Finite Group Databasebeta

← #13277087

Subgroups — #13277087

Order 1792.

1562 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×#89716C211yesmaximal, characteristic
2C2×#89716C211yesmaximal, characteristic
3C2×#89723C211yesmaximal, characteristic
4C2×#89419C211yesmaximal, characteristic, complemented
5C2×#89422C211yesmaximal, characteristic, complemented
6C7×#1437C211yesmaximal, characteristic
7#11729301C211yesmaximal, characteristic
8#11729301C211yesmaximal, characteristic
9#11729299C211yesmaximal, characteristic
10C4×C7⋊#95C211yesmaximal, characteristic, complemented
11C4×C7⋊#95C211yesmaximal, characteristic, complemented
12#11727169C211yesmaximal, characteristic, complemented
13#11727163C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15#11727156C211yesmaximal, characteristic, complemented
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×C22⋊Dic7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
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
51#89723—24no—
52#89716—24no—
53#89716C418yescomplemented
54#89422—24no—
55#89419—24no—
56#14010—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×C22⋊C4—22no—
73C2×C7×C22⋊C4—22no—
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—41no—
79C2×C7×C22⋊C4—41no—
80C2×C7×C22⋊C4C2×C414yes—
81C2×C42×C7—22no—
82C2×C42×C7—22no—
83C2×C42×C7—41no—
84C2×C22⋊Dic7—22no—
85C2×C22⋊Dic7—22no—
86C2×C22⋊Dic7—22no—
87C2×C22⋊Dic7—22no—
88C2×C22⋊Dic7—22no—
89C2×C22⋊Dic7—22no—
90C2×C22⋊Dic7—22no—
91C2×C22⋊Dic7—22no—
92C2×C22⋊Dic7—41no—
93C2×C22⋊Dic7—41no—
94C2×C22⋊Dic7C2×C414yes—
95C2×C22⋊Dic7C2×C414yes—
96C2×C4⋊Dic7—22no—
97C2×C4⋊Dic7—22no—
98C2×C4⋊Dic7—41no—
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—41no—
108C2×Dic7⋊C4—41no—
109C2×Dic7⋊C4—41no—
110C2×Dic7⋊C4C2×C414yes—
111C2×C4×Dic7—22no—
112C2×C4×Dic7—22no—
113C2×C4×Dic7—22no—
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—41no—
121C2×C4×Dic7—41no—
122C2×C4×Dic7C2×C414yes—
123C7×#95—22no—
124C7×#95—22no—
125C7×#95—41no—
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—22no—
136C7⋊#95—22no—
137C7⋊#95C2×C414yes—
138C7⋊#95C2×C414yes—
139C7⋊#95D414yes—
140C7⋊#95D414yes—
141C2×#389—71no—
142C2×#388—71no—
143C2×#388—71no—
144C2×#388—71no—
145C2×#382—71no—
146#1442—71no—
147#1441—71no—
148#1439—71no—
149#1439—71no—
150#1437—71no—
151#1437D711yescharacteristic
152#1436—71no—
153#1434—71no—
154C4×#95—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×C7#4112yes—
211C22×C4×C7#4112yes—
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×Dic7C22×C412yes—
259C22×Dic7C22×C412yes—
260C22×Dic7C22×C412yes—
261C22×Dic7C22×C412yes—
262C22×Dic7C2×D412yes—
263C22×Dic7C2×D412yes—
264C22×Dic7C2×D412yes—
265C22×Dic7C2×D412yes—
266C22×Dic7#4112yes—
267C22×Dic7#4112yes—
268C22×Dic7#4112yes—
269C22×Dic7#4112yes—
270C7×C22⋊C4—28no—
271C7×C22⋊C4—44no—
272C7×C22⋊C4—44no—
273C42×C7—44no—
274C22⋊Dic7—28no—
275C22⋊Dic7—28no—
276C22⋊Dic7—44no—
277C22⋊Dic7—44no—
278C4⋊Dic7—44no—
279Dic7⋊C4—28no—
280Dic7⋊C4—44no—
281Dic7⋊C4—44no—
282Dic7⋊C4—44no—
283C4×Dic7—28no—
284C4×Dic7—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×C22⋊C4—71no—
293C22×C22⋊C4—71no—
294C22×C22⋊C4—71no—
295C22×C22⋊C4—71no—
296C22×C22⋊C4C2×D711yescharacteristic
297C22×C22⋊C4C2×D711yescharacteristic
298C22×C22⋊C4C2×D711yescharacteristic
299C22×C42—71no—
300C22×C42—71no—
301C22×C42—71no—
302C22×C42—71no—
303C22×C42C2×D711yescharacteristic
304#389—144no—
305#388—78no—
306#388—144no—
307#388—144no—
308#382—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×#95C2×D711yescharacteristic
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×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7C2×#4111yescharacteristic
373C23×C7H(5,𝔽2)11yescharacteristic
374C23×C7H(5,𝔽2)11yescharacteristic
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—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×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×C7C4×D414yes—
418C2×C4×C7#12414yes—
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—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
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#11714yes—
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—74no—
491C2×C4⋊C4—142no—
492C2×C4⋊C4—142no—
493C2×C4⋊C4—142no—
494C2×C4⋊C4—142no—
495C2×C4⋊C4—142no—
496C2×C4⋊C4—142no—
497C2×C4⋊C4—142no—
498C2×C4⋊C4—142no—
499C2×C4⋊C4—142no—
500C2×C4⋊C4—142no—
501C2×C4⋊C4—281no—
502C2×C4⋊C4—281no—
503C2×C4⋊C4—281no—
504C2×C4⋊C4—281no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—41no—
512C2×C22⋊C4—41no—
513C2×C22⋊C4—74no—
514C2×C22⋊C4—74no—
515C2×C22⋊C4—142no—
516C2×C22⋊C4—142no—
517C2×C22⋊C4—142no—
518C2×C22⋊C4—142no—
519C2×C22⋊C4—142no—
520C2×C22⋊C4—142no—
521C2×C22⋊C4—142no—
522C2×C22⋊C4—142no—
523C2×C22⋊C4—281no—
524C2×C22⋊C4—281no—
525C2×C22⋊C4C4×D714yes—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—41no—
529C2×C42—74no—
530C2×C42—142no—
531C2×C42—142no—
532C2×C42—142no—
533C2×C42—142no—
534C2×C42—142no—
535C2×C42—142no—
536C2×C42—142no—
537C2×C42—142no—
538C2×C42—142no—
539C2×C42—281no—
540C2×C42—281no—
541#95—22no—
542#95—22no—
543#95—41no—
544#95—74no—
545#95—74no—
546#95—74no—
547#95—74no—
548#95—142no—
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—
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×#11711yescharacteristic
575C22×C7C2×C4×D411yescharacteristic
576C22×C7C2×C4×D411yescharacteristic
577C22×C7C4×#4111yescharacteristic
578C22×C7C4×#4111yescharacteristic
579C22×C7#52011yescharacteristic
580C22×C7#52011yescharacteristic
581C22×C7C2×#12411yescharacteristic
582C22×C7#52911yescharacteristic
583C22×C7#52911yescharacteristic
584C22×C7#52911yescharacteristic
585C22×C7#52911yescharacteristic
586C22×C7#53211yescharacteristic
587C22×C7#53211yescharacteristic
588C22×C7#53211yescharacteristic
589C22×C7#53811yescharacteristic
590C22×C7#53911yescharacteristic
591C22×C7#54111yescharacteristic
592C22×C7#54211yescharacteristic
593C22×C7D4211yescharacteristic
594C22×C7#54611yescharacteristic
595C22×C7#54611yescharacteristic
596C22×C7#54711yescharacteristic
597C22×C7#54711yescharacteristic
598C22×C7#54811yescharacteristic
599C22×C7#54811yescharacteristic
600C22×C7#55111yescharacteristic
601C22×C7#55211yescharacteristic
602C22×C7#55211yescharacteristic
603C22×C7#55211yescharacteristic
604C22×C7#55211yescharacteristic
605C22×C7#55311yescharacteristic
606C22×C7#55311yescharacteristic
607C22×C7#55511yescharacteristic
608C22×C7#55511yescharacteristic
609C4×C7—24no—
610C4×C7—24no—
611C4×C7—42no—
612C4×C7—42no—
613C4×C7—81no—
614C4×C7—81no—
615Dic7—24no—
616Dic7—24no—
617Dic7—42no—
618Dic7—42no—
619Dic7—42no—
620Dic7—42no—
621Dic7—42no—
622Dic7—42no—
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—72no—
682C22×C4—72no—
683C22×C4—72no—
684C22×C4—72no—
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×C4#115712yes—
733C22×C4D4×D712yes—
734C22×C4D4×D712yes—
735C22×C4#115912yes—
736C22×C4#115912yes—
737C4⋊C4—148no—
738C4⋊C4—284no—
739C4⋊C4—284no—
740C4⋊C4—284no—
741C4⋊C4—284no—
742C22⋊C4—28no—
743C22⋊C4—44no—
744C22⋊C4—44no—
745C22⋊C4—148no—
746C22⋊C4—148no—
747C22⋊C4—284no—
748C22⋊C4—284no—
749C42—44no—
750C42—148no—
751C42—284no—
752C42—284no—
753C42—284no—
754C2×C7—82no—
755C2×C7#229311yescharacteristic
756C2×C7C4×#12411yescharacteristic
757C2×C7#233411yescharacteristic
758C2×C7#234611yescharacteristic
759C2×C7#235211yescharacteristic
760C2×C7#235911yescharacteristic
761C2×C7#236111yescharacteristic
762C2×C7#248811yescharacteristic
763C2×C7#249111yescharacteristic
764C2×C7#251811yescharacteristic
765C2×C7#251911yescharacteristic
766C2×C7#251911yescharacteristic
767C2×C7#252911yescharacteristic
768C2×C7#255511yescharacteristic
769C2×C7#255811yescharacteristic
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×#115711yescharacteristic
808C23C2×D4×D711yescharacteristic
809C23C2×D4×D711yescharacteristic
810C23C2×#115911yescharacteristic
811C23C2×#115911yescharacteristic
812C23#654811yescharacteristic
813C23#654811yescharacteristic
814C23D7×#4111yescharacteristic
815C23D7×#4111yescharacteristic
816C23D7×#4111yescharacteristic
817C23D7×#4111yescharacteristic
818C23#655411yescharacteristic
819C23#655411yescharacteristic
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—41no—
839C2×C4—41no—
840C2×C4—41no—
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—74no—
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—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(C22⋊D7)⋊C414yes—
917C2×C4#644814yes—
918C7#1401011yescharacteristic, 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—
934C22C4×#115711yescharacteristic
935C22C2×(C22⋊D7)⋊C411yescharacteristic
936C22C2×#644811yescharacteristic
937C22#9018511yescharacteristic
938C22#9020911yescharacteristic
939C22D7×#11711yescharacteristic
940C22#9021911yescharacteristic
941C22C4×#115911yescharacteristic
942C22#9022911yescharacteristic
943C22#9022911yescharacteristic
944C22#9022911yescharacteristic
945C22C4×D4×D711yescharacteristic
946C22#9023711yescharacteristic
947C22#9023711yescharacteristic
948C22#9023911yescharacteristic
949C22#9023911yescharacteristic
950C22#9023911yescharacteristic
951C22#9025211yescharacteristic
952C22#9025511yescharacteristic
953C22#9027811yescharacteristic
954C22#9030111yescharacteristic
955C22#9030111yescharacteristic
956C22#9030211yescharacteristic
957C22#9030211yescharacteristic
958C22#9030511yescharacteristic
959C22#9030711yescharacteristic
960C22#9034111yescharacteristic
961C22#9034111yescharacteristic
962C22#9035211yescharacteristic
963C22#9036111yescharacteristic
964C22#9036811yescharacteristic
965C22#9036811yescharacteristic
966C22#9039911yescharacteristic
967C22#9039911yescharacteristic
968C22#9040811yescharacteristic
969C4—24no—
970C4—24no—
971C4—42no—
972C4—42no—
973C4—81no—
974C4—81no—
975C4—144no—
976C4—144no—
977C4—282no—
978C4—282no—
979C4—282no—
980C4—282no—
981C4—282no—
982C4—282no—
983C2—82no—
984C2#1173088411yescharacteristic
985C2C4×#644811yescharacteristic
986C2#1173089511yescharacteristic
987C2#1173212011yescharacteristic
988C2#1173218411yescharacteristic
989C2#1173219211yescharacteristic
990C2#1173291811yescharacteristic
991C2#1173300811yescharacteristic
992C2#1173300811yescharacteristic
993C2#1173302411yescharacteristic
994C2#1173327911yescharacteristic
995C2#1173333011yescharacteristic
996C2#1173380111yescharacteristic
997C2#1173387811yescharacteristic
998C2#1173389611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1437C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenter#1437D7
hypocenterC7#14010
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×#89419C2semidirect
5. C2×#89422C2semidirect
10. C4×C7⋊#95C2semidirect
11. C4×C7⋊#95C2semidirect
12. #11727169C2semidirect
13. #11727163C2semidirect
14. #11727160C2semidirect
15. #11727156C2semidirect
53. #89716C4semidirect
918. C7#14010semidirect

Maximal subgroups

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

subgroupindex
C2×#897162
C2×#897232
C2×#894192
C2×#894222
C7×#14372
#117293012
#117292992
C4×C7⋊#952
#117271692
#117271632
#117271602
#117271562
#140107