Finite Group Databasebeta

← #13285712

Subgroups — #13285712

Order 1792.

2242 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6441C211yesmaximal, characteristic
2C2×#89984C211yesmaximal, characteristic
3C22×C7⋊#95C211yesmaximal, characteristic
4C2×#89722C211yesmaximal, characteristic
5C2×#89714C211yesmaximal, characteristic
6C2×#89428C211yesmaximal, characteristic, complemented
7C7×C22⋊#95C211yesmaximal, characteristic
8#11729298C211yesmaximal, characteristic
9#11727178C211yesmaximal, characteristic, complemented
10#11727174C211yesmaximal, characteristic, complemented
11#11727174C211yesmaximal, characteristic, complemented
12#11727173C211yesmaximal, characteristic, complemented
13#11727165C211yesmaximal, characteristic, complemented
14#11727165C211yesmaximal, characteristic, complemented
15#11727164C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C24×Dic7C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C23×Dic14C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C2×#6441—24no—
34C2×#6441—24no—
35C2×#6441—24no—
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2211yescharacteristic
40#89984—24no—
41C2×C7⋊#95—24no—
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
55C2×C7⋊#95C2211yescharacteristic
56#89722—24no—
57#89714—24no—
58#89428—24no—
59#14758—71nomaximal, Sylow
60C25×C7C2311yescharacteristic
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—22no—
65C23×C4×C7—41no—
66C23×C4×C7—41no—
67C23×C4×C7Q814yescomplemented
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×Dic7—22no—
75C23×Dic7—22no—
76C23×Dic7—22no—
77C23×Dic7—22no—
78C23×Dic7—22no—
79C23×Dic7—22no—
80C23×Dic7—22no—
81C23×Dic7—22no—
82C23×Dic7—41no—
83C23×Dic7—41no—
84C23×Dic7—41no—
85C23×Dic7—41no—
86C23×Dic7D414yes—
87C23×Dic7Q814yescomplemented
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C22×Dic14—22no—
97C22×Dic14—22no—
98C22×Dic14—22no—
99C22×Dic14—22no—
100C22×Dic14—22no—
101C22×Dic14—41no—
102C22×Dic14—41no—
103C2×C7×C22⋊C4—22no—
104C2×C7×C22⋊C4—22no—
105C2×C7×C22⋊C4—22no—
106C2×C7×C22⋊C4—22no—
107C2×C7×C22⋊C4D414yes—
108C2×C7×C22⋊C4Q814yescomplemented
109C2×C22⋊Dic7—22no—
110C2×C22⋊Dic7—22no—
111C2×C22⋊Dic7—22no—
112C2×C22⋊Dic7—22no—
113C2×C22⋊Dic7—22no—
114C2×C22⋊Dic7D414yes—
115C2×C4⋊Dic7—22no—
116C2×C4⋊Dic7—22no—
117C2×C4⋊Dic7—22no—
118C2×C4⋊Dic7—22no—
119C2×C4⋊Dic7—22no—
120C2×C4⋊Dic7—22no—
121C2×C4⋊Dic7—22no—
122C2×C4⋊Dic7—22no—
123C2×C4⋊Dic7—22no—
124C2×C4⋊Dic7—22no—
125C2×C4⋊Dic7—22no—
126C2×C4⋊Dic7—41no—
127C2×C4⋊Dic7—41no—
128C2×C4⋊Dic7—41no—
129C2×C4⋊Dic7—41no—
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—22no—
138C2×Dic7⋊C4—22no—
139C2×Dic7⋊C4—22no—
140C2×Dic7⋊C4—41no—
141C2×Dic7⋊C4—41no—
142#6441—232no—
143C7×#95—22no—
144C7×#95—22no—
145C7×#95—41no—
146C7×#95—41no—
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⋊#95D414yes—
161C22×C22⋊Q8—71no—
162C2×#395—71no—
163C2×#385—71no—
164C2×#380—71no—
165C2×#380—71no—
166C22×#95—71no—
167#1446—71no—
168#1444—71no—
169#1444—71no—
170#1444—71no—
171#1441—71no—
172#1441—71no—
173#1441—71no—
174C22⋊#95—71no—
175C22⋊#95D711yescharacteristic
176C24×C7—21no—
177C24×C7—21no—
178C24×C7—21no—
179C24×C7—21no—
180C24×C7—21no—
181C24×C7—21no—
182C24×C7—21no—
183C24×C7—21no—
184C24×C7C2×D412yes—
185C24×C7C2×D412yes—
186C24×C7C2×D412yes—
187C24×C7C2×Q812yes—
188C24×C7C2×Q812yes—
189C24×C7C2×Q812yes—
190C24×C7#4112yes—
191C24×C7C2411yescharacteristic
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—28no—
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—28no—
228C22×C4×C7—44no—
229C22×C4×C7—44no—
230C22×C4×C7—44no—
231C22×C4×C7—44no—
232C22×C4×C7—44no—
233C22×C4×C7C2×D412yes—
234C22×C4×C7C2×D412yes—
235C22×C4×C7C2×D412yes—
236C22×C4×C7C2×Q812yes—
237C22×C4×C7C2×Q812yes—
238C22×C4×C7C2×Q812yes—
239C22×C4×C7C2×Q812yes—
240C22×C4×C7#4112yes—
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—21no—
273C22×Dic7—21no—
274C22×Dic7—21no—
275C22×Dic7—28no—
276C22×Dic7—28no—
277C22×Dic7—21no—
278C22×Dic7—21no—
279C22×Dic7—21no—
280C22×Dic7—21no—
281C22×Dic7—21no—
282C22×Dic7—21no—
283C22×Dic7—21no—
284C22×Dic7—21no—
285C22×Dic7—21no—
286C22×Dic7—21no—
287C22×Dic7—21no—
288C22×Dic7—21no—
289C22×Dic7—21no—
290C22×Dic7—21no—
291C22×Dic7—44no—
292C22×Dic7—44no—
293C22×Dic7—44no—
294C22×Dic7—44no—
295C22×Dic7—44no—
296C22×Dic7—44no—
297C22×Dic7—44no—
298C22×Dic7—44no—
299C22×Dic7—44no—
300C22×Dic7—44no—
301C22×Dic7C2×D412yes—
302C22×Dic7C2×D412yes—
303C22×Dic7C2×D412yes—
304C22×Dic7C2×D412yes—
305C22×Dic7C2×D412yes—
306C22×Dic7C2×D412yes—
307C22×Dic7C2×Q812yes—
308C22×Dic7C2×Q812yes—
309C22×Dic7#4112yes—
310C22×Dic7#4112yes—
311C2×Dic14—28no—
312C2×Dic14—44no—
313C2×Dic14—44no—
314C2×Dic14—44no—
315C2×Dic14—44no—
316C2×Dic14—44no—
317C2×Dic14—44no—
318C7×C22⋊C4—28no—
319C7×C22⋊C4—28no—
320C22⋊Dic7—28no—
321C22⋊Dic7—44no—
322C4⋊Dic7—28no—
323C4⋊Dic7—44no—
324C4⋊Dic7—44no—
325C4⋊Dic7—44no—
326C4⋊Dic7—44no—
327Dic7⋊C4—28no—
328Dic7⋊C4—28no—
329Dic7⋊C4—44no—
330Dic7⋊C4—44no—
331C23×Q8—71no—
332C24×C4—71no—
333C24×C4—71no—
334C24×C4C2×D711yescharacteristic
335C2×C22⋊Q8—144no—
336C2×C22⋊Q8—144no—
337C2×C22⋊Q8—144no—
338C22×C4⋊C4—71no—
339C22×C4⋊C4—71no—
340C22×C4⋊C4—71no—
341C22×C4⋊C4—71no—
342C22×C4⋊C4—71no—
343C22×C4⋊C4—71no—
344C22×C4⋊C4—71no—
345C22×C4⋊C4—71no—
346C22×C4⋊C4—71no—
347C22×C22⋊C4—71no—
348C22×C22⋊C4—71no—
349C22×C22⋊C4C2×D711yescharacteristic
350C22×C22⋊C4C2×D711yescharacteristic
351#395—144no—
352#385—144no—
353#380—144no—
354#380—144no—
355C2×#95—71no—
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—144no—
370C2×#95C2×D711yescharacteristic
371C2×#95C2×D711yescharacteristic
372C2×#95C2×D711yescharacteristic
373C2×#95C2×D711yescharacteristic
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—22no—
378C23×C7—22no—
379C23×C7—22no—
380C23×C7—22no—
381C23×C7—22no—
382C23×C7—22no—
383C23×C7—22no—
384C23×C7—22no—
385C23×C7—22no—
386C23×C7—22no—
387C23×C7—22no—
388C23×C7—22no—
389C23×C7—22no—
390C23×C7—22no—
391C23×C7—22no—
392C23×C7—22no—
393C23×C7—22no—
394C23×C7—22no—
395C23×C7—22no—
396C23×C7—22no—
397C23×C7—22no—
398C23×C7—22no—
399C23×C7—22no—
400C23×C7—22no—
401C23×C7—22no—
402C23×C7#12014yes—
403C23×C7C22⋊Q814yes—
404C23×C7C22⋊Q814yes—
405C23×C7C22⋊Q814yes—
406C23×C7C4⋊Q814yes—
407C23×C7C4⋊Q814yes—
408C23×C7C4⋊Q814yes—
409C23×C7C22×D411yescharacteristic
410C23×C7C22×D411yescharacteristic
411C23×C7C22×D411yescharacteristic
412C23×C7C22×D411yescharacteristic
413C23×C7C22×Q811yescharacteristic
414C23×C7C22×Q811yescharacteristic
415C23×C7C22×Q811yescharacteristic
416C23×C7C2×#4111yescharacteristic
417C23×C7C2×#4111yescharacteristic
418C23×C7C2×#4111yescharacteristic
419C23×C7C2×#4111yescharacteristic
420C23×C7H(5,𝔽2)11yescharacteristic
421C23×C7H(5,𝔽2)11yescharacteristic
422C23×C7H(5,𝔽2)11yescharacteristic
423C23×C72−1+411yescharacteristic
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—416no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
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×C7C22⋊Q814yescomplemented
467C2×Dic7—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
470C2×Dic7—22no—
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—416no—
492C2×Dic7—416no—
493C2×Dic7—41no—
494C2×Dic7—41no—
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×Dic7—41no—
519C2×Dic7—41no—
520C2×Dic7—41no—
521C2×Dic7—41no—
522C2×Dic7—41no—
523C2×Dic7#12114yes—
524C2×Dic7C22⋊Q814yescomplemented
525Dic14—416no—
526C25C22×D711yescharacteristic
527C22×Q8—142no—
528C22×Q8—142no—
529C22×Q8—142no—
530C22×Q8—142no—
531C22×Q8—142no—
532C22×Q8—281no—
533C22×Q8—281no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—22no—
537C23×C4—22no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4—71no—
541C23×C4—71no—
542C23×C4—71no—
543C23×C4—71no—
544C23×C4—71no—
545C23×C4—71no—
546C23×C4—74no—
547C23×C4—74no—
548C23×C4—71no—
549C23×C4—71no—
550C23×C4—142no—
551C23×C4—142no—
552C23×C4—142no—
553C23×C4—142no—
554C23×C4—142no—
555C23×C4—142no—
556C23×C4—142no—
557C23×C4—142no—
558C23×C4—281no—
559C23×C4—281no—
560C23×C4—281no—
561C23×C4—281no—
562C23×C4Dic1414yescomplemented
563C23×C4C22×D711yescharacteristic
564C23×C4C22×D711yescharacteristic
565C23×C4C22×D711yescharacteristic
566C23×C4C22×D711yescharacteristic
567C23×C4C22×D711yescharacteristic
568C23×C4C22×D711yescharacteristic
569C22⋊Q8—1432no—
570C2×C4⋊C4—142no—
571C2×C4⋊C4—142no—
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—142no—
586C2×C4⋊C4—142no—
587C2×C4⋊C4—142no—
588C2×C4⋊C4—142no—
589C2×C4⋊C4—142no—
590C2×C4⋊C4—142no—
591C2×C4⋊C4—281no—
592C2×C4⋊C4—281no—
593C2×C4⋊C4—281no—
594C2×C4⋊C4—281no—
595C2×C4⋊C4—281no—
596C2×C4⋊C4—281no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—74no—
602C2×C22⋊C4—142no—
603C2×C22⋊C4—142no—
604C2×C22⋊C4—142no—
605C2×C22⋊C4—142no—
606C2×C22⋊C4—142no—
607C2×C22⋊C4Dic1414yescomplemented
608C2×C22⋊C4D2814yes—
609#95—22no—
610#95—22no—
611#95—41no—
612#95—41no—
613#95—74no—
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—142no—
623#95—142no—
624#95—142no—
625#95—281no—
626#95—281no—
627C22×C7—24no—
628C22×C7—24no—
629C22×C7—24no—
630C22×C7—24no—
631C22×C7—24no—
632C22×C7—24no—
633C22×C7—24no—
634C22×C7—24no—
635C22×C7—24no—
636C22×C7—24no—
637C22×C7—24no—
638C22×C7—24no—
639C22×C7—24no—
640C22×C7—24no—
641C22×C7#39518yescomplemented
642C22×C7C2×#12011yescharacteristic
643C22×C7C2×#12111yescharacteristic
644C22×C7C2×C22⋊Q811yescharacteristic
645C22×C7C2×C22⋊Q811yescharacteristic
646C22×C7C2×C22⋊Q811yescharacteristic
647C22×C7C2×C22⋊Q811yescharacteristic
648C22×C7C2×C22⋊Q811yescharacteristic
649C22×C7C2×C4⋊Q811yescharacteristic
650C22×C7C2×C4⋊Q811yescharacteristic
651C22×C7C2×C4⋊Q811yescharacteristic
652C22×C7#53211yescharacteristic
653C22×C7#53311yescharacteristic
654C22×C7#53311yescharacteristic
655C22×C7#53411yescharacteristic
656C22×C7#53711yescharacteristic
657C22×C7#54311yescharacteristic
658C22×C7#54311yescharacteristic
659C22×C7#54411yescharacteristic
660C22×C7#54411yescharacteristic
661C22×C7D4211yescharacteristic
662C22×C7D4211yescharacteristic
663C22×C7#54611yescharacteristic
664C22×C7#54611yescharacteristic
665C22×C7#54611yescharacteristic
666C22×C7#54611yescharacteristic
667C22×C7#54611yescharacteristic
668C22×C7#54711yescharacteristic
669C22×C7#54711yescharacteristic
670C22×C7D4×Q811yescharacteristic
671C22×C7#55111yescharacteristic
672C22×C7#55111yescharacteristic
673C22×C7#55211yescharacteristic
674C22×C7#55411yescharacteristic
675C22×C7#55411yescharacteristic
676C22×C7#55411yescharacteristic
677C4×C7—24no—
678C4×C7—42no—
679C4×C7—42no—
680C4×C7—42no—
681C4×C7—42no—
682C4×C7—42no—
683Dic7—24no—
684Dic7—24no—
685Dic7—42no—
686Dic7—42no—
687Dic7—42no—
688Dic7—42no—
689Dic7—81no—
690Dic7—81no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24C2×Dic1412yes—
700C24C2×Dic1412yes—
701C24C2×D2812yes—
702C24D4×D712yes—
703C24D4×D712yes—
704C24#115912yes—
705C24Q8×D712yes—
706C24C23×D711yescharacteristic
707C2×Q8—148no—
708C2×Q8—284no—
709C2×Q8—284no—
710C2×Q8—284no—
711C2×Q8—284no—
712C2×Q8—284no—
713C2×Q8—284no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—28no—
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—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—28no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—72no—
756C22×C4—72no—
757C22×C4—72no—
758C22×C4—72no—
759C22×C4—72no—
760C22×C4—72no—
761C22×C4—72no—
762C22×C4—72no—
763C22×C4—72no—
764C22×C4—72no—
765C22×C4—148no—
766C22×C4—148no—
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—148no—
776C22×C4—148no—
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—141no—
793C22×C4—141no—
794C22×C4—141no—
795C22×C4—141no—
796C22×C4—141no—
797C22×C4—141no—
798C22×C4—141no—
799C22×C4—141no—
800C22×C4—141no—
801C22×C4—141no—
802C22×C4—141no—
803C22×C4—141no—
804C22×C4—141no—
805C22×C4—141no—
806C22×C4—141no—
807C22×C4—141no—
808C22×C4—141no—
809C22×C4—141no—
810C22×C4—141no—
811C22×C4—141no—
812C22×C4—141no—
813C22×C4—141no—
814C22×C4—141no—
815C22×C4—284no—
816C22×C4—284no—
817C22×C4—284no—
818C22×C4—284no—
819C22×C4—284no—
820C22×C4—284no—
821C22×C4—284no—
822C22×C4—284no—
823C22×C4—284no—
824C22×C4—284no—
825C22×C4C2×Dic1412yes—
826C22×C4C2×Dic1412yes—
827C22×C4C2×Dic1412yes—
828C22×C4C2×Dic1412yes—
829C22×C4C2×D2812yes—
830C22×C4C2×D2812yes—
831C22×C4D4×D712yes—
832C22×C4#115912yes—
833C4⋊C4—148no—
834C4⋊C4—148no—
835C4⋊C4—148no—
836C4⋊C4—284no—
837C4⋊C4—284no—
838C4⋊C4—284no—
839C4⋊C4—284no—
840C4⋊C4—284no—
841C4⋊C4—284no—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—148no—
845C22⋊C4—284no—
846C2×C7—28no—
847C2×C7C2×#39511yescharacteristic
848C2×C7#241011yescharacteristic
849C2×C7#241711yescharacteristic
850C2×C7#243011yescharacteristic
851C2×C7#243711yescharacteristic
852C2×C7#243711yescharacteristic
853C2×C7#243811yescharacteristic
854C2×C7#243811yescharacteristic
855C2×C7#244011yescharacteristic
856C2×C7#244011yescharacteristic
857C2×C7#254911yescharacteristic
858C2×C7#254911yescharacteristic
859C2×C7#256411yescharacteristic
860C2×C7#265911yescharacteristic
861C2×C7#285711yescharacteristic
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23#643214yes—
891C23#644114yes—
892C23#644114yes—
893C23#644514yes—
894C23#645114yes—
895C23#645114yes—
896C23#646014yes—
897C23C22×Dic1411yescharacteristic
898C23C22×Dic1411yescharacteristic
899C23C22×D2811yescharacteristic
900C23C2×D4×D711yescharacteristic
901C23C2×D4×D711yescharacteristic
902C23C2×D4×D711yescharacteristic
903C23C2×#115911yescharacteristic
904C23C2×#115911yescharacteristic
905C23#654811yescharacteristic
906C23#654811yescharacteristic
907C23C2×Q8×D711yescharacteristic
908C23D7×#4111yescharacteristic
909C23D7×#4111yescharacteristic
910C23#655311yescharacteristic
911C23#655411yescharacteristic
912Q8—2816no—
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—22no—
933C2×C4—22no—
934C2×C4—416no—
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—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—74no—
956C2×C4—74no—
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—142no—
979C2×C4—142no—
980C2×C4—142no—
981C2×C4—2816no—
982C2×C4—2816no—
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×C4—281no—
1004C2×C4—281no—
1005C2×C4—281no—
1006C2×C4—281no—
1007C2×C4—281no—
1008C2×C4—281no—
1009C2×C4—281no—
1010C2×C4—281no—
1011C2×C4—281no—
1012C2×C4—281no—
1013C2×C4#644114yescomplemented
1014C7#1475811yescharacteristic, complemented, Sylow
1015C22—24no—
1016C22—24no—
1017C22—24no—
1018C22—24no—
1019C22—24no—
1020C22—24no—
1021C22—24no—
1022C22—24no—
1023C22—24no—
1024C22—24no—
1025C22—24no—
1026C22—24no—
1027C22—24no—
1028C22—24no—
1029C22#8942818yescomplemented
1030C22C2×#643211yescharacteristic
1031C22C2×#644111yescharacteristic
1032C22C2×#644111yescharacteristic
1033C22C2×#644111yescharacteristic
1034C22#9017411yescharacteristic
1035C22C2×#644511yescharacteristic
1036C22C2×#645111yescharacteristic
1037C22C2×#645111yescharacteristic
1038C22C2×#646011yescharacteristic
1039C22#9020811yescharacteristic
1040C22#9021011yescharacteristic
1041C22D4×Dic1411yescharacteristic
1042C22#9023011yescharacteristic
1043C22#9023011yescharacteristic
1044C22#9023411yescharacteristic
1045C22D4×D2811yescharacteristic
1046C22#9024511yescharacteristic
1047C22#9024511yescharacteristic
1048C22#9024611yescharacteristic
1049C22#9027811yescharacteristic
1050C22#9028111yescharacteristic
1051C22#9028211yescharacteristic
1052C22#9028211yescharacteristic
1053C22#9028711yescharacteristic
1054C22#9028811yescharacteristic
1055C22D7×#12111yescharacteristic
1056C22#9029611yescharacteristic
1057C22#9031311yescharacteristic
1058C22#9031411yescharacteristic
1059C22D7×C22⋊Q811yescharacteristic
1060C22#9032511yescharacteristic
1061C22#9034111yescharacteristic
1062C22#9034511yescharacteristic
1063C22#9034611yescharacteristic
1064C22#9034911yescharacteristic
1065C4—24no—
1066C4—42no—
1067C4—42no—
1068C4—42no—
1069C4—42no—
1070C4—42no—
1071C4—144no—
1072C4—144no—
1073C4—282no—
1074C4—282no—
1075C4—282no—
1076C4—282no—
1077C4—561no—
1078C4—561no—
1079C2—28no—
1080C2C2×#8942811yescharacteristic
1081C2#1173093811yescharacteristic
1082C2#1173097911yescharacteristic
1083C2#1173127311yescharacteristic
1084C2#1173140211yescharacteristic
1085C2#1173144611yescharacteristic
1086C2#1173151211yescharacteristic
1087C2#1173185811yescharacteristic
1088C2#1173186011yescharacteristic
1089C2#1173186111yescharacteristic
1090C2#1173191711yescharacteristic
1091C2#1173213811yescharacteristic
1092C2#1173214411yescharacteristic
1093C2#1173220811yescharacteristic
1094C2#1173233311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutator, socle, cosocleC24×C7C24
FittingC7×C22⋊#95C2
prime radicalC25×C7C23
hypercenterC22⋊#95D7
hypocenterC7#14758
LCSG ▷ C24×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
6. C2×#89428C2semidirect
9. #11727178C2semidirect
10. #11727174C2semidirect
11. #11727174C2semidirect
12. #11727173C2semidirect
13. #11727165C2semidirect
14. #11727165C2semidirect
15. #11727164C2semidirect
67. C23×C4×C7Q8semidirect
87. C23×Dic7Q8semidirect
108. C2×C7×C22⋊C4Q8semidirect
466. C2×C4×C7C22⋊Q8semidirect
524. C2×Dic7C22⋊Q8semidirect
562. C23×C4Dic14semidirect
607. C2×C22⋊C4Dic14semidirect
641. C22×C7#395semidirect
1013. C2×C4#6441semidirect
1014. C7#14758semidirect
1029. C22#89428semidirect

Maximal subgroups

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

subgroupindex
C22×#64412
C2×#899842
C22×C7⋊#952
C2×#897222
C2×#897142
C2×#894282
C7×C22⋊#952
#117292982
#117271782
#117271742
#117271732
#117271652
#117271642
#147587