Finite Group Databasebeta

← #13281144

Subgroups — #13281144

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×#6441C211yesmaximal, characteristic
2C2×#89714C211yesmaximal, characteristic
3C2×#89700C211yesmaximal, characteristic, complemented
4C2×#89418C211yesmaximal, characteristic, complemented
5C2×#89426C211yesmaximal, characteristic, complemented
6C7×#1437C211yesmaximal, characteristic
7#11729301C211yesmaximal, characteristic
8#11729300C211yesmaximal, characteristic
9#11729299C211yesmaximal, characteristic
10#11729298C211yesmaximal, characteristic
11#11729290C211yesmaximal, characteristic, complemented
12#11727178C211yesmaximal, characteristic, complemented
13#11727164C211yesmaximal, characteristic, complemented
14#11727163C211yesmaximal, characteristic, complemented
15#11727163C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C23×Dic14C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C2×#6441—24no—
34C2×#6441—24no—
35C2×#6441C418yescomplemented
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
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54#89714—24no—
55#89700—24no—
56#89426—24no—
57#89418—24no—
58#14362—71nomaximal, Sylow
59C25×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×Dic7—22no—
67C23×Dic7—22no—
68C23×Dic7—22no—
69C23×Dic7—22no—
70C23×Dic7—41no—
71C23×Dic7—41no—
72C23×Dic7C2×C414yes—
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C22×Dic14—22no—
82C22×Dic14—22no—
83C22×Dic14—22no—
84C22×Dic14—22no—
85C22×Dic14—41no—
86C22×Dic14—41no—
87C22×Dic14C2×C414yes—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—41no—
93C2×C7×C22⋊C4—41no—
94C2×C7×C22⋊C4—41no—
95C2×C7×C22⋊C4C2×C414yes—
96C2×C7×C22⋊C4Q814yescomplemented
97C2×C42×C7—22no—
98C2×C42×C7—41no—
99C2×C42×C7—41no—
100C2×C22⋊Dic7—22no—
101C2×C22⋊Dic7—22no—
102C2×C22⋊Dic7—22no—
103C2×C22⋊Dic7—22no—
104C2×C22⋊Dic7—22no—
105C2×C22⋊Dic7—41no—
106C2×C22⋊Dic7—41no—
107C2×C22⋊Dic7—41no—
108C2×C22⋊Dic7C2×C414yes—
109C2×C4⋊Dic7—22no—
110C2×C4⋊Dic7—41no—
111C2×C4⋊Dic7—41no—
112C2×C4⋊Dic7C2×C414yes—
113C2×C4⋊Dic7D414yes—
114C2×C4⋊Dic7D414yes—
115C2×Dic7⋊C4—22no—
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—22no—
124C2×Dic7⋊C4—22no—
125C2×Dic7⋊C4—41no—
126C2×Dic7⋊C4—41no—
127C2×Dic7⋊C4—41no—
128C2×Dic7⋊C4C2×C414yes—
129C2×Dic7⋊C4C2×C414yes—
130C2×C4×Dic7—22no—
131C2×C4×Dic7—22no—
132C2×C4×Dic7—41no—
133#6441—232no—
134C7×#95—22no—
135C7×#95—22no—
136C7×#95—41no—
137C7⋊#95—22no—
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⋊#95D414yes—
152C22×C22⋊Q8—71no—
153C2×#391—71no—
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#1437D711yescharacteristic
165#1436—71no—
166C22⋊#95—71no—
167C24×C7—21no—
168C24×C7—21no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—21no—
173C24×C7—21no—
174C24×C7—21no—
175C24×C7—21no—
176C24×C7—21no—
177C24×C7—21no—
178C24×C7—21no—
179C24×C7C22×C412yes—
180C24×C7C2×Q812yes—
181C24×C7#4112yes—
182C24×C7C2411yescharacteristic
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×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×C7C22×C412yes—
219C22×C4×C7C22×C412yes—
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2×D412yes—
222C22×C4×C7C2×D412yes—
223C22×C4×C7C2×Q812yes—
224C22×C4×C7C2×Q812yes—
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—28no—
250C22×Dic7—28no—
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—44no—
273C22×Dic7—44no—
274C22×Dic7—44no—
275C22×Dic7—44no—
276C22×Dic7—44no—
277C22×Dic7C22×C412yes—
278C22×Dic7C22×C412yes—
279C22×Dic7C22×C412yes—
280C22×Dic7C22×C412yes—
281C22×Dic7C2×D412yes—
282C22×Dic7C2×D412yes—
283C22×Dic7C2×D412yes—
284C22×Dic7C2×D412yes—
285C22×Dic7C2×D412yes—
286C22×Dic7C2×D412yes—
287C22×Dic7#4112yes—
288C2×Dic14—28no—
289C2×Dic14—28no—
290C2×Dic14—44no—
291C2×Dic14—44no—
292C2×Dic14—44no—
293C2×Dic14—44no—
294C2×Dic14—44no—
295C7×C22⋊C4—28no—
296C7×C22⋊C4—44no—
297C7×C22⋊C4—44no—
298C42×C7—44no—
299C22⋊Dic7—28no—
300C22⋊Dic7—44no—
301C22⋊Dic7—44no—
302C4⋊Dic7—44no—
303C4⋊Dic7C22⋊C4116yescomplemented
304Dic7⋊C4—28no—
305Dic7⋊C4—28no—
306Dic7⋊C4—44no—
307Dic7⋊C4—44no—
308Dic7⋊C4—44no—
309C4×Dic7—44no—
310C23×Q8—71no—
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⋊C4—71no—
322C22×C22⋊C4—71no—
323C22×C22⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C22⋊C4C2×D711yescharacteristic
326C22×C22⋊C4C2×D711yescharacteristic
327C22×C22⋊C4C2×D711yescharacteristic
328C22×C42—71no—
329C22×C42C2×D711yescharacteristic
330#391—144no—
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×#95—71no—
349C2×#95C2×D711yescharacteristic
350C2×#95C2×D711yescharacteristic
351C2×#95C2×D711yescharacteristic
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—41no—
371C23×C7—41no—
372C23×C7—41no—
373C23×C7—41no—
374C23×C7—41no—
375C23×C7—41no—
376C23×C7—41no—
377C23×C7—41no—
378C23×C7—41no—
379C23×C7—41no—
380C23×C7—41no—
381C23×C7—41no—
382C23×C7—41no—
383C23×C7—41no—
384C23×C7—41no—
385C23×C7—41no—
386C23×C7C4×Q814yes—
387C23×C7C23×C411yescharacteristic
388C23×C7C22×D411yescharacteristic
389C23×C7C22×D411yescharacteristic
390C23×C7C22×D411yescharacteristic
391C23×C7C22×Q811yescharacteristic
392C23×C7C2×#4111yescharacteristic
393C23×C7C2×#4111yescharacteristic
394C23×C7H(5,𝔽2)11yescharacteristic
395C23×C7H(5,𝔽2)11yescharacteristic
396C23×C7H(5,𝔽2)11yescharacteristic
397C23×C7H(5,𝔽2)11yescharacteristic
398C23×C72−1+411yescharacteristic
399C23×C72−1+411yescharacteristic
400C23×C72−1+411yescharacteristic
401C23×C72−1+411yescharacteristic
402C2×C4×C7—22no—
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—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
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×C7C2×C22⋊C414yes—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
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—416no—
469C2×Dic7—41no—
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×Dic7C2×C22⋊C414yes—
499C2×Dic7C2×C22⋊C414yes—
500C2×Dic7C4×D414yes—
501Dic14—416no—
502C25C22×D711yescharacteristic
503C22×Q8—74no—
504C22×Q8—142no—
505C22×Q8—142no—
506C22×Q8—142no—
507C22×Q8—142no—
508C22×Q8—281no—
509C22×Q8—281no—
510C23×C4—71no—
511C23×C4—71no—
512C23×C4—71no—
513C23×C4—71no—
514C23×C4—71no—
515C23×C4—74no—
516C23×C4—71no—
517C23×C4—71no—
518C23×C4—71no—
519C23×C4—142no—
520C23×C4—142no—
521C23×C4—142no—
522C23×C4—142no—
523C23×C4—281no—
524C23×C4—281no—
525C23×C4C22×D711yescharacteristic
526C23×C4C22×D711yescharacteristic
527C23×C4C22×D711yescharacteristic
528C23×C4C22×D711yescharacteristic
529C23×C4C22×D711yescharacteristic
530C23×C4C22×D711yescharacteristic
531C22⋊Q8—1432no—
532C2×C4⋊C4—74no—
533C2×C4⋊C4—74no—
534C2×C4⋊C4—74no—
535C2×C4⋊C4—74no—
536C2×C4⋊C4—74no—
537C2×C4⋊C4—142no—
538C2×C4⋊C4—142no—
539C2×C4⋊C4—142no—
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—281no—
549C2×C4⋊C4—281no—
550C2×C4⋊C4—281no—
551C2×C4⋊C4—281no—
552C2×C4⋊C4—281no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—41no—
558C2×C22⋊C4—41no—
559C2×C22⋊C4—41no—
560C2×C22⋊C4—74no—
561C2×C22⋊C4—142no—
562C2×C22⋊C4—142no—
563C2×C22⋊C4—142no—
564C2×C22⋊C4—142no—
565C2×C22⋊C4—142no—
566C2×C22⋊C4—281no—
567C2×C22⋊C4—281no—
568C2×C22⋊C4—281no—
569C2×C22⋊C4Dic1414yescomplemented
570C2×C22⋊C4C4×D714yes—
571C2×C42—22no—
572C2×C42—41no—
573C2×C42—41no—
574C2×C42—142no—
575C2×C42—142no—
576C2×C42—281no—
577#95—22no—
578#95—22no—
579#95—41no—
580#95—74no—
581#95—142no—
582#95—142no—
583#95—142no—
584#95—142no—
585#95—142no—
586#95—142no—
587#95—142no—
588#95—142no—
589#95—142no—
590#95—281no—
591#95—281no—
592#95—281no—
593#95—281no—
594#95—281no—
595C22×C7—24no—
596C22×C7—24no—
597C22×C7—24no—
598C22×C7—42no—
599C22×C7—42no—
600C22×C7—42no—
601C22×C7—42no—
602C22×C7—42no—
603C22×C7—42no—
604C22×C7—42no—
605C22×C7—42no—
606C22×C7—42no—
607C22×C7—42no—
608C22×C7—42no—
609C22×C7—42no—
610C22×C7C22×C22⋊C411yescharacteristic
611C22×C7C2×C4×D411yescharacteristic
612C22×C7C2×C4×Q811yescharacteristic
613C22×C7#51811yescharacteristic
614C22×C7#51911yescharacteristic
615C22×C7#52011yescharacteristic
616C22×C7#52011yescharacteristic
617C22×C7#53511yescharacteristic
618C22×C7#53611yescharacteristic
619C22×C7#53611yescharacteristic
620C22×C7#53711yescharacteristic
621C22×C7#53711yescharacteristic
622C22×C7#53711yescharacteristic
623C22×C7#53811yescharacteristic
624C22×C7#53911yescharacteristic
625C22×C7#54111yescharacteristic
626C22×C7#54211yescharacteristic
627C22×C7#54311yescharacteristic
628C22×C7#54411yescharacteristic
629C22×C7D4211yescharacteristic
630C22×C7D4211yescharacteristic
631C22×C7#54611yescharacteristic
632C22×C7#54611yescharacteristic
633C22×C7#54611yescharacteristic
634C22×C7#54811yescharacteristic
635C22×C7#54811yescharacteristic
636C22×C7D4×Q811yescharacteristic
637C22×C7D4×Q811yescharacteristic
638C22×C7D4×Q811yescharacteristic
639C22×C7#55211yescharacteristic
640C22×C7#55411yescharacteristic
641C22×C7#56211yescharacteristic
642C22×C7#56211yescharacteristic
643C22×C7#56311yescharacteristic
644C22×C7#56311yescharacteristic
645C4×C7—24no—
646C4×C7—42no—
647C4×C7—42no—
648C4×C7—42no—
649C4×C7—42no—
650C4×C7—81no—
651Dic7—24no—
652Dic7—24no—
653Dic7—24no—
654Dic7—42no—
655Dic7—42no—
656Dic7—81no—
657Dic7—81no—
658Dic7—81no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24C2×Dic1412yes—
672C24C2×C4×D712yes—
673C24#115712yes—
674C24C23×D711yescharacteristic
675C2×Q8—148no—
676C2×Q8—148no—
677C2×Q8—284no—
678C2×Q8—284no—
679C2×Q8—284no—
680C2×Q8—284no—
681C2×Q8—284no—
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—72no—
718C22×C4—72no—
719C22×C4—72no—
720C22×C4—72no—
721C22×C4—72no—
722C22×C4—72no—
723C22×C4—72no—
724C22×C4—72no—
725C22×C4—72no—
726C22×C4—72no—
727C22×C4—72no—
728C22×C4—148no—
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—141no—
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—141no—
773C22×C4—141no—
774C22×C4—141no—
775C22×C4—284no—
776C22×C4—284no—
777C22×C4—284no—
778C22×C4—284no—
779C22×C4—284no—
780C22×C4C2×Dic1412yes—
781C22×C4C2×Dic1412yes—
782C22×C4C2×C4×D712yes—
783C22×C4C2×C4×D712yes—
784C22×C4D4×D712yes—
785C22×C4D4×D712yes—
786C22×C4D4×D712yes—
787C4⋊C4—716no—
788C4⋊C4—148no—
789C4⋊C4—148no—
790C4⋊C4—284no—
791C4⋊C4—284no—
792C4⋊C4—284no—
793C4⋊C4—284no—
794C22⋊C4—28no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—148no—
798C22⋊C4—284no—
799C22⋊C4—284no—
800C42—44no—
801C42—284no—
802C2×C7—44no—
803C2×C7#231111yescharacteristic
804C2×C7#232311yescharacteristic
805C2×C7#232911yescharacteristic
806C2×C7D4×C22⋊C411yescharacteristic
807C2×C7Q8×C22⋊C411yescharacteristic
808C2×C7#236011yescharacteristic
809C2×C7#237811yescharacteristic
810C2×C7#267611yescharacteristic
811C2×C7#267711yescharacteristic
812C2×C7#268111yescharacteristic
813C2×C7#268311yescharacteristic
814C2×C7#269011yescharacteristic
815C2×C7#269211yescharacteristic
816C2×C7#270211yescharacteristic
817C2×C7#270411yescharacteristic
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23C4×Dic1414yes—
853C23C22×Dic1411yescharacteristic
854C23C22×C4×D711yescharacteristic
855C23C2×#115711yescharacteristic
856C23C2×D4×D711yescharacteristic
857C23C2×D4×D711yescharacteristic
858C23C2×D4×D711yescharacteristic
859C23#654811yescharacteristic
860C23#654811yescharacteristic
861C23#654811yescharacteristic
862C23D7×#4111yescharacteristic
863C23#655311yescharacteristic
864C23#655411yescharacteristic
865C23#655411yescharacteristic
866C23#655411yescharacteristic
867C23#655411yescharacteristic
868Q8—2816no—
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—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
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—74no—
911C2×C4—74no—
912C2×C4—74no—
913C2×C4—142no—
914C2×C4—142no—
915C2×C4—142no—
916C2×C4—142no—
917C2×C4—142no—
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—142no—
937C2×C4—2816no—
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×C4—281no—
967C2×C4D7×C22⋊C414yes—
968C7#1436211yescharacteristic, complemented, Sylow
969C22—24no—
970C22—24no—
971C22—24no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22C2×C4×Dic1411yescharacteristic
985C22#9017411yescharacteristic
986C22C2×D7×C22⋊C411yescharacteristic
987C22#9018111yescharacteristic
988C22#9020711yescharacteristic
989C22#9021011yescharacteristic
990C22#9022211yescharacteristic
991C22D4×Dic1411yescharacteristic
992C22D4×Dic1411yescharacteristic
993C22D4×Dic1411yescharacteristic
994C22#9023011yescharacteristic
995C22C4×D4×D711yescharacteristic
996C22#9023611yescharacteristic
997C22#9023711yescharacteristic
998C22#9023711yescharacteristic
999C22#9024311yescharacteristic
1000C22#9024311yescharacteristic
1001C22#9025111yescharacteristic
1002C22#9025511yescharacteristic
1003C22#9028311yescharacteristic
1004C22#9028811yescharacteristic
1005C22#9028811yescharacteristic
1006C22#9028811yescharacteristic
1007C22#9030011yescharacteristic
1008C22#9030311yescharacteristic
1009C22#9031211yescharacteristic
1010C22#9033911yescharacteristic
1011C22#9035311yescharacteristic
1012C22#9035811yescharacteristic
1013C22#9036311yescharacteristic
1014C22#9036611yescharacteristic
1015C22#9036711yescharacteristic
1016C22#9039211yescharacteristic
1017C22#9040311yescharacteristic
1018C22#9040811yescharacteristic
1019C4—24no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—144no—
1026C4—144no—
1027C4—144no—
1028C4—282no—
1029C4—282no—
1030C4—561no—
1031C4—561no—
1032C4—561no—
1033C2—44no—
1034C2#1173089211yescharacteristic
1035C2C22⋊C4×Dic1411yescharacteristic
1036C2#1173091111yescharacteristic
1037C2#1173210711yescharacteristic
1038C2#1173223811yescharacteristic
1039C2#1173224811yescharacteristic
1040C2#1173290411yescharacteristic
1041C2#1173293611yescharacteristic
1042C2#1173311211yescharacteristic
1043C2#1173311711yescharacteristic
1044C2#1173312611yescharacteristic
1045C2#1173313011yescharacteristic
1046C2#1173382511yescharacteristic
1047C2#1173387611yescharacteristic
1048C2#1173391011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1437C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenter#1437D7
hypocenterC7#14362
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×#89700C2semidirect
4. C2×#89418C2semidirect
5. C2×#89426C2semidirect
11. #11729290C2semidirect
12. #11727178C2semidirect
13. #11727164C2semidirect
14. #11727163C2semidirect
15. #11727163C2semidirect
35. C2×#6441C4semidirect
96. C2×C7×C22⋊C4Q8semidirect
303. C4⋊Dic7C22⋊C4semidirect
569. C2×C22⋊C4Dic14semidirect
968. C7#14362semidirect

Maximal subgroups

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

subgroupindex
C22×#64412
C2×#897142
C2×#897002
C2×#894182
C2×#894262
C7×#14372
#117293012
#117293002
#117292992
#117292982
#117292902
#117271782
#117271642
#117271632
#143627