Finite Group Databasebeta

← #13277256

Subgroups — #13277256

Order 1792.

2054 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6451C211yesmaximal, characteristic
2C22×#6450C211yesmaximal, characteristic
3C2×#89418C211yesmaximal, characteristic
4C2×#89418C211yesmaximal, characteristic
5C2×#89418C211yesmaximal, characteristic
6C7×#1441C211yesmaximal, characteristic
7#11729320C211yesmaximal, characteristic
8#11729318C211yesmaximal, characteristic
9#11727165C211yesmaximal, characteristic
10#11727163C211yesmaximal, characteristic
11#11727161C211yesmaximal, characteristic
12#11727160C211yesmaximal, characteristic
13#11727159C211yesmaximal, characteristic
14Dic7⋊#95C211yesmaximal, characteristic
15Dic7×#95C211yesmaximal, characteristic
16C23×Dic14C2211yescharacteristic
17C23×Dic14C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×Dic7⋊C4C2211yescharacteristic
22C22×Dic7⋊C4C2211yescharacteristic
23C22×Dic7⋊C4C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C2×#6451—24no—
32C2×#6451—24no—
33C2×#6451C418yescomplemented
34C2×#6450—24no—
35C2×#6450—24no—
36C2×#6450—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
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89418—24no—
58#89418—24no—
59#89418—24no—
60#14024—71nomaximal, Sylow
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C22×Dic14—22no—
77C22×Dic14—22no—
78C22×Dic14—22no—
79C22×Dic14—22no—
80C22×Dic14—22no—
81C22×Dic14—22no—
82C22×Dic14—22no—
83C22×Dic14—22no—
84C22×Dic14—22no—
85C22×Dic14—22no—
86C22×Dic14C2×C414yes—
87C22×Dic14C2×C414yes—
88C22×Dic14D414yes—
89C22×Dic14D414yes—
90C2×C7×C4⋊C4—22no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4C2×C414yes—
96C2×C4⋊Dic7—22no—
97C2×C4⋊Dic7—22no—
98C2×C4⋊Dic7C2×C414yes—
99C2×Dic7⋊C4—22no—
100C2×Dic7⋊C4—22no—
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—22no—
103C2×Dic7⋊C4—22no—
104C2×Dic7⋊C4—22no—
105C2×Dic7⋊C4—22no—
106C2×Dic7⋊C4—22no—
107C2×Dic7⋊C4—22no—
108C2×Dic7⋊C4—22no—
109C2×Dic7⋊C4—22no—
110C2×Dic7⋊C4—22no—
111C2×Dic7⋊C4C2×C414yes—
112C2×Dic7⋊C4C2×C414yes—
113C2×Dic7⋊C4D414yes—
114C2×C4×Dic7—22no—
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—22no—
127C2×C4×Dic7C2×C414yes—
128C2×C4×Dic7D414yes—
129#6451—232no—
130#6450—232no—
131C7×#95—22no—
132C7×#95—22no—
133C7×#95—22no—
134C7×#95—22no—
135C7×#95—22no—
136C7⋊#95—22no—
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—22no—
147C7⋊#95—22no—
148C7⋊#95—22no—
149C7⋊#95Q814yescomplemented
150C7⋊#95Q814yescomplemented
151C22×C4⋊Q8—71no—
152C22×C4×Q8—71no—
153C2×#391—71no—
154C2×#391—71no—
155C2×#391—71no—
156#1441—71no—
157#1441—71no—
158#1441—71no—
159#1441D711yescharacteristic
160#1436—71no—
161#1436—71no—
162#1436—71no—
163#1436—71no—
164C4⋊#95—71no—
165C4×#95—71no—
166C24×C7C2411yescharacteristic
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—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7C22×C412yes—
207C22×C4×C7C22×C412yes—
208C22×C4×C7C22×C412yes—
209C22×C4×C7C2×D412yes—
210C22×C4×C7C2×D412yes—
211C22×C4×C7C2×D412yes—
212C22×C4×C7C2×D412yes—
213C22×C4×C7C2×Q812yes—
214C22×C4×C7C2×Q812yes—
215C22×C4×C7#4112yes—
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×Dic7C22×C412yes—
254C22×Dic7C22×C412yes—
255C22×Dic7C22×C412yes—
256C22×Dic7C22×C412yes—
257C22×Dic7C2×D412yes—
258C22×Dic7C2×D412yes—
259C22×Dic7C2×D412yes—
260C22×Dic7C2×D412yes—
261C22×Dic7C2×D412yes—
262C22×Dic7C2×D412yes—
263C22×Dic7C2×D412yes—
264C22×Dic7C2×D412yes—
265C22×Dic7C2×Q812yes—
266C22×Dic7C2×Q812yes—
267C22×Dic7C2×Q812yes—
268C22×Dic7C2×Q812yes—
269C22×Dic7#4112yes—
270C22×Dic7#4112yes—
271C22×Dic7#4112yes—
272C2×Dic14—28no—
273C2×Dic14—28no—
274C2×Dic14—28no—
275C2×Dic14—28no—
276C2×Dic14—28no—
277C2×Dic14—28no—
278C2×Dic14—28no—
279C2×Dic14—28no—
280C2×Dic14—28no—
281C2×Dic14—44no—
282C2×Dic14—44no—
283C2×Dic14—44no—
284C2×Dic14—44no—
285C2×Dic14C22⋊C4116yes—
286C7×C4⋊C4—28no—
287C7×C4⋊C4—28no—
288C4⋊Dic7—28no—
289Dic7⋊C4—28no—
290Dic7⋊C4—28no—
291Dic7⋊C4—28no—
292Dic7⋊C4—28no—
293Dic7⋊C4—44no—
294C4×Dic7—28no—
295C4×Dic7—28no—
296C4×Dic7—28no—
297C4×Dic7—28no—
298C4×Dic7—44no—
299C23×Q8—71no—
300C23×Q8—71no—
301C2×C4⋊Q8—78no—
302C2×C4⋊Q8—144no—
303C2×C4⋊Q8—144no—
304C2×C4×Q8—144no—
305C2×C4×Q8—144no—
306C2×C4×Q8—144no—
307C22×C4⋊C4—71no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4—71no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4—71no—
312C22×C4⋊C4—71no—
313C22×C4⋊C4C2×D711yescharacteristic
314C22×C4⋊C4C2×D711yescharacteristic
315C22×C42—71no—
316C22×C42—71no—
317C22×C42—71no—
318C22×C42—71no—
319C22×C42—71no—
320#391—144no—
321#391—144no—
322#391—144no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95—71no—
328C2×#95—71no—
329C2×#95—71no—
330C2×#95—71no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95C2×D711yescharacteristic
339C2×#95C2×D711yescharacteristic
340C2×#95C2×D711yescharacteristic
341C2×#95C2×D711yescharacteristic
342C2×#95C2×D711yescharacteristic
343C23×C7C23×C411yescharacteristic
344C23×C7C22×D411yescharacteristic
345C23×C7C22×D411yescharacteristic
346C23×C7C22×D411yescharacteristic
347C23×C7C22×D411yescharacteristic
348C23×C7C22×Q811yescharacteristic
349C23×C7C22×Q811yescharacteristic
350C23×C7C2×#4111yescharacteristic
351C23×C7C2×#4111yescharacteristic
352C23×C7C2×#4111yescharacteristic
353C23×C7C2×#4111yescharacteristic
354C23×C72−1+411yescharacteristic
355C23×C72−1+411yescharacteristic
356C23×C72−1+411yescharacteristic
357C23×C72−1+411yescharacteristic
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
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—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
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×C7C2×C22⋊C414yes—
406C2×C4×C7C4×Q814yescomplemented
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
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—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—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×Dic7C2×C22⋊C414yes—
454C2×Dic7C2×C22⋊C414yes—
455C2×Dic7C4×D414yes—
456C2×Dic7C4×D414yes—
457C2×Dic7C4×Q814yescomplemented
458C2×Dic7#12014yes—
459C2×Dic7#12114yes—
460C2×Dic7#12114yes—
461C2×Dic7#12314yes—
462C2×Dic7C4⋊Q814yescomplemented
463Dic14—232no—
464Dic14—416no—
465C22×Q8—74no—
466C22×Q8—74no—
467C22×Q8—74no—
468C22×Q8—74no—
469C22×Q8—142no—
470C22×Q8—142no—
471C22×Q8—142no—
472C22×Q8—142no—
473C22×Q8—142no—
474C22×Q8—142no—
475C22×Q8—142no—
476C22×Q8—142no—
477C22×Q8—142no—
478C22×Q8—142no—
479C23×C4—71no—
480C23×C4—71no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4C22×D711yescharacteristic
488C23×C4C22×D711yescharacteristic
489C23×C4C22×D711yescharacteristic
490C23×C4C22×D711yescharacteristic
491C23×C4C22×D711yescharacteristic
492C23×C4C22×D711yescharacteristic
493C23×C4C22×D711yescharacteristic
494C4⋊Q8—1432no—
495C4×Q8—1432no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—74no—
502C2×C4⋊C4—74no—
503C2×C4⋊C4—74no—
504C2×C4⋊C4—74no—
505C2×C4⋊C4—142no—
506C2×C4⋊C4—142no—
507C2×C4⋊C4—142no—
508C2×C4⋊C4—142no—
509C2×C4⋊C4—142no—
510C2×C4⋊C4—142no—
511C2×C4⋊C4—142no—
512C2×C4⋊C4—142no—
513C2×C4⋊C4—142no—
514C2×C4⋊C4—142no—
515C2×C4⋊C4—142no—
516C2×C4⋊C4—142no—
517C2×C4⋊C4—142no—
518C2×C4⋊C4—142no—
519C2×C4⋊C4C4×D714yes—
520C2×C42—74no—
521C2×C42—74no—
522C2×C42—142no—
523C2×C42—142no—
524C2×C42—142no—
525C2×C42—142no—
526C2×C42—142no—
527C2×C42—142no—
528C2×C42—142no—
529C2×C42—142no—
530C2×C42—142no—
531C2×C42—142no—
532C2×C42—142no—
533C2×C42—142no—
534C2×C42—142no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—74no—
541#95—74no—
542#95—142no—
543#95—142no—
544#95—142no—
545#95—142no—
546#95—142no—
547#95—142no—
548#95—142no—
549#95—142no—
550#95—142no—
551#95—142no—
552#95—142no—
553#95—142no—
554#95—142no—
555C22×C7C22×C22⋊C411yescharacteristic
556C22×C7C2×C4×D411yescharacteristic
557C22×C7C2×C4×D411yescharacteristic
558C22×C7C2×C4×Q811yescharacteristic
559C22×C7C2×C4×Q811yescharacteristic
560C22×C7#51911yescharacteristic
561C22×C7#51911yescharacteristic
562C22×C7C2×#12011yescharacteristic
563C22×C7C2×#12111yescharacteristic
564C22×C7C2×#12111yescharacteristic
565C22×C7C2×#12311yescharacteristic
566C22×C7C2×C4⋊Q811yescharacteristic
567C22×C7#53211yescharacteristic
568C22×C7#53311yescharacteristic
569C22×C7#53311yescharacteristic
570C22×C7#53611yescharacteristic
571C22×C7#53611yescharacteristic
572C22×C7#54111yescharacteristic
573C22×C7#54111yescharacteristic
574C22×C7#54711yescharacteristic
575C22×C7#54711yescharacteristic
576C22×C7#54811yescharacteristic
577C22×C7#54811yescharacteristic
578C22×C7#54811yescharacteristic
579C22×C7#54811yescharacteristic
580C22×C7D4×Q811yescharacteristic
581C22×C7D4×Q811yescharacteristic
582C22×C7D4×Q811yescharacteristic
583C22×C7D4×Q811yescharacteristic
584C22×C7D4×Q811yescharacteristic
585C22×C7D4×Q811yescharacteristic
586C22×C7#55611yescharacteristic
587C22×C7#55611yescharacteristic
588C22×C7#55711yescharacteristic
589C22×C7#55711yescharacteristic
590C4×C7—24no—
591C4×C7—24no—
592C4×C7—42no—
593C4×C7—42no—
594C4×C7—42no—
595C4×C7—42no—
596C4×C7—81no—
597Dic7—24no—
598Dic7—24no—
599Dic7—24no—
600Dic7—42no—
601Dic7—42no—
602Dic7—42no—
603Dic7—81no—
604Dic7#38618yes—
605C24C23×D711yescharacteristic
606C2×Q8—716no—
607C2×Q8—148no—
608C2×Q8—148no—
609C2×Q8—148no—
610C2×Q8—148no—
611C2×Q8—148no—
612C2×Q8—148no—
613C2×Q8—148no—
614C2×Q8—148no—
615C2×Q8—148no—
616C2×Q8—284no—
617C2×Q8—284no—
618C2×Q8—284no—
619C2×Q8—284no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
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—72no—
660C22×C4—72no—
661C22×C4—72no—
662C22×C4—72no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—72no—
671C22×C4—72no—
672C22×C4—72no—
673C22×C4—72no—
674C22×C4—72no—
675C22×C4—72no—
676C22×C4—72no—
677C22×C4—72no—
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×C4C2×C4×D712yes—
716C22×C4C2×C4×D712yes—
717C22×C4C2×C4×D712yes—
718C22×C4D4×D712yes—
719C22×C4D4×D712yes—
720C22×C4D4×D712yes—
721C22×C4D4×D712yes—
722C22×C4#115912yes—
723C22×C4Q8×D712yes—
724C22×C4Q8×D712yes—
725C4⋊C4—28no—
726C4⋊C4—28no—
727C4⋊C4—148no—
728C4⋊C4—148no—
729C4⋊C4—148no—
730C4⋊C4—148no—
731C4⋊C4—148no—
732C4⋊C4—284no—
733C42—148no—
734C42—148no—
735C42—148no—
736C42—148no—
737C42—284no—
738C2×C7C2×#38611yescharacteristic
739C2×C7C4×C4⋊Q811yescharacteristic
740C2×C7#232711yescharacteristic
741C2×C7Q8×C22⋊C411yescharacteristic
742C2×C7Q8×C22⋊C411yescharacteristic
743C2×C7#236511yescharacteristic
744C2×C7#236511yescharacteristic
745C2×C7#242911yescharacteristic
746C2×C7#242911yescharacteristic
747C2×C7#243211yescharacteristic
748C2×C7#243411yescharacteristic
749C2×C7#244611yescharacteristic
750C2×C7#244611yescharacteristic
751C2×C7#254511yescharacteristic
752C2×C7#254611yescharacteristic
753C23C22×C4×D711yescharacteristic
754C23C2×D4×D711yescharacteristic
755C23C2×D4×D711yescharacteristic
756C23C2×D4×D711yescharacteristic
757C23C2×D4×D711yescharacteristic
758C23C2×#115911yescharacteristic
759C23C2×Q8×D711yescharacteristic
760C23C2×Q8×D711yescharacteristic
761C23#655111yescharacteristic
762C23D7×#4111yescharacteristic
763C23D7×#4111yescharacteristic
764C23D7×#4111yescharacteristic
765C23#655411yescharacteristic
766C23#655411yescharacteristic
767C23#655411yescharacteristic
768Q8—1432no—
769Q8—2816no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—74no—
818C2×C4—74no—
819C2×C4—74no—
820C2×C4—74no—
821C2×C4—74no—
822C2×C4—74no—
823C2×C4—74no—
824C2×C4—74no—
825C2×C4—74no—
826C2×C4—74no—
827C2×C4—142no—
828C2×C4—142no—
829C2×C4—142no—
830C2×C4—142no—
831C2×C4—142no—
832C2×C4—142no—
833C2×C4—142no—
834C2×C4—142no—
835C2×C4—142no—
836C2×C4—142no—
837C2×C4—142no—
838C2×C4—142no—
839C2×C4—142no—
840C2×C4—142no—
841C2×C4—142no—
842C2×C4—142no—
843C2×C4—142no—
844C2×C4—142no—
845C2×C4—142no—
846C2×C4—142no—
847C2×C4—142no—
848C2×C4—142no—
849C2×C4—142no—
850C2×C4—142no—
851C2×C4—142no—
852C2×C4—142no—
853C2×C4—142no—
854C2×C4—281no—
855C2×C4—281no—
856C2×C4—281no—
857C2×C4—281no—
858C2×C4—281no—
859C2×C4—281no—
860C2×C4—281no—
861C2×C4—281no—
862C2×C4—281no—
863C2×C4—281no—
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×C4D7×C22⋊C414yes—
874C2×C4#645014yescomplemented
875C7#1402411yescharacteristic, complemented, Sylow
876C22C2×D7×C22⋊C411yescharacteristic
877C22C2×#645011yescharacteristic
878C22#9020711yescharacteristic
879C22C4×D4×D711yescharacteristic
880C22C4×D4×D711yescharacteristic
881C22C4×Q8×D711yescharacteristic
882C22#9026311yescharacteristic
883C22D7×#12011yescharacteristic
884C22#9028711yescharacteristic
885C22#9028911yescharacteristic
886C22#9028911yescharacteristic
887C22D7×#12111yescharacteristic
888C22D7×#12111yescharacteristic
889C22#9030211yescharacteristic
890C22#9031311yescharacteristic
891C22#9031911yescharacteristic
892C22#9032311yescharacteristic
893C22#9032311yescharacteristic
894C22#9032311yescharacteristic
895C22#9032311yescharacteristic
896C22#9032411yescharacteristic
897C22#9033211yescharacteristic
898C22#9033911yescharacteristic
899C22D7×#12311yescharacteristic
900C22#9034611yescharacteristic
901C22#9036811yescharacteristic
902C22#9037611yescharacteristic
903C22#9037611yescharacteristic
904C22#9037911yescharacteristic
905C22#9038711yescharacteristic
906C22#9039211yescharacteristic
907C22#9039311yescharacteristic
908C22D7×C4⋊Q811yescharacteristic
909C22#9041811yescharacteristic
910C22#9041811yescharacteristic
911C4—24no—
912C4—24no—
913C4—42no—
914C4—42no—
915C4—42no—
916C4—42no—
917C4—78no—
918C4—81no—
919C4—144no—
920C4—144no—
921C4—144no—
922C4—282no—
923C4—282no—
924C4—282no—
925C4—561no—
926C2#1173132111yescharacteristic
927C2D7×#38611yescharacteristic
928C2#1173239311yescharacteristic
929C2#1173241211yescharacteristic
930C2#1173341211yescharacteristic
931C2#1173343111yescharacteristic
932C2#1173405911yescharacteristic
933C2#1173434911yescharacteristic
934C2#1173461811yescharacteristic
935C2#1173473211yescharacteristic
936C2#1173476011yescharacteristic
937C2#1173518911yescharacteristic
938C2#1173519211yescharacteristic
939C2#1173523011yescharacteristic
940C2#1173558111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1441C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1441D7
hypocenterC7#14024
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
33. C2×#6451C4semidirect
149. C7⋊#95Q8semidirect
150. C7⋊#95Q8semidirect
406. C2×C4×C7C4×Q8semidirect
457. C2×Dic7C4×Q8semidirect
462. C2×Dic7C4⋊Q8semidirect
874. C2×C4#6450semidirect
875. C7#14024semidirect

Maximal subgroups

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

subgroupindex
C22×#64512
C22×#64502
C2×#894182
C7×#14412
#117293202
#117293182
#117271652
#117271632
#117271612
#117271602
#117271592
Dic7⋊#952
Dic7×#952
#140247