⋊C4—142no—
560C2×C22⋊C4—142no—
561C2×C22⋊C4—142no—
562C2×C22⋊C4—142no—
563C2×C22⋊C4—142no—
564C2×C22⋊C4—142no—
565C2×C22⋊C4—281no—
566C2×C22⋊C4—281no—
567C2×C22⋊C4—281no—
568C2×C22⋊C4—281no—
569C2×C22⋊C4—281no—
570C2×C22⋊C4—281no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—41no—
574C2×C42—142no—
575C2×C42—281no—
576C2×C42—281no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—142no—
581#95—142no—
582#95—142no—
583#95—142no—
584#95—142no—
585#95—142no—
586#95—142no—
587#95—142no—
588#95—281no—
589#95—281no—
590#95—281no—
591#95—281no—
592#95—281no—
593#95—281no—
594#95C22⋊D714yes—
595C22×C7C22×C22⋊C411yescharacteristic
596C22×C7C2×C4×D411yescharacteristic
597C22×C7C2×C4×Q811yescharacteristic
598C22×C7#51811yescharacteristic
599C22×C7#51911yescharacteristic
600C22×C7#52011yescharacteristic
601C22×C7#52011yescharacteristic
602C22×C7#53511yescharacteristic
603C22×C7#53611yescharacteristic
604C22×C7#53611yescharacteristic
605C22×C7#53711yescharacteristic
606C22×C7#53711yescharacteristic
607C22×C7#53711yescharacteristic
608C22×C7#53811yescharacteristic
609C22×C7#53911yescharacteristic
610C22×C7#54111yescharacteristic
611C22×C7#54211yescharacteristic
612C22×C7#54311yescharacteristic
613C22×C7#54411yescharacteristic
614C22×C7D4211yescharacteristic
615C22×C7D4211yescharacteristic
616C22×C7#54611yescharacteristic
617C22×C7#54611yescharacteristic
618C22×C7#54611yescharacteristic
619C22×C7#54811yescharacteristic
620C22×C7#54811yescharacteristic
621C22×C7D4×Q811yescharacteristic
622C22×C7D4×Q811yescharacteristic
623C22×C7D4×Q811yescharacteristic
624C22×C7#55211yescharacteristic
625C22×C7#55411yescharacteristic
626C22×C7#56211yescharacteristic
627C22×C7#56211yescharacteristic
628C22×C7#56311yescharacteristic
629C22×C7#56311yescharacteristic
630C2×D7—24no—
631C2×D7—24no—
632C2×D7—24no—
633C2×D7—42no—
634C2×D7—42no—
635C2×D7—42no—
636C2×D7—42no—
637C2×D7—42no—
638C2×D7—42no—
639C2×D7—42no—
640C2×D7—42no—
641C2×D7—42no—
642C2×D7—42no—
643C2×D7—42no—
644C2×D7—42no—
645C4×C7—24no—
646C4×C7—24no—
647C4×C7—42no—
648C4×C7—42no—
649C4×C7—42no—
650C4×C7—42no—
651C4×C7—81no—
652Dic7—24no—
653Dic7—24no—
654Dic7—42no—
655Dic7—42no—
656Dic7—81no—
657Dic7—81no—
658Dic7—81no—
659C24—72no—
660C24—72no—
661C24—72no—
662C24—141no—
663C24—141no—
664C24—141no—
665C24—141no—
666C24—141no—
667C24—141no—
668C24—141no—
669C24—141no—
670C24—141no—
671C24—141no—
672C24—141no—
673C24—141no—
674C24C23×D711yescharacteristic
675C2×Q8—28no—
676C2×Q8—28no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—44no—
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—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—72no—
722C22×C4—72no—
723C22×C4—72no—
724C22×C4—72no—
725C22×C4—72no—
726C22×C4—72no—
727C22×C4—72no—
728C22×C4—72no—
729C22×C4—148no—
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—141no—
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—148no—
751C22×C4—141no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—141no—
755C22×C4—141no—
756C22×C4—141no—
757C22×C4—141no—
758C22×C4—141no—
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—141no—
768C22×C4—141no—
769C22×C4—141no—
770C22×C4—141no—
771C22×C4—141no—
772C22×C4—284no—
773C22×C4—284no—
774C22×C4—284no—
775C22×C4—284no—
776C22×C4—284no—
777C22×C4C2×C4×D712yes—
778C22×C4C2×C4×D712yes—
779C22×C4C2×C4×D712yes—
780C22×C4#115712yes—
781C22×C4D4×D712yes—
782C22×C4D4×D712yes—
783C22×C4Q8×D712yes—
784C22×C4C2×C22⋊D712yes—
785C22×C4C2×C22⋊D712yes—
786C22×C4C2×C22⋊D712yes—
787C4⋊C4—44no—
788C4⋊C4—716no—
789C4⋊C4—148no—
790C4⋊C4—148no—
791C4⋊C4—284no—
792C4⋊C4—284no—
793C4⋊C4—284no—
794C22⋊C4—148no—
795C22⋊C4—148no—
796C22⋊C4—284no—
797C22⋊C4—284no—
798C22⋊C4—284no—
799C22⋊C4—284no—
800C42—44no—
801C42—284no—
802C2×C7#231111yescharacteristic
803C2×C7#232311yescharacteristic
804C2×C7#232911yescharacteristic
805C2×C7D4×C22⋊C411yescharacteristic
806C2×C7Q8×C22⋊C411yescharacteristic
807C2×C7#236011yescharacteristic
808C2×C7#237811yescharacteristic
809C2×C7#267611yescharacteristic
810C2×C7#267711yescharacteristic
811C2×C7#268111yescharacteristic
812C2×C7#268311yescharacteristic
813C2×C7#269011yescharacteristic
814C2×C7#269211yescharacteristic
815C2×C7#270211yescharacteristic
816C2×C7#270411yescharacteristic
817D7—44no—
818C23—74no—
819C23—142no—
820C23—142no—
821C23—142no—
822C23—142no—
823C23—142no—
824C23—142no—
825C23—142no—
826C23—142no—
827C23—142no—
828C23—142no—
829C23—142no—
830C23—142no—
831C23—142no—
832C23—142no—
833C23—142no—
834C23—142no—
835C23—142no—
836C23—142no—
837C23—281no—
838C23—281no—
839C23—281no—
840C23—281no—
841C23—281no—
842C23—281no—
843C23—281no—
844C23—281no—
845C23—281no—
846C23—281no—
847C23—281no—
848C23—281no—
849C23—281no—
850C23—281no—
851C23—281no—
852C23—281no—
853C23C22×C4×D711yescharacteristic
854C23C2×#115711yescharacteristic
855C23C2×D4×D711yescharacteristic
856C23C2×D4×D711yescharacteristic
857C23#654811yescharacteristic
858C23#654811yescharacteristic
859C23C2×Q8×D711yescharacteristic
860C23#655111yescharacteristic
861C23#655111yescharacteristic
862C23#655111yescharacteristic
863C23D7×#4111yescharacteristic
864C23#655311yescharacteristic
865C23#655311yescharacteristic
866C23#655411yescharacteristic
867C23C22×C22⋊D711yescharacteristic
868Q8—416no—
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—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—74no—
917C2×C4—74no—
918C2×C4—142no—
919C2×C4—142no—
920C2×C4—142no—
921C2×C4—142no—
922C2×C4—142no—
923C2×C4—142no—
924C2×C4—142no—
925C2×C4—142no—
926C2×C4—142no—
927C2×C4—142no—
928C2×C4—142no—
929C2×C4—142no—
930C2×C4—142no—
931C2×C4—142no—
932C2×C4—142no—
933C2×C4—142no—
934C2×C4—142no—
935C2×C4—142no—
936C2×C4—2816no—
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×C4—281no—
950C2×C4—281no—
951C2×C4—281no—
952C2×C4—281no—
953C2×C4—281no—
954C2×C4—281no—
955C2×C4—281no—
956C2×C4—281no—
957C2×C4—281no—
958C2×C4—281no—
959C2×C4—281no—
960C2×C4—281no—
961C2×C4—281no—
962C2×C4—281no—
963C2×C4—281no—
964C2×C4—281no—
965C2×C4—281no—
966C2×C4D7×C22⋊C414yes—
967C2×C4C4×C22⋊D714yes—
968C7#1436211yescharacteristic, complemented, Sylow
969C22—144no—
970C22—144no—
971C22—144no—
972C22—282no—
973C22—282no—
974C22—282no—
975C22—282no—
976C22—282no—
977C22—282no—
978C22—282no—
979C22—282no—
980C22—282no—
981C22—282no—
982C22—282no—
983C22—282no—
984C22C2×D7×C22⋊C411yescharacteristic
985C22#9017711yescharacteristic
986C22#9018111yescharacteristic
987C22#9018111yescharacteristic
988C22C4×Q8×D711yescharacteristic
989C22#9026311yescharacteristic
990C22#9026511yescharacteristic
991C22#9026511yescharacteristic
992C22#9027011yescharacteristic
993C22#9027211yescharacteristic
994C22#9027311yescharacteristic
995C22#9027411yescharacteristic
996C22#9032011yescharacteristic
997C22#9032011yescharacteristic
998C22#9032311yescharacteristic
999C22#9032411yescharacteristic
1000C22#9032511yescharacteristic
1001C22#9032911yescharacteristic
1002C22#9033711yescharacteristic
1003C22#9033811yescharacteristic
1004C22#9036511yescharacteristic
1005C22#9036811yescharacteristic
1006C22#9036911yescharacteristic
1007C22#9037511yescharacteristic
1008C22#9041511yescharacteristic
1009C22#9041811yescharacteristic
1010C22#9042011yescharacteristic
1011C22#9042611yescharacteristic
1012C22C2×C4×C22⋊D711yescharacteristic
1013C22D4×C22⋊D711yescharacteristic
1014C22D4×C22⋊D711yescharacteristic
1015C22Q8×C22⋊D711yescharacteristic
1016C22#9050711yescharacteristic
1017C22#9052011yescharacteristic
1018C22#9052411yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—42no—
1025C4—81no—
1026C4—144no—
1027C4—144no—
1028C4—282no—
1029C4—282no—
1030C4—561no—
1031C4—561no—
1032C4—561no—
1033C2—284no—
1034C2#1173392711yescharacteristic
1035C2#1173400811yescharacteristic
1036C2#1173400911yescharacteristic
1037C2#1173401011yescharacteristic
1038C2#1173401111yescharacteristic
1039C2#1173405711yescharacteristic
1040C2#1173405911yescharacteristic
1041C2#1173406211yescharacteristic
1042C2C22⋊C4×C22⋊D711yescharacteristic
1043C2#1173993311yescharacteristic
1044C2#1173993511yescharacteristic
1045C2#1174023711yescharacteristic
1046C2#1174023811yescharacteristic
1047C2#1174042811yescharacteristic
1048C2#1174071111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#391C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#391D7
hypocenterC7#14362
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×C7×#391C2semidirect
3. C2×#89744C2semidirect
4. C2×#89705C2semidirect
6. #11729888C2semidirect
11. #11727165C2semidirect
12. #11727163C2semidirect
13. #11727163C2semidirect
15. #11727161C2semidirect
22. C2×#6509C4semidirect
112. C2×(C2×D7)⋊C4Q8semidirect
153. C2×#391D7semidirect
308. Dic7⋊C4C22⋊C4semidirect
968. C7#14362semidirect

Maximal subgroups

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

subgroupindex
C22×#65092
C2×C7×#3912
C2×#897442
C2×#897052
C2×#894392
#117298882
#117293242
#117292912
#117271822
(C2×D7)⋊#952
#117271652
#117271632
#117271622
#117271612
#143627