Finite Group Databasebeta

← #13284594

Subgroups — #13284594

Order 1792.

1378 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89720C211yesmaximal, characteristic
2C7×C22⋊#95C211yesmaximal, characteristic
3#11729881C211yesmaximal, characteristic
4#11729881C211yesmaximal, characteristic
5#11729301C211yesmaximal, characteristic
6#11729301C211yesmaximal, characteristic
7#11729300C211yesmaximal, characteristic
8#11727177C211yesmaximal, characteristic, complemented
9#11727175C211yesmaximal, characteristic, complemented
10#11727175C211yesmaximal, characteristic, complemented
11#11727174C211yesmaximal, characteristic, complemented
12#11727171C211yesmaximal, characteristic, complemented
13#11727165C211yesmaximal, characteristic, complemented
14#11727164C211yesmaximal, characteristic, complemented
15#11727163C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic7C2211yescharacteristic
20C22×C22⋊Dic7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
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#89720C418yescomplemented
52#14637—71nomaximal, Sylow
53C25×C7C2311yescharacteristic
54C23×C4×C7—41no—
55C23×C4×C7—41no—
56C23×C4×C7—41no—
57C23×C4×C7—41no—
58C23×C4×C7—41no—
59C23×C4×C7—41no—
60C23×C4×C7Q814yes—
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—41no—
77C2×C7×C22⋊C4—41no—
78C2×C7×C22⋊C4—41no—
79C2×C7×C22⋊C4—41no—
80C2×C7×C22⋊C4C2×C414yes—
81C2×C22⋊Dic7—22no—
82C2×C22⋊Dic7—22no—
83C2×C22⋊Dic7—41no—
84C2×C22⋊Dic7—41no—
85C2×C22⋊Dic7—41no—
86C2×C22⋊Dic7—41no—
87C2×C22⋊Dic7—41no—
88C2×C22⋊Dic7—41no—
89C2×C22⋊Dic7—41no—
90C2×C22⋊Dic7—41no—
91C2×C22⋊Dic7C2×C414yes—
92C2×C22⋊Dic7C2×C414yes—
93C2×C4⋊Dic7—41no—
94C2×C4⋊Dic7—41no—
95C2×C4⋊Dic7—41no—
96C2×C4⋊Dic7—41no—
97C2×C4⋊Dic7—41no—
98C2×C4⋊Dic7C2×C414yescomplemented
99C2×Dic7⋊C4—41no—
100C2×Dic7⋊C4—41no—
101C2×Dic7⋊C4—41no—
102C2×Dic7⋊C4—41no—
103C2×Dic7⋊C4—41no—
104C2×Dic7⋊C4—41no—
105C2×Dic7⋊C4—41no—
106C2×Dic7⋊C4—41no—
107C2×Dic7⋊C4—41no—
108C2×Dic7⋊C4—41no—
109C2×Dic7⋊C4C2×C414yescomplemented
110C2×Dic7⋊C4C2×C414yescomplemented
111C7×#95—41no—
112C7×#95—41no—
113C7×#95—41no—
114C7×#95—41no—
115C7⋊#95—41no—
116C7⋊#95—41no—
117C7⋊#95—41no—
118C7⋊#95—41no—
119C7⋊#95—41no—
120C7⋊#95—41no—
121C7⋊#95—41no—
122C7⋊#95—41no—
123C7⋊#95—41no—
124C7⋊#95—41no—
125C7⋊#95—41no—
126C7⋊#95—41no—
127C7⋊#95—41no—
128C7⋊#95—41no—
129C7⋊#95—41no—
130C7⋊#95—41no—
131C7⋊#95—41no—
132C7⋊#95C2×C414yescomplemented
133C2×#396—71no—
134#1445—71no—
135#1445—71no—
136#1445—71no—
137#1444—71no—
138#1443—71no—
139#1441—71no—
140#1441—71no—
141#1441—71no—
142#1439—71no—
143#1439—71no—
144#1439—71no—
145C22⋊#95—71no—
146C22⋊#95—71no—
147C22⋊#95D711yescharacteristic
148C24×C7—21no—
149C24×C7—21no—
150C24×C7—21no—
151C24×C7—21no—
152C24×C7—21no—
153C24×C7—21no—
154C24×C7—21no—
155C24×C7—21no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7—21no—
159C24×C7—21no—
160C24×C7C22×C412yes—
161C24×C7C2×Q812yes—
162C24×C7#4112yes—
163C24×C7C2411yescharacteristic
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×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—44no—
203C22×C4×C7—44no—
204C22×C4×C7—44no—
205C22×C4×C7—44no—
206C22×C4×C7—44no—
207C22×C4×C7—44no—
208C22×C4×C7—44no—
209C22×C4×C7C22×C412yes—
210C22×C4×C7C22×C412yes—
211C22×C4×C7C2×Q812yes—
212C22×C4×C7C2×Q812yes—
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—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7—21no—
265C22×Dic7C22×C412yes—
266C22×Dic7C22×C412yes—
267C22×Dic7C22×C412yes—
268C22×Dic7C22×C412yes—
269C7×C22⋊C4—44no—
270C7×C22⋊C4—44no—
271C22⋊Dic7—44no—
272C22⋊Dic7—44no—
273C22⋊Dic7—44no—
274C22⋊Dic7—44no—
275C4⋊Dic7—44no—
276C4⋊Dic7—44no—
277Dic7⋊C4—44no—
278Dic7⋊C4—44no—
279Dic7⋊C4—44no—
280Dic7⋊C4—44no—
281C24×C4C2×D711yescharacteristic
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×C22⋊C4—71no—
289C22×C22⋊C4—71no—
290C22×C22⋊C4—71no—
291C22×C22⋊C4—71no—
292C22×C22⋊C4C2×D711yescharacteristic
293C22×C22⋊C4C2×D711yescharacteristic
294#396—78no—
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×#95—71no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95C2×D711yescharacteristic
314C2×#95C2×D711yescharacteristic
315C2×#95C2×D711yescharacteristic
316C2×#95C2×D711yescharacteristic
317C23×C7—22no—
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—22no—
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—22no—
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—41no—
336C23×C7—41no—
337C23×C7—41no—
338C23×C7—41no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—41no—
344C23×C7—41no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7C4×Q814yes—
352C23×C7C23×C411yescharacteristic
353C23×C7C22×Q811yescharacteristic
354C23×C7C2×#4111yescharacteristic
355C23×C7H(5,𝔽2)11yescharacteristic
356C23×C7H(5,𝔽2)11yescharacteristic
357C23×C7H(5,𝔽2)11yescharacteristic
358C23×C7H(5,𝔽2)11yescharacteristic
359C23×C7H(5,𝔽2)11yescharacteristic
360C23×C7H(5,𝔽2)11yescharacteristic
361C23×C7H(5,𝔽2)11yescharacteristic
362C23×C7H(5,𝔽2)11yescharacteristic
363C23×C7H(5,𝔽2)11yescharacteristic
364C23×C72−1+411yescharacteristic
365C23×C72−1+411yescharacteristic
366C23×C72−1+411yescharacteristic
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—416no—
380C2×C4×C7—41no—
381C2×C4×C7—41no—
382C2×C4×C7—41no—
383C2×C4×C7—41no—
384C2×C4×C7—41no—
385C2×C4×C7—41no—
386C2×C4×C7—41no—
387C2×C4×C7—41no—
388C2×C4×C7—41no—
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×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
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×Dic7—41no—
431C2×Dic7—41no—
432C2×Dic7—41no—
433C2×Dic7—41no—
434C2×Dic7—41no—
435C2×Dic7—41no—
436C2×Dic7—41no—
437C2×Dic7—41no—
438C2×Dic7—41no—
439C2×Dic7—41no—
440C2×Dic7—41no—
441C2×Dic7—41no—
442C2×Dic7—41no—
443C2×Dic7—41no—
444C2×Dic7—41no—
445C2×Dic7—41no—
446C2×Dic7—41no—
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—
466C25C22×D711yescharacteristic
467C23×C4—41no—
468C23×C4—41no—
469C23×C4—41no—
470C23×C4—41no—
471C23×C4—41no—
472C23×C4—41no—
473C23×C4—71no—
474C23×C4—71no—
475C23×C4—71no—
476C23×C4—71no—
477C23×C4—71no—
478C23×C4—71no—
479C23×C4—71no—
480C23×C4—71no—
481C23×C4Dic1414yes—
482C23×C4C22×D711yescharacteristic
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D711yescharacteristic
485C23×C4C22×D711yescharacteristic
486C23×C4C22×D711yescharacteristic
487C23×C4C22×D711yescharacteristic
488C2×C4⋊C4—74no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—281no—
492C2×C4⋊C4—281no—
493C2×C4⋊C4—281no—
494C2×C4⋊C4—281no—
495C2×C4⋊C4—281no—
496C2×C4⋊C4—281no—
497C2×C4⋊C4—281no—
498C2×C4⋊C4—281no—
499C2×C4⋊C4—281no—
500C2×C4⋊C4—281no—
501C2×C4⋊C4—281no—
502C2×C4⋊C4—281no—
503C2×C4⋊C4—281no—
504C2×C4⋊C4—281no—
505C2×C4⋊C4—281no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—41no—
508C2×C22⋊C4—41no—
509C2×C22⋊C4—41no—
510C2×C22⋊C4—41no—
511C2×C22⋊C4—74no—
512C2×C22⋊C4—74no—
513C2×C22⋊C4—142no—
514C2×C22⋊C4—142no—
515C2×C22⋊C4—281no—
516C2×C22⋊C4—281no—
517C2×C22⋊C4—281no—
518C2×C22⋊C4—281no—
519C2×C22⋊C4—281no—
520C2×C22⋊C4—281no—
521C2×C22⋊C4—281no—
522C2×C22⋊C4—281no—
523C2×C22⋊C4C4×D714yes—
524#95—41no—
525#95—41no—
526#95—41no—
527#95—41no—
528#95—74no—
529#95—281no—
530#95—281no—
531#95—281no—
532#95—281no—
533#95—281no—
534#95—281no—
535#95—281no—
536#95—281no—
537#95—281no—
538#95—281no—
539#95—281no—
540#95—281no—
541#95—281no—
542#95—281no—
543#95—281no—
544#95—281no—
545#95—281no—
546C22×C7—24no—
547C22×C7—24no—
548C22×C7—24no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—42no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7C2×C4×Q811yescharacteristic
562C22×C7#51811yescharacteristic
563C22×C7#51811yescharacteristic
564C22×C7#51811yescharacteristic
565C22×C7#52011yescharacteristic
566C22×C7#52011yescharacteristic
567C22×C7#52011yescharacteristic
568C22×C7#53811yescharacteristic
569C22×C7#53811yescharacteristic
570C22×C7#53811yescharacteristic
571C22×C7#53911yescharacteristic
572C22×C7#53911yescharacteristic
573C22×C7#53911yescharacteristic
574C22×C7#54311yescharacteristic
575C22×C7#54311yescharacteristic
576C22×C7#54311yescharacteristic
577C22×C7#54411yescharacteristic
578C22×C7#54411yescharacteristic
579C22×C7#54411yescharacteristic
580C22×C7#56011yescharacteristic
581C22×C7#56011yescharacteristic
582C22×C7#56011yescharacteristic
583C22×C7#56011yescharacteristic
584C22×C7#56011yescharacteristic
585C22×C7#56011yescharacteristic
586C22×C7#56011yescharacteristic
587C22×C7#56211yescharacteristic
588C22×C7#56211yescharacteristic
589C22×C7#56211yescharacteristic
590C22×C7#56211yescharacteristic
591C22×C7#56211yescharacteristic
592C22×C7#56211yescharacteristic
593C22×C7#56311yescharacteristic
594C22×C7#56311yescharacteristic
595C22×C7#56311yescharacteristic
596C4×C7—42no—
597C4×C7—42no—
598C4×C7—42no—
599C4×C7—42no—
600C4×C7—81no—
601C4×C7—81no—
602Dic7—42no—
603Dic7—42no—
604Dic7—42no—
605Dic7—42no—
606Dic7—81no—
607Dic7—81no—
608Dic7—81no—
609Dic7—81no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24C2×Dic1412yes—
623C24C2×C4×D712yes—
624C24#115712yes—
625C24C23×D711yescharacteristic
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
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—44no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—72no—
672C22×C4—72no—
673C22×C4—72no—
674C22×C4—72no—
675C22×C4—141no—
676C22×C4—141no—
677C22×C4—141no—
678C22×C4—141no—
679C22×C4—141no—
680C22×C4—141no—
681C22×C4—141no—
682C22×C4—141no—
683C22×C4—141no—
684C22×C4—141no—
685C22×C4—141no—
686C22×C4—141no—
687C22×C4—141no—
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×C4C2×Dic1412yes—
728C22×C4C2×Dic1412yes—
729C22×C4C2×C4×D712yes—
730C22×C4C2×C4×D712yes—
731C4⋊C4—284no—
732C4⋊C4—284no—
733C4⋊C4—284no—
734C4⋊C4—284no—
735C4⋊C4—284no—
736C4⋊C4—284no—
737C22⋊C4—44no—
738C22⋊C4—44no—
739C22⋊C4—284no—
740C22⋊C4—284no—
741C22⋊C4—284no—
742C22⋊C4—284no—
743C2×C7—44no—
744C2×C7#232911yescharacteristic
745C2×C7#232911yescharacteristic
746C2×C7#232911yescharacteristic
747C2×C7#237711yescharacteristic
748C2×C7#237711yescharacteristic
749C2×C7#237711yescharacteristic
750C2×C7#238311yescharacteristic
751C2×C7#282511yescharacteristic
752C2×C7#282711yescharacteristic
753C2×C7#282711yescharacteristic
754C2×C7#282711yescharacteristic
755C2×C7#284111yescharacteristic
756C2×C7#284111yescharacteristic
757C2×C7#284111yescharacteristic
758C2×C7#284211yescharacteristic
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23C4×Dic1414yes—
794C23C22×Dic1411yescharacteristic
795C23C22×C4×D711yescharacteristic
796C23C2×#115711yescharacteristic
797C23#654811yescharacteristic
798C23#654811yescharacteristic
799C23#654811yescharacteristic
800C23#654811yescharacteristic
801C23#654811yescharacteristic
802C23#654811yescharacteristic
803C23#654811yescharacteristic
804C23#655111yescharacteristic
805C23#655311yescharacteristic
806C23#655311yescharacteristic
807C23#655411yescharacteristic
808C23#655411yescharacteristic
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—416no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
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—142no—
853C2×C4—142no—
854C2×C4—142no—
855C2×C4—142no—
856C2×C4—142no—
857C2×C4—142no—
858C2×C4—142no—
859C2×C4—142no—
860C2×C4—142no—
861C2×C4—142no—
862C2×C4—142no—
863C2×C4—142no—
864C2×C4—281no—
865C2×C4—281no—
866C2×C4—281no—
867C2×C4—281no—
868C2×C4—281no—
869C2×C4—281no—
870C2×C4—281no—
871C2×C4—281no—
872C2×C4—281no—
873C2×C4—281no—
874C2×C4—281no—
875C2×C4—281no—
876C2×C4—281no—
877C2×C4—281no—
878C2×C4—281no—
879C2×C4—281no—
880C2×C4—281no—
881C2×C4—281no—
882C2×C4—281no—
883C2×C4—281no—
884C2×C4—281no—
885C2×C4—281no—
886C2×C4—281no—
887C2×C4—281no—
888C2×C4—281no—
889C2×C4—281no—
890C2×C4—281no—
891C2×C4—281no—
892C2×C4—281no—
893C2×C4—281no—
894C2×C4—281no—
895C2×C4—281no—
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—
908C7#1463711yescharacteristic, complemented, Sylow
909C22—24no—
910C22—24no—
911C22—24no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22C2×C4×Dic1411yescharacteristic
925C22#9017411yescharacteristic
926C22#9017411yescharacteristic
927C22#9017411yescharacteristic
928C22#9017711yescharacteristic
929C22#9018511yescharacteristic
930C22#9019111yescharacteristic
931C22#9019511yescharacteristic
932C22#9020611yescharacteristic
933C22#9021011yescharacteristic
934C22#9021011yescharacteristic
935C22#9023611yescharacteristic
936C22#9023611yescharacteristic
937C22#9023711yescharacteristic
938C22#9023711yescharacteristic
939C22#9025111yescharacteristic
940C22#9025111yescharacteristic
941C22#9025511yescharacteristic
942C22#9025511yescharacteristic
943C22#9028611yescharacteristic
944C22#9028611yescharacteristic
945C22#9028611yescharacteristic
946C22#9028611yescharacteristic
947C22#9031111yescharacteristic
948C22#9031111yescharacteristic
949C22#9031211yescharacteristic
950C22#9031211yescharacteristic
951C22#9033711yescharacteristic
952C22#9033711yescharacteristic
953C22#9033811yescharacteristic
954C22#9033811yescharacteristic
955C22#9034211yescharacteristic
956C22#9035711yescharacteristic
957C22#9035811yescharacteristic
958C22#9035811yescharacteristic
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—81no—
964C4—81no—
965C4—282no—
966C4—282no—
967C4—282no—
968C4—282no—
969C4—561no—
970C4—561no—
971C4—561no—
972C4—561no—
973C2—44no—
974C2#1173077911yescharacteristic
975C2#1173089211yescharacteristic
976C2#1173089211yescharacteristic
977C2#1173129011yescharacteristic
978C2#1173144211yescharacteristic
979C2#1173144211yescharacteristic
980C2#1173156011yescharacteristic
981C2#1173184611yescharacteristic
982C2#1173184811yescharacteristic
983C2#1173209811yescharacteristic
984C2#1173209911yescharacteristic
985C2#1173212811yescharacteristic
986C2#1173231311yescharacteristic
987C2#1173232811yescharacteristic
988C2#1173237911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C22⋊#95C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC22⋊#95D7
hypocenterC7#14637
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
8. #11727177C2semidirect
9. #11727175C2semidirect
10. #11727175C2semidirect
11. #11727174C2semidirect
12. #11727171C2semidirect
13. #11727165C2semidirect
14. #11727164C2semidirect
15. #11727163C2semidirect
51. #89720C4semidirect
98. C2×C4⋊Dic7C2×C4semidirect
109. C2×Dic7⋊C4C2×C4semidirect
110. C2×Dic7⋊C4C2×C4semidirect
132. C7⋊#95C2×C4semidirect
908. C7#14637semidirect

Maximal subgroups

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

subgroupindex
C2×#897202
C7×C22⋊#952
#117298812
#117293012
#117293002
#117271772
#117271752
#117271742
#117271712
#117271652
#117271642
#117271632
#146377