Finite Group Databasebeta

← #13279156

Subgroups — #13279156

Order 1792.

1694 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
2C2×#89982C211yesmaximal, characteristic
3C2×#89724C211yesmaximal, characteristic
4C2×#89717C211yesmaximal, characteristic
5C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
6#11729881C211yesmaximal, characteristic
7#11729302C211yesmaximal, characteristic
8#11729299C211yesmaximal, characteristic
9#11729290C211yesmaximal, characteristic, complemented
10#11729290C211yesmaximal, characteristic, complemented
11#11729288C211yesmaximal, characteristic, complemented
12#11727175C211yesmaximal, characteristic, complemented
13#11727167C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15#11727159C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C4×C7×C22⋊C4—24no—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34#89982—24no—
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
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53#89724C418yescomplemented
54#89717—24no—
55C4×Dic7⋊C4—24no—
56#14177—71nomaximal, Sylow
57C25×C7C2311yescharacteristic
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—41no—
64C23×C4×C7—41no—
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4C2×C414yes—
84C2×C7×C22⋊C4D414yes—
85C2×C42×C7—22no—
86C2×C42×C7—22no—
87C2×C42×C7—22no—
88C2×C42×C7—22no—
89C2×C42×C7—41no—
90C2×C42×C7—41no—
91C2×C22⋊Dic7—22no—
92C2×C22⋊Dic7—22no—
93C2×C22⋊Dic7—22no—
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—22no—
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—22no—
99C2×C22⋊Dic7—41no—
100C2×C22⋊Dic7—41no—
101C2×C22⋊Dic7C2×C414yes—
102C2×C22⋊Dic7C2×C414yes—
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⋊C4—22no—
112C2×Dic7⋊C4—41no—
113C2×Dic7⋊C4C2×C414yescomplemented
114C2×Dic7⋊C4D414yes—
115C2×C4×Dic7—22no—
116C2×C4×Dic7—22no—
117C2×C4×Dic7—22no—
118C2×C4×Dic7—22no—
119C2×C4×Dic7—22no—
120C2×C4×Dic7—41no—
121C7×#95—22no—
122C7×#95—22no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—22no—
128C7⋊#95—22no—
129C7⋊#95—22no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—41no—
135C7⋊#95—41no—
136C7⋊#95—41no—
137C7⋊#95—41no—
138C7⋊#95C2×C414yescomplemented
139C7⋊#95C2×C414yescomplemented
140C7⋊#95C2×C414yescomplemented
141C2×#397—71no—
142C2×#388—71no—
143C2×#385—71no—
144C2×C4×C4⋊C4—71no—
145C2×C4×C22⋊C4D711yescharacteristic
146#1445—71no—
147#1442—71no—
148#1440—71no—
149#1437—71no—
150#1436—71no—
151#1436—71no—
152#1436—71no—
153#1436—71no—
154#1434—71no—
155C22⋊#95—71no—
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×C7—21no—
167C24×C7—21no—
168C24×C7C22×C412yes—
169C24×C7C2×D412yes—
170C24×C7#4112yes—
171C24×C7C2411yescharacteristic
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—28no—
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—44no—
206C22×C4×C7—44no—
207C22×C4×C7—44no—
208C22×C4×C7—44no—
209C22×C4×C7—44no—
210C22×C4×C7—44no—
211C22×C4×C7C22×C412yes—
212C22×C4×C7C22×C412yes—
213C22×C4×C7C2×D412yes—
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7#4112yes—
217C22×C4×C7#4112yes—
218C22×C4×C7#4112yes—
219C22×C4×C7#4112yes—
220C22×C4×C7#4112yes—
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×Dic7—21no—
266C22×Dic7—21no—
267C22×Dic7—21no—
268C22×Dic7—21no—
269C22×Dic7C22×C412yes—
270C22×Dic7C22×C412yes—
271C22×Dic7C22×C412yes—
272C22×Dic7C22×C412yes—
273C22×Dic7C2×D412yes—
274C22×Dic7C2×D412yes—
275C22×Dic7#4112yes—
276C22×Dic7#4112yes—
277C7×C22⋊C4—28no—
278C7×C22⋊C4—28no—
279C42×C7—44no—
280C42×C7—44no—
281C22⋊Dic7—28no—
282C22⋊Dic7—28no—
283C22⋊Dic7—44no—
284C22⋊Dic7—44no—
285Dic7⋊C4—28no—
286Dic7⋊C4—28no—
287Dic7⋊C4—44no—
288Dic7⋊C4—44no—
289C4×Dic7—28no—
290C4×Dic7—44no—
291C24×C4C2×D711yescharacteristic
292C22×C4⋊C4—71no—
293C22×C4⋊C4—71no—
294C22×C4⋊C4—71no—
295C22×C4⋊C4—71no—
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4—71no—
299C22×C22⋊C4—71no—
300C22×C22⋊C4C2×D711yescharacteristic
301C22×C22⋊C4C2×D711yescharacteristic
302C22×C42—71no—
303C22×C42—71no—
304C22×C42C2×D711yescharacteristic
305C22×C42C2×D711yescharacteristic
306#397—78no—
307#388—144no—
308#385—144no—
309C4×C4⋊C4—144no—
310C4×C22⋊C4—24no—
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×#95—71no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95—71no—
328C2×#95—71no—
329C2×#95C2×D711yescharacteristic
330C2×#95C2×D711yescharacteristic
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—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
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×C7—41no—
362C23×C7—41no—
363C23×C7—41no—
364C23×C7—41no—
365C23×C7C4×D414yes—
366C23×C7C23×C411yescharacteristic
367C23×C7C22×D411yescharacteristic
368C23×C7C22×D411yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7C2×#4111yescharacteristic
373C23×C7C2×#4111yescharacteristic
374C23×C7C2×#4111yescharacteristic
375C23×C7C2×#4111yescharacteristic
376C23×C7C2×#4111yescharacteristic
377C23×C7H(5,𝔽2)11yescharacteristic
378C23×C7H(5,𝔽2)11yescharacteristic
379C23×C72−1+411yescharacteristic
380C23×C72−1+411yescharacteristic
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—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—416no—
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×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7#12314yes—
423C2×C4×C7#12314yes—
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—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—
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×Dic7—41no—
476C2×Dic7—41no—
477C2×Dic7—41no—
478C2×Dic7—41no—
479C2×Dic7C4×D414yes—
480C25C22×D711yescharacteristic
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—22no—
486C23×C4—41no—
487C23×C4—41no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4—71no—
492C23×C4—71no—
493C23×C4—71no—
494C23×C4—71no—
495C23×C4—71no—
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500C23×C4C22×D711yescharacteristic
501C23×C4C22×D711yescharacteristic
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—142no—
510C2×C4⋊C4—142no—
511C2×C4⋊C4—142no—
512C2×C4⋊C4—142no—
513C2×C4⋊C4—281no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—74no—
519C2×C22⋊C4—74no—
520C2×C22⋊C4—142no—
521C2×C22⋊C4—142no—
522C2×C22⋊C4—142no—
523C2×C22⋊C4—142no—
524C2×C22⋊C4—142no—
525C2×C22⋊C4—142no—
526C2×C22⋊C4—142no—
527C2×C22⋊C4—142no—
528C2×C22⋊C4—281no—
529C2×C22⋊C4—281no—
530C2×C22⋊C4C4×D714yes—
531C2×C22⋊C4C22⋊D714yes—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—41no—
537C2×C42—41no—
538C2×C42—142no—
539C2×C42—142no—
540C2×C42—142no—
541C2×C42—142no—
542C2×C42—142no—
543C2×C42—281no—
544#95—22no—
545#95—22no—
546#95—74no—
547#95—74no—
548#95—74no—
549#95—142no—
550#95—142no—
551#95—142no—
552#95—142no—
553#95—142no—
554#95—142no—
555#95—142no—
556#95—142no—
557#95—142no—
558#95—142no—
559#95—142no—
560#95—281no—
561#95—281no—
562#95—281no—
563#95—281no—
564C22×C7—24no—
565C22×C7—24no—
566C22×C7—24no—
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×C7—42no—
576C22×C7—42no—
577C22×C7—42no—
578C22×C7—42no—
579C22×C7C2×C4×D411yescharacteristic
580C22×C7C2×C4×D411yescharacteristic
581C22×C7C4×#4111yescharacteristic
582C22×C7C4×#4111yescharacteristic
583C22×C7C4×#4111yescharacteristic
584C22×C7#52011yescharacteristic
585C22×C7#52011yescharacteristic
586C22×C7C2×#12311yescharacteristic
587C22×C7C2×#12311yescharacteristic
588C22×C7#52511yescharacteristic
589C22×C7#52511yescharacteristic
590C22×C7#52911yescharacteristic
591C22×C7#52911yescharacteristic
592C22×C7#52911yescharacteristic
593C22×C7#52911yescharacteristic
594C22×C7#53811yescharacteristic
595C22×C7#53911yescharacteristic
596C22×C7#54111yescharacteristic
597C22×C7#54211yescharacteristic
598C22×C7D4211yescharacteristic
599C22×C7#54611yescharacteristic
600C22×C7#54611yescharacteristic
601C22×C7#54711yescharacteristic
602C22×C7#54711yescharacteristic
603C22×C7#54811yescharacteristic
604C22×C7#54811yescharacteristic
605C22×C7#55111yescharacteristic
606C22×C7#55111yescharacteristic
607C22×C7#55211yescharacteristic
608C22×C7#55211yescharacteristic
609C22×C7#55311yescharacteristic
610C22×C7#55311yescharacteristic
611C22×C7#55611yescharacteristic
612C22×C7#55611yescharacteristic
613C22×C7#55911yescharacteristic
614C4×C7—24no—
615C4×C7—24no—
616C4×C7—42no—
617C4×C7—42no—
618C4×C7—42no—
619C4×C7—42no—
620Dic7—24no—
621Dic7—42no—
622Dic7—42no—
623Dic7—42no—
624Dic7—42no—
625Dic7—42no—
626Dic7—81no—
627Dic7—81no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24C2×C4×D712yes—
641C24#115712yes—
642C24C2×C22⋊D712yes—
643C24C23×D711yescharacteristic
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—28no—
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—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—72no—
684C22×C4—72no—
685C22×C4—72no—
686C22×C4—72no—
687C22×C4—72no—
688C22×C4—72no—
689C22×C4—72no—
690C22×C4—72no—
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—141no—
735C22×C4—141no—
736C22×C4—141no—
737C22×C4—141no—
738C22×C4—141no—
739C22×C4C2×C4×D712yes—
740C22×C4C2×C4×D712yes—
741C22×C4#115712yes—
742C22×C4#115712yes—
743C22×C4#115712yes—
744C22×C4#115712yes—
745C22×C4D4×D712yes—
746C22×C4#115912yes—
747C22×C4C2×C22⋊D712yes—
748C22×C4C2×C22⋊D712yes—
749C4⋊C4—148no—
750C4⋊C4—148no—
751C4⋊C4—284no—
752C4⋊C4—284no—
753C22⋊C4—28no—
754C22⋊C4—28no—
755C22⋊C4—148no—
756C22⋊C4—148no—
757C22⋊C4—284no—
758C22⋊C4—284no—
759C42—44no—
760C42—44no—
761C42—148no—
762C42—284no—
763C2×C7—44no—
764C2×C7C4×#12311yescharacteristic
765C2×C7C4×#12311yescharacteristic
766C2×C7#233411yescharacteristic
767C2×C7#235911yescharacteristic
768C2×C7#236111yescharacteristic
769C2×C7#236711yescharacteristic
770C2×C7#237311yescharacteristic
771C2×C7#241811yescharacteristic
772C2×C7#242111yescharacteristic
773C2×C7#244311yescharacteristic
774C2×C7#244711yescharacteristic
775C2×C7#247711yescharacteristic
776C2×C7#247811yescharacteristic
777C2×C7#257711yescharacteristic
778C2×C7#259711yescharacteristic
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—22no—
794C23—22no—
795C23—22no—
796C23—22no—
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—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23C4×C22⋊D714yes—
814C23C22×C4×D711yescharacteristic
815C23C2×#115711yescharacteristic
816C23C2×#115711yescharacteristic
817C23C2×#115711yescharacteristic
818C23C2×#115711yescharacteristic
819C23C2×#115711yescharacteristic
820C23C2×D4×D711yescharacteristic
821C23C2×#115911yescharacteristic
822C23#654811yescharacteristic
823C23#654811yescharacteristic
824C23D7×#4111yescharacteristic
825C23D7×#4111yescharacteristic
826C23#655411yescharacteristic
827C23#655411yescharacteristic
828C23C22×C22⋊D711yescharacteristic
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—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—416no—
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—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—74no—
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—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—
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—
924C2×C4—281no—
925C2×C4—281no—
926C2×C4#644614yes—
927C2×C4#649214yes—
928C7#1417711yescharacteristic, complemented, Sylow
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C4×#115711yescharacteristic
945C22C4×#115711yescharacteristic
946C22#9017011yescharacteristic
947C22#9017011yescharacteristic
948C22C2×#644611yescharacteristic
949C22#9018111yescharacteristic
950C22#9018511yescharacteristic
951C22#9018611yescharacteristic
952C22#9020911yescharacteristic
953C22#9021911yescharacteristic
954C22#9022011yescharacteristic
955C22#9022411yescharacteristic
956C22C4×#115911yescharacteristic
957C22#9023111yescharacteristic
958C22#9023111yescharacteristic
959C22#9023211yescharacteristic
960C22#9023311yescharacteristic
961C22C4×D4×D711yescharacteristic
962C22#9023711yescharacteristic
963C22#9023711yescharacteristic
964C22#9023811yescharacteristic
965C22#9024311yescharacteristic
966C22#9024311yescharacteristic
967C22#9024711yescharacteristic
968C22#9024811yescharacteristic
969C22#9025011yescharacteristic
970C22#9025211yescharacteristic
971C22#9025511yescharacteristic
972C22C2×C4×C22⋊D711yescharacteristic
973C22C2×#649211yescharacteristic
974C22#9048211yescharacteristic
975C22D4×C22⋊D711yescharacteristic
976C22#9049711yescharacteristic
977C22#9051511yescharacteristic
978C22#9051511yescharacteristic
979C4—24no—
980C4—24no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—144no—
986C4—282no—
987C4—282no—
988C4—282no—
989C4—282no—
990C4—282no—
991C4—561no—
992C4—561no—
993C2—44no—
994C2#1173089511yescharacteristic
995C2#1173091711yescharacteristic
996C2#1173092211yescharacteristic
997C2#1173092811yescharacteristic
998C2#1173094711yescharacteristic
999C2#1173099011yescharacteristic
1000C2#1173099711yescharacteristic
1001C2C4×#644611yescharacteristic
1002C2C4×#649211yescharacteristic
1003C2#1173957311yescharacteristic
1004C2#1173969711yescharacteristic
1005C2#1173978411yescharacteristic
1006C2#1173978511yescharacteristic
1007C2#1173980111yescharacteristic
1008C2#1173980411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C22⋊C4C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×C4×C22⋊C4D7
hypocenterC7#14177
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. C2×C4×Dic7⋊C4C2semidirect
9. #11729290C2semidirect
10. #11729290C2semidirect
11. #11729288C2semidirect
12. #11727175C2semidirect
13. #11727167C2semidirect
14. #11727160C2semidirect
15. #11727159C2semidirect
53. #89724C4semidirect
113. C2×Dic7⋊C4C2×C4semidirect
138. C7⋊#95C2×C4semidirect
139. C7⋊#95C2×C4semidirect
140. C7⋊#95C2×C4semidirect
928. C7#14177semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C22⋊C42
C2×#899822
C2×#897242
C2×#897172
C2×C4×Dic7⋊C42
#117298812
#117293022
#117292992
#117292902
#117292882
#117271752
#117271672
#117271602
#117271592
#141777