Finite Group Databasebeta

← #13283270

Subgroups — #13283270

Order 1792.

1490 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic
2C2×#89744C211yesmaximal, characteristic, complemented
3C2×#89721C211yesmaximal, characteristic
4C2×#89716C211yesmaximal, characteristic
5C2×#89426C211yesmaximal, characteristic, complemented
6#11729320C211yesmaximal, characteristic, complemented
7#11729303C211yesmaximal, characteristic
8#11729301C211yesmaximal, characteristic
9#11729300C211yesmaximal, characteristic
10#11729299C211yesmaximal, characteristic
11#11729290C211yesmaximal, characteristic, complemented
12#11729289C211yesmaximal, characteristic, complemented
13#11727175C211yesmaximal, characteristic, complemented
14#11727161C211yesmaximal, characteristic, complemented
15#11727160C211yesmaximal, characteristic, complemented
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
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×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C7×#388—24no—
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
51C2×C7⋊#95C2211yescharacteristic
52#89744—24no—
53#89721C418yescomplemented
54#89716—24no—
55#89426—24no—
56#14529—71nomaximal, Sylow
57C25×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—41no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—41no—
82C2×C7×C22⋊C4—41no—
83C2×C7×C22⋊C4C2×C414yes—
84C2×C42×C7—22no—
85C2×C42×C7—22no—
86C2×C42×C7—41no—
87C2×C22⋊Dic7—22no—
88C2×C22⋊Dic7—22no—
89C2×C22⋊Dic7—22no—
90C2×C22⋊Dic7—22no—
91C2×C22⋊Dic7—41no—
92C2×C22⋊Dic7—41no—
93C2×C22⋊Dic7—41no—
94C2×C22⋊Dic7—41no—
95C2×C22⋊Dic7—41no—
96C2×C22⋊Dic7—41no—
97C2×C22⋊Dic7C2×C414yes—
98C2×C22⋊Dic7C2×C414yes—
99C2×C4⋊Dic7—22no—
100C2×C4⋊Dic7—22no—
101C2×C4⋊Dic7—22no—
102C2×C4⋊Dic7—22no—
103C2×C4⋊Dic7—41no—
104C2×C4⋊Dic7C2×C414yes—
105C2×Dic7⋊C4—22no—
106C2×Dic7⋊C4—22no—
107C2×Dic7⋊C4—22no—
108C2×Dic7⋊C4—22no—
109C2×Dic7⋊C4—41no—
110C2×Dic7⋊C4—41no—
111C2×Dic7⋊C4—41no—
112C2×Dic7⋊C4—41no—
113C2×Dic7⋊C4—41no—
114C2×Dic7⋊C4C2×C414yes—
115C2×Dic7⋊C4C2×C414yes—
116C2×Dic7⋊C4D414yes—
117C2×C4×Dic7—22no—
118C2×C4×Dic7—22no—
119C2×C4×Dic7—22no—
120C2×C4×Dic7—41no—
121C2×C4×Dic7—41no—
122C2×C4×Dic7—41no—
123C7×#95—22no—
124C7×#95D414yes—
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—22no—
135C7⋊#95—41no—
136C7⋊#95—41no—
137C7⋊#95—41no—
138C7⋊#95—41no—
139C7⋊#95—41no—
140C7⋊#95C2×C414yes—
141C2×#399—71no—
142C2×#389—71no—
143C2×#388—71no—
144C2×#388D711yescharacteristic
145C2×#387—71no—
146#1445—71no—
147#1441—71no—
148#1440—71no—
149#1439—71no—
150#1439—71no—
151#1437—71no—
152#1436—71no—
153#1436—71no—
154#1436—71no—
155C4⋊#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×C7—21no—
169C24×C7—21no—
170C24×C7C22×C412yes—
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—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×C7C2×D412yes—
209C22×C4×C7C2×D412yes—
210C22×C4×C7C2×D412yes—
211C22×C4×C7C2×D412yes—
212C22×C4×C7#4112yes—
213C22×C4×C7#4112yes—
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×Dic7C22×C412yes—
263C22×Dic7C22×C412yes—
264C22×Dic7C22×C412yes—
265C22×Dic7C22×C412yes—
266C22×Dic7C2×D412yes—
267C22×Dic7C2×D412yes—
268C22×Dic7#4112yes—
269C22×Dic7#4112yes—
270C7×C4⋊C4—44no—
271C7×C22⋊C4—28no—
272C7×C22⋊C4—44no—
273C7×C22⋊C4—44no—
274C42×C7—44no—
275C22⋊Dic7—28no—
276C22⋊Dic7—44no—
277C22⋊Dic7—44no—
278C22⋊Dic7—44no—
279C4⋊Dic7—28no—
280C4⋊Dic7—44no—
281Dic7⋊C4—28no—
282Dic7⋊C4—44no—
283Dic7⋊C4—44no—
284Dic7⋊C4—44no—
285C4×Dic7—44no—
286C4×Dic7—44no—
287C22×C4⋊C4—71no—
288C22×C4⋊C4—71no—
289C22×C4⋊C4—71no—
290C22×C4⋊C4—71no—
291C22×C4⋊C4—71no—
292C22×C4⋊C4—71no—
293C22×C4⋊C4C2×D711yescharacteristic
294C22×C22⋊C4—71no—
295C22×C22⋊C4—71no—
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4C2×D711yescharacteristic
299C22×C22⋊C4C2×D711yescharacteristic
300C22×C22⋊C4C2×D711yescharacteristic
301C22×C42—71no—
302C22×C42—71no—
303C22×C42C2×D711yescharacteristic
304#399—78no—
305#389—144no—
306#388—24no—
307#388—144no—
308#387—144no—
309C2×#95—71no—
310C2×#95—71no—
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×#95C2×D711yescharacteristic
326C2×#95C2×D711yescharacteristic
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—41no—
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×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×C7C23×C411yescharacteristic
363C23×C7C22×D411yescharacteristic
364C23×C7C22×D411yescharacteristic
365C23×C7C2×#4111yescharacteristic
366C23×C7C2×#4111yescharacteristic
367C23×C7C2×#4111yescharacteristic
368C23×C7C2×#4111yescharacteristic
369C23×C7H(5,𝔽2)11yescharacteristic
370C23×C7H(5,𝔽2)11yescharacteristic
371C23×C7H(5,𝔽2)11yescharacteristic
372C23×C7H(5,𝔽2)11yescharacteristic
373C23×C72−1+411yescharacteristic
374C23×C72−1+411yescharacteristic
375C23×C72−1+411yescharacteristic
376C23×C72−1+411yescharacteristic
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
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—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×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×C7C4×D414yes—
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—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
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—
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×Dic7C4×D414yes—
475C25C22×D711yescharacteristic
476C23×C4—71no—
477C23×C4—71no—
478C23×C4—71no—
479C23×C4—71no—
480C23×C4—71no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4C22×D711yescharacteristic
485C23×C4C22×D711yescharacteristic
486C23×C4C22×D711yescharacteristic
487C23×C4C22×D711yescharacteristic
488C23×C4C22×D711yescharacteristic
489C23×C4C22×D711yescharacteristic
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—41no—
493C2×C4⋊C4—74no—
494C2×C4⋊C4—74no—
495C2×C4⋊C4—74no—
496C2×C4⋊C4—74no—
497C2×C4⋊C4—142no—
498C2×C4⋊C4—142no—
499C2×C4⋊C4—142no—
500C2×C4⋊C4—142no—
501C2×C4⋊C4—142no—
502C2×C4⋊C4—142no—
503C2×C4⋊C4—142no—
504C2×C4⋊C4—142no—
505C2×C4⋊C4—281no—
506C2×C4⋊C4—281no—
507C2×C4⋊C4—281no—
508C2×C4⋊C4—281no—
509C2×C4⋊C4—281no—
510C2×C4⋊C4—281no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—41no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4—74no—
520C2×C22⋊C4—74no—
521C2×C22⋊C4—142no—
522C2×C22⋊C4—142no—
523C2×C22⋊C4—142no—
524C2×C22⋊C4—142no—
525C2×C22⋊C4—281no—
526C2×C22⋊C4—281no—
527C2×C22⋊C4—281no—
528C2×C22⋊C4—281no—
529C2×C22⋊C4—281no—
530C2×C22⋊C4—281no—
531C2×C22⋊C4C4×D714yes—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—41no—
535C2×C42—142no—
536C2×C42—142no—
537C2×C42—142no—
538C2×C42—281no—
539C2×C42—281no—
540C2×C42—281no—
541#95—22no—
542#95—74no—
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—281no—
554#95—281no—
555#95—281no—
556#95—281no—
557#95—281no—
558#95C22⋊D714yes—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—81no—
567C22×C7—81no—
568C22×C7—81no—
569C22×C7—81no—
570C22×C7—81no—
571C22×C7—81no—
572C22×C7—81no—
573C22×C7—81no—
574C22×C7C2×C4×D411yescharacteristic
575C22×C7C2×C4×D411yescharacteristic
576C22×C7C4×#4111yescharacteristic
577C22×C7#51811yescharacteristic
578C22×C7#51911yescharacteristic
579C22×C7#52011yescharacteristic
580C22×C7#52011yescharacteristic
581C22×C7#53411yescharacteristic
582C22×C7#53611yescharacteristic
583C22×C7#53611yescharacteristic
584C22×C7#53711yescharacteristic
585C22×C7#53811yescharacteristic
586C22×C7#53911yescharacteristic
587C22×C7#53911yescharacteristic
588C22×C7#53911yescharacteristic
589C22×C7#54011yescharacteristic
590C22×C7#54111yescharacteristic
591C22×C7#54211yescharacteristic
592C22×C7#54211yescharacteristic
593C22×C7D4211yescharacteristic
594C22×C7#54611yescharacteristic
595C22×C7#54711yescharacteristic
596C22×C7#54711yescharacteristic
597C22×C7#54811yescharacteristic
598C22×C7#55011yescharacteristic
599C22×C7#55011yescharacteristic
600C22×C7#55111yescharacteristic
601C22×C7#55211yescharacteristic
602C22×C7#55211yescharacteristic
603C22×C7#55611yescharacteristic
604C22×C7#55911yescharacteristic
605C22×C7#56211yescharacteristic
606C22×C7#56211yescharacteristic
607C22×C7#56311yescharacteristic
608C22×C7#56311yescharacteristic
609C4×C7—24no—
610C4×C7—42no—
611C4×C7—42no—
612C4×C7—42no—
613C4×C7—42no—
614C4×C7—42no—
615Dic7—24no—
616Dic7—42no—
617Dic7—42no—
618Dic7—42no—
619Dic7—42no—
620Dic7—42no—
621Dic7—81no—
622Dic7—81no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24C2×C4×D712yes—
638C24C23×D711yescharacteristic
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—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—72no—
674C22×C4—72no—
675C22×C4—72no—
676C22×C4—72no—
677C22×C4—72no—
678C22×C4—72no—
679C22×C4—72no—
680C22×C4—72no—
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×C4—141no—
728C22×C4—141no—
729C22×C4C2×C4×D712yes—
730C22×C4C2×C4×D712yes—
731C22×C4#115712yes—
732C22×C4D4×D712yes—
733C22×C4#115912yes—
734C22×C4C2×C22⋊D712yes—
735C22×C4C2×C22⋊D712yes—
736C22×C4C2×C22⋊D712yes—
737C4⋊C4—44no—
738C4⋊C4—148no—
739C4⋊C4—148no—
740C4⋊C4—284no—
741C4⋊C4—284no—
742C4⋊C4—284no—
743C4⋊C4—284no—
744C22⋊C4—28no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—148no—
748C22⋊C4—284no—
749C22⋊C4—284no—
750C22⋊C4—284no—
751C42—44no—
752C42—284no—
753C42—284no—
754C2×C7—82no—
755C2×C7#232211yescharacteristic
756C2×C7#232311yescharacteristic
757C2×C7#233511yescharacteristic
758C2×C7#235911yescharacteristic
759C2×C7#236211yescharacteristic
760C2×C7#236611yescharacteristic
761C2×C7#237811yescharacteristic
762C2×C7#267111yescharacteristic
763C2×C7#267411yescharacteristic
764C2×C7#269411yescharacteristic
765C2×C7#272111yescharacteristic
766C2×C7#272711yescharacteristic
767C2×C7#273011yescharacteristic
768C2×C7#277311yescharacteristic
769C2×C7#279811yescharacteristic
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—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23C22×C4×D711yescharacteristic
806C23C2×#115711yescharacteristic
807C23C2×D4×D711yescharacteristic
808C23C2×#115911yescharacteristic
809C23#654811yescharacteristic
810C23#654811yescharacteristic
811C23D7×#4111yescharacteristic
812C23D7×#4111yescharacteristic
813C23#655311yescharacteristic
814C23#655311yescharacteristic
815C23#655411yescharacteristic
816C23#655411yescharacteristic
817C23#655411yescharacteristic
818C23#655411yescharacteristic
819C23C22×C22⋊D711yescharacteristic
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
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—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—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—74no—
862C2×C4—142no—
863C2×C4—142no—
864C2×C4—142no—
865C2×C4—142no—
866C2×C4—142no—
867C2×C4—142no—
868C2×C4—142no—
869C2×C4—142no—
870C2×C4—142no—
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—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—
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×C4C4×C22⋊D714yes—
918C7#1452911yescharacteristic, complemented, Sylow
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22#9020711yescharacteristic
935C22#9020911yescharacteristic
936C22#9021411yescharacteristic
937C22#9022511yescharacteristic
938C22C4×#115911yescharacteristic
939C22#9023211yescharacteristic
940C22C4×D4×D711yescharacteristic
941C22#9023611yescharacteristic
942C22#9023711yescharacteristic
943C22#9024411yescharacteristic
944C22#9024711yescharacteristic
945C22#9025011yescharacteristic
946C22#9029611yescharacteristic
947C22#9030211yescharacteristic
948C22#9031011yescharacteristic
949C22#9031211yescharacteristic
950C22#9034111yescharacteristic
951C22#9035111yescharacteristic
952C22#9035611yescharacteristic
953C22#9035811yescharacteristic
954C22#9036011yescharacteristic
955C22#9036311yescharacteristic
956C22#9036611yescharacteristic
957C22#9036811yescharacteristic
958C22#9039311yescharacteristic
959C22#9039511yescharacteristic
960C22#9039811yescharacteristic
961C22#9040311yescharacteristic
962C22C2×C4×C22⋊D711yescharacteristic
963C22D4×C22⋊D711yescharacteristic
964C22#9049711yescharacteristic
965C22#9051511yescharacteristic
966C22#9051611yescharacteristic
967C22#9052411yescharacteristic
968C22#9052511yescharacteristic
969C4—24no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—144no—
976C4—282no—
977C4—282no—
978C4—282no—
979C4—282no—
980C4—282no—
981C4—561no—
982C4—561no—
983C2—82no—
984C2#1173291511yescharacteristic
985C2#1173292311yescharacteristic
986C2#1173293611yescharacteristic
987C2#1173314411yescharacteristic
988C2#1173315411yescharacteristic
989C2#1173320511yescharacteristic
990C2#1173324411yescharacteristic
991C2#1173327311yescharacteristic
992C2#1173968011yescharacteristic
993C2#1173978411yescharacteristic
994C2#1173978811yescharacteristic
995C2#1174016111yescharacteristic
996C2#1174032111yescharacteristic
997C2#1174042711yescharacteristic
998C2#1174054711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#388C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#388D7
hypocenterC7#14529
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#89744C2semidirect
5. C2×#89426C2semidirect
6. #11729320C2semidirect
11. #11729290C2semidirect
12. #11729289C2semidirect
13. #11727175C2semidirect
14. #11727161C2semidirect
15. #11727160C2semidirect
53. #89721C4semidirect
918. C7#14529semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×#897442
C2×#897212
C2×#897162
C2×#894262
#117293202
#117293032
#117293012
#117293002
#117292992
#117292902
#117292892
#117271752
#117271612
#117271602
#145297