Finite Group Databasebeta

← #13284016

Subgroups — #13284016

Order 1792.

1542 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89750C211yesmaximal, characteristic, complemented
2C2×#89721C211yesmaximal, characteristic
3C2×#89718C211yesmaximal, characteristic
4C7×#1439C211yesmaximal, characteristic
5#11729320C211yesmaximal, characteristic, complemented
6#11729299C211yesmaximal, characteristic
7#11729299C211yesmaximal, characteristic
8#11729298C211yesmaximal, characteristic
9#11729298C211yesmaximal, characteristic
10#11727167C211yesmaximal, characteristic, complemented
11#11727165C211yesmaximal, characteristic, complemented
12#11727163C211yesmaximal, characteristic, complemented
13#11727161C211yesmaximal, characteristic, complemented
14Dic7⋊#95C211yesmaximal, characteristic, complemented
15#11727156C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
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
51#89750—24no—
52#89721C418yescomplemented
53#89718—24no—
54#14584—71nomaximal, Sylow
55C25×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×Dic7—22no—
63C23×Dic7—22no—
64C23×Dic7—22no—
65C23×Dic7—41no—
66C23×Dic7—41no—
67C23×Dic7—41no—
68C23×Dic7—41no—
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—41no—
79C2×C7×C4⋊C4—41no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—41no—
85C2×C7×C22⋊C4—41no—
86C2×C7×C22⋊C4—41no—
87C2×C7×C22⋊C4—41no—
88C2×C7×C22⋊C4C2×C414yes—
89C2×C22⋊Dic7—22no—
90C2×C22⋊Dic7—22no—
91C2×C22⋊Dic7—41no—
92C2×C22⋊Dic7—41no—
93C2×C22⋊Dic7—41no—
94C2×C22⋊Dic7—41no—
95C2×C22⋊Dic7C2×C414yes—
96C2×C22⋊Dic7C2×C414yes—
97C2×C22⋊Dic7Q814yes—
98C2×C4⋊Dic7—41no—
99C2×C4⋊Dic7—41no—
100C2×C4⋊Dic7C2×C414yescomplemented
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—22no—
103C2×Dic7⋊C4—22no—
104C2×Dic7⋊C4—22no—
105C2×Dic7⋊C4—22no—
106C2×Dic7⋊C4—41no—
107C2×Dic7⋊C4—41no—
108C2×Dic7⋊C4—41no—
109C2×Dic7⋊C4—41no—
110C2×Dic7⋊C4—41no—
111C2×Dic7⋊C4C2×C414yescomplemented
112C2×Dic7⋊C4C2×C414yescomplemented
113C2×C4×Dic7—22no—
114C2×C4×Dic7—22no—
115C2×C4×Dic7—22no—
116C2×C4×Dic7—41no—
117C2×C4×Dic7—41no—
118C2×C4×Dic7—41no—
119C7×#95—22no—
120C7×#95—41no—
121C7×#95—41no—
122C7⋊#95—22no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—41no—
128C7⋊#95—41no—
129C7⋊#95—41no—
130C7⋊#95—41no—
131C7⋊#95—41no—
132C7⋊#95—41no—
133C7⋊#95—41no—
134C7⋊#95—41no—
135C7⋊#95—41no—
136C7⋊#95—41no—
137C7⋊#95C2×C414yescomplemented
138C7⋊#95D414yes—
139C2×#399—71no—
140C2×#387—71no—
141C2×#385—71no—
142#1442—71no—
143#1441—71no—
144#1441—71no—
145#1441—71no—
146#1439D711yescharacteristic
147#1437—71no—
148#1437—71no—
149#1436—71no—
150C4⋊#95—71no—
151#1434—71no—
152C22⋊#95—71no—
153C22⋊#95—71no—
154C24×C7—21no—
155C24×C7—21no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7—21no—
159C24×C7—21no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—21no—
166C24×C7C22×C412yes—
167C24×C7C2×Q812yes—
168C24×C7#4112yes—
169C24×C7C2411yescharacteristic
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×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×C7C22×C412yes—
209C22×C4×C7C22×C412yes—
210C22×C4×C7C2×D412yes—
211C22×C4×C7#4112yes—
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×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—44no—
259C22×Dic7—44no—
260C22×Dic7—44no—
261C22×Dic7—44no—
262C22×Dic7—44no—
263C22×Dic7—44no—
264C22×Dic7—44no—
265C22×Dic7C22×C412yes—
266C22×Dic7C22×C412yes—
267C22×Dic7C22×C412yes—
268C22×Dic7C22×C412yes—
269C22×Dic7C2×D412yes—
270C22×Dic7C2×D412yes—
271C22×Dic7C2×Q812yes—
272C22×Dic7C2×Q812yes—
273C22×Dic7#4112yes—
274C22×Dic7#4112yes—
275C7×C4⋊C4—44no—
276C7×C22⋊C4—44no—
277C7×C22⋊C4—44no—
278C7×C22⋊C4—44no—
279C22⋊Dic7—28no—
280C22⋊Dic7—44no—
281C22⋊Dic7—44no—
282C4⋊Dic7—44no—
283Dic7⋊C4—28no—
284Dic7⋊C4—44no—
285Dic7⋊C4—44no—
286Dic7⋊C4—44no—
287C4×Dic7—44no—
288C4×Dic7—44no—
289C24×C4—71no—
290C22×C4⋊C4—71no—
291C22×C4⋊C4—71no—
292C22×C4⋊C4—71no—
293C22×C4⋊C4—71no—
294C22×C4⋊C4—71no—
295C22×C4⋊C4C2×D711yescharacteristic
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4—71no—
299C22×C22⋊C4C2×D711yescharacteristic
300C22×C22⋊C4C2×D711yescharacteristic
301C22×C22⋊C4C2×D711yescharacteristic
302C22×C42—71no—
303C22×C42—71no—
304#399—78no—
305#387—144no—
306#385—144no—
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×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95C2×D711yescharacteristic
325C2×#95C2×D711yescharacteristic
326C2×#95C2×D711yescharacteristic
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—41no—
352C23×C7—41no—
353C23×C7—41no—
354C23×C7—41no—
355C23×C7—41no—
356C23×C7—41no—
357C23×C7—41no—
358C23×C7—41no—
359C23×C7—41no—
360C23×C7—41no—
361C23×C7C4×Q814yes—
362C23×C7C23×C411yescharacteristic
363C23×C7C22×D411yescharacteristic
364C23×C7C22×Q811yescharacteristic
365C23×C7C2×#4111yescharacteristic
366C23×C7C2×#4111yescharacteristic
367C23×C7C2×#4111yescharacteristic
368C23×C7C2×#4111yescharacteristic
369C23×C7H(5,𝔽2)11yescharacteristic
370C23×C7H(5,𝔽2)11yescharacteristic
371C23×C7H(5,𝔽2)11yescharacteristic
372C23×C7H(5,𝔽2)11yescharacteristic
373C23×C7H(5,𝔽2)11yescharacteristic
374C23×C7H(5,𝔽2)11yescharacteristic
375C23×C72−1+411yescharacteristic
376C23×C72−1+411yescharacteristic
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—41no—
390C2×C4×C7—41no—
391C2×C4×C7—41no—
392C2×C4×C7—41no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—416no—
447C2×Dic7—41no—
448C2×Dic7—41no—
449C2×Dic7—41no—
450C2×Dic7—41no—
451C2×Dic7—41no—
452C2×Dic7—41no—
453C2×Dic7—41no—
454C2×Dic7—41no—
455C2×Dic7—41no—
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×Dic7C4×D414yes—
476C25C22×D711yescharacteristic
477C23×C4—71no—
478C23×C4—71no—
479C23×C4—71no—
480C23×C4—71no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—142no—
486C23×C4—142no—
487C23×C4—142no—
488C23×C4—281no—
489C23×C4—281no—
490C23×C4—281no—
491C23×C4—281no—
492C23×C4C22×D711yescharacteristic
493C23×C4C22×D711yescharacteristic
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C2×C4⋊C4—22no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4—74no—
502C2×C4⋊C4—74no—
503C2×C4⋊C4—74no—
504C2×C4⋊C4—142no—
505C2×C4⋊C4—142no—
506C2×C4⋊C4—142no—
507C2×C4⋊C4—142no—
508C2×C4⋊C4—142no—
509C2×C4⋊C4—281no—
510C2×C4⋊C4—281no—
511C2×C4⋊C4—281no—
512C2×C4⋊C4—281no—
513C2×C4⋊C4—281no—
514C2×C4⋊C4—281no—
515C2×C4⋊C4—281no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—41no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—41no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—74no—
525C2×C22⋊C4—74no—
526C2×C22⋊C4—74no—
527C2×C22⋊C4—142no—
528C2×C22⋊C4—142no—
529C2×C22⋊C4—281no—
530C2×C22⋊C4—281no—
531C2×C22⋊C4—281no—
532C2×C22⋊C4—281no—
533C2×C22⋊C4C4×D714yes—
534C2×C42—142no—
535C2×C42—142no—
536C2×C42—142no—
537C2×C42—281no—
538C2×C42—281no—
539C2×C42—281no—
540#95—22no—
541#95—41no—
542#95—41no—
543#95—74no—
544#95—74no—
545#95—142no—
546#95—142no—
547#95—142no—
548#95—142no—
549#95—142no—
550#95—281no—
551#95—281no—
552#95—281no—
553#95—281no—
554#95—281no—
555#95—281no—
556#95—281no—
557#95—281no—
558#95—281no—
559#95—281no—
560C22×C7—24no—
561C22×C7—24no—
562C22×C7—24no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7—42no—
573C22×C7—42no—
574C22×C7—42no—
575C22×C7C2×C4×D411yescharacteristic
576C22×C7C2×C4×Q811yescharacteristic
577C22×C7C4×#4111yescharacteristic
578C22×C7#51811yescharacteristic
579C22×C7#51811yescharacteristic
580C22×C7#52011yescharacteristic
581C22×C7#52011yescharacteristic
582C22×C7#53511yescharacteristic
583C22×C7#53511yescharacteristic
584C22×C7#53811yescharacteristic
585C22×C7#53811yescharacteristic
586C22×C7#53911yescharacteristic
587C22×C7#53911yescharacteristic
588C22×C7#54011yescharacteristic
589C22×C7#54011yescharacteristic
590C22×C7#54011yescharacteristic
591C22×C7#54211yescharacteristic
592C22×C7#54311yescharacteristic
593C22×C7#54411yescharacteristic
594C22×C7#54611yescharacteristic
595C22×C7#54611yescharacteristic
596C22×C7#54711yescharacteristic
597C22×C7D4×Q811yescharacteristic
598C22×C7#55111yescharacteristic
599C22×C7#55111yescharacteristic
600C22×C7#55111yescharacteristic
601C22×C7#55211yescharacteristic
602C22×C7#55211yescharacteristic
603C22×C7#55411yescharacteristic
604C22×C7#55411yescharacteristic
605C22×C7#55411yescharacteristic
606C22×C7#56011yescharacteristic
607C22×C7#56211yescharacteristic
608C22×C7#56211yescharacteristic
609C22×C7#56311yescharacteristic
610C4×C7—42no—
611C4×C7—42no—
612C4×C7—42no—
613C4×C7—42no—
614C4×C7—81no—
615C4×C7—81no—
616Dic7—24no—
617Dic7—42no—
618Dic7—42no—
619Dic7—42no—
620Dic7—42no—
621Dic7—42no—
622Dic7—42no—
623Dic7—42no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24C2×C4×D712yes—
637C24#115912yes—
638C24Q8×D712yes—
639C24C23×D711yescharacteristic
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
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—72no—
679C22×C4—72no—
680C22×C4—72no—
681C22×C4—72no—
682C22×C4—72no—
683C22×C4—72no—
684C22×C4—72no—
685C22×C4—72no—
686C22×C4—72no—
687C22×C4—72no—
688C22×C4—141no—
689C22×C4—141no—
690C22×C4—141no—
691C22×C4—141no—
692C22×C4—141no—
693C22×C4—141no—
694C22×C4—141no—
695C22×C4—141no—
696C22×C4—141no—
697C22×C4—141no—
698C22×C4—141no—
699C22×C4—141no—
700C22×C4—141no—
701C22×C4—141no—
702C22×C4—141no—
703C22×C4—141no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—141no—
709C22×C4—141no—
710C22×C4—141no—
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—284no—
735C22×C4—284no—
736C22×C4—284no—
737C22×C4—284no—
738C22×C4—284no—
739C22×C4—284no—
740C22×C4—284no—
741C22×C4C2×C4×D712yes—
742C22×C4C2×C4×D712yes—
743C22×C4D4×D712yes—
744C22×C4#115912yes—
745C4⋊C4—44no—
746C4⋊C4—148no—
747C4⋊C4—284no—
748C4⋊C4—284no—
749C4⋊C4—284no—
750C4⋊C4—284no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—148no—
755C22⋊C4—284no—
756C22⋊C4—284no—
757C42—284no—
758C42—284no—
759C2×C7—44no—
760C2×C7#232811yescharacteristic
761C2×C7#232911yescharacteristic
762C2×C7#233511yescharacteristic
763C2×C7#235911yescharacteristic
764C2×C7#236011yescharacteristic
765C2×C7#236811yescharacteristic
766C2×C7#237611yescharacteristic
767C2×C7#268511yescharacteristic
768C2×C7#269211yescharacteristic
769C2×C7#270611yescharacteristic
770C2×C7#272011yescharacteristic
771C2×C7#273811yescharacteristic
772C2×C7#274311yescharacteristic
773C2×C7#274811yescharacteristic
774C2×C7#276811yescharacteristic
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23#645014yes—
810C23C22×C4×D711yescharacteristic
811C23C2×D4×D711yescharacteristic
812C23C2×#115911yescharacteristic
813C23C2×#115911yescharacteristic
814C23#654811yescharacteristic
815C23#654811yescharacteristic
816C23#654811yescharacteristic
817C23#654811yescharacteristic
818C23C2×Q8×D711yescharacteristic
819C23D7×#4111yescharacteristic
820C23D7×#4111yescharacteristic
821C23#655311yescharacteristic
822C23#655311yescharacteristic
823C23#655411yescharacteristic
824C23#655411yescharacteristic
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—74no—
868C2×C4—142no—
869C2×C4—142no—
870C2×C4—142no—
871C2×C4—142no—
872C2×C4—142no—
873C2×C4—142no—
874C2×C4—142no—
875C2×C4—142no—
876C2×C4—142no—
877C2×C4—142no—
878C2×C4—142no—
879C2×C4—142no—
880C2×C4—142no—
881C2×C4—142no—
882C2×C4—142no—
883C2×C4—142no—
884C2×C4—142no—
885C2×C4—142no—
886C2×C4—142no—
887C2×C4—142no—
888C2×C4—142no—
889C2×C4—142no—
890C2×C4—142no—
891C2×C4—142no—
892C2×C4—142no—
893C2×C4—142no—
894C2×C4—142no—
895C2×C4—2816no—
896C2×C4—281no—
897C2×C4—281no—
898C2×C4—281no—
899C2×C4—281no—
900C2×C4—281no—
901C2×C4—281no—
902C2×C4—281no—
903C2×C4—281no—
904C2×C4—281no—
905C2×C4—281no—
906C2×C4—281no—
907C2×C4—281no—
908C2×C4—281no—
909C2×C4—281no—
910C2×C4—281no—
911C2×C4—281no—
912C2×C4—281no—
913C2×C4—281no—
914C2×C4—281no—
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—
924C7#1458411yescharacteristic, complemented, Sylow
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22#9017711yescharacteristic
941C22C2×#645011yescharacteristic
942C22#9021411yescharacteristic
943C22C4×#115911yescharacteristic
944C22C4×D4×D711yescharacteristic
945C22#9023611yescharacteristic
946C22#9023711yescharacteristic
947C22#9027811yescharacteristic
948C22#9028211yescharacteristic
949C22#9028311yescharacteristic
950C22#9029311yescharacteristic
951C22#9029311yescharacteristic
952C22#9029811yescharacteristic
953C22#9030211yescharacteristic
954C22#9030411yescharacteristic
955C22#9030611yescharacteristic
956C22#9030811yescharacteristic
957C22#9031211yescharacteristic
958C22#9031411yescharacteristic
959C22#9032311yescharacteristic
960C22#9032511yescharacteristic
961C22#9032611yescharacteristic
962C22#9032711yescharacteristic
963C22#9032711yescharacteristic
964C22#9034111yescharacteristic
965C22#9034911yescharacteristic
966C22#9034911yescharacteristic
967C22#9035411yescharacteristic
968C22#9035711yescharacteristic
969C22#9036011yescharacteristic
970C22#9036711yescharacteristic
971C22#9037511yescharacteristic
972C22#9039911yescharacteristic
973C22#9040311yescharacteristic
974C22#9041011yescharacteristic
975C4—42no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—81no—
980C4—81no—
981C4—144no—
982C4—282no—
983C4—282no—
984C4—282no—
985C4—282no—
986C4—282no—
987C4—282no—
988C4—282no—
989C2—44no—
990C2#1173131911yescharacteristic
991C2#1173184111yescharacteristic
992C2#1173184411yescharacteristic
993C2#1173211211yescharacteristic
994C2#1173328311yescharacteristic
995C2#1173328611yescharacteristic
996C2#1173374511yescharacteristic
997C2#1173417011yescharacteristic
998C2#1173426911yescharacteristic
999C2#1173449711yescharacteristic
1000C2#1173458811yescharacteristic
1001C2#1173480811yescharacteristic
1002C2#1173482811yescharacteristic
1003C2#1173504311yescharacteristic
1004C2#1173556811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1439C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenter#1439D7
hypocenterC7#14584
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#89750C2semidirect
5. #11729320C2semidirect
10. #11727167C2semidirect
11. #11727165C2semidirect
12. #11727163C2semidirect
13. #11727161C2semidirect
14. Dic7⋊#95C2semidirect
15. #11727156C2semidirect
52. #89721C4semidirect
100. C2×C4⋊Dic7C2×C4semidirect
111. C2×Dic7⋊C4C2×C4semidirect
112. C2×Dic7⋊C4C2×C4semidirect
137. C7⋊#95C2×C4semidirect
924. C7#14584semidirect

Maximal subgroups

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

subgroupindex
C2×#897502
C2×#897212
C2×#897182
C7×#14392
#117293202
#117292992
#117292982
#117271672
#117271652
#117271632
#117271612
Dic7⋊#952
#117271562
#145847