Finite Group Databasebeta

← #13277233

Subgroups — #13277233

Order 1792.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89760C211yesmaximal, characteristic
2C2×#89760C211yesmaximal, characteristic
3C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
4C2×#89711C211yesmaximal, characteristic
5C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
6C2×#89442C212yesmaximal, complemented
7C7×C4⋊#95C211yesmaximal, characteristic, complemented
8#11729317C211yesmaximal, characteristic, complemented
9#11727183C212yesmaximal, complemented
10#11727181C212yesmaximal, complemented
11#11727162C212yesmaximal, complemented
12C23×D28C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×(C2×D7)⋊C4C2212yes—
17C22×(C2×D7)⋊C4C2212yes—
18C22×(C2×D7)⋊C4C2212yes—
19C22×(C2×D7)⋊C4C2212yes—
20C22×(C2×D7)⋊C4C2212yes—
21C22×(C2×D7)⋊C4C2212yes—
22C22×C4⋊Dic7C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2212yes—
27C22×C4×Dic7C2211yescharacteristic
28C2×C7×#95C2212yes—
29C2×C7×#95C2212yes—
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2211yescharacteristic
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35#89760—24no—
36#89760—24no—
37C4⋊C4×Dic7—24no—
38#89711C418yescomplemented
39C4×C4⋊Dic7—24no—
40#89442—28no—
41#14022—71nomaximal, Sylow
42C24×D7C2312yes—
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2312yes—
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×Dic7C2312yes—
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C23×Dic7C2311yescharacteristic
53C22×D28—22no—
54C22×D28—22no—
55C22×D28—22no—
56C22×D28—22no—
57C22×D28—22no—
58C22×D28—22no—
59C22×D28C2×C414yes—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4D414yes—
66C2×C42×C7—22no—
67C2×C42×C7—22no—
68C2×C42×C7C2×C414yes—
69C2×(C2×D7)⋊C4—24no—
70C2×(C2×D7)⋊C4—24no—
71C2×(C2×D7)⋊C4—24no—
72C2×(C2×D7)⋊C4—24no—
73C2×(C2×D7)⋊C4—24no—
74C2×(C2×D7)⋊C4—24no—
75C2×(C2×D7)⋊C4—24no—
76C2×(C2×D7)⋊C4—24no—
77C2×(C2×D7)⋊C4—24no—
78C2×(C2×D7)⋊C4—24no—
79C2×(C2×D7)⋊C4—42no—
80C2×(C2×D7)⋊C4—42no—
81C2×(C2×D7)⋊C4—42no—
82C2×(C2×D7)⋊C4—42no—
83C2×(C2×D7)⋊C4—42no—
84C2×(C2×D7)⋊C4—42no—
85C2×(C2×D7)⋊C4C2×C418yes—
86C2×(C2×D7)⋊C4C2×C418yes—
87C2×C4⋊Dic7—22no—
88C2×C4⋊Dic7—22no—
89C2×C4⋊Dic7—22no—
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7—22no—
92C2×C4⋊Dic7—22no—
93C2×C4⋊Dic7—22no—
94C2×C4⋊Dic7C2×C414yes—
95C2×C4⋊Dic7D414yescomplemented
96C2×C4×Dic7—22no—
97C2×C4×Dic7—22no—
98C2×C4×Dic7—22no—
99C2×C4×Dic7—24no—
100C2×C4×Dic7—22no—
101C2×C4×Dic7—22no—
102C2×C4×Dic7—24no—
103C2×C4×Dic7—42no—
104C2×C4×Dic7D414yes—
105C7×#95—24no—
106C7×#95—42no—
107C7⋊#95—24no—
108C7⋊#95—24no—
109C7⋊#95—22no—
110C7⋊#95—22no—
111C7⋊#95—42no—
112C2×#390—71no—
113C2×#390—71no—
114C2×#390—71no—
115C2×#388—72no—
116C2×C4×C4⋊C4—71no—
117C2×C4×C4⋊C4—71no—
118#1440—72no—
119#1439—72no—
120#1437—72no—
121C4⋊#95—71no—
122C4⋊#95D711yescharacteristic, complemented
123C24×C7C2411yescharacteristic
124C23×D7—22no—
125C23×D7—22no—
126C23×D7—22no—
127C23×D7—22no—
128C23×D7—22no—
129C23×D7—22no—
130C23×D7—22no—
131C23×D7—22no—
132C23×D7—22no—
133C23×D7—22no—
134C23×D7—22no—
135C23×D7—22no—
136C23×D7—22no—
137C23×D7—22no—
138C23×D7C22×C414yes—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—21no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—21no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7C22×C412yes—
163C22×C4×C7C22×C412yes—
164C22×C4×C7C22×C412yes—
165C22×C4×C7C2×D414yes—
166C22×C4×C7C2×D412yes—
167C22×C4×C7C2×D412yes—
168C22×C4×C7C2×D412yes—
169C22×C4×C7#4112yes—
170C22×C4×C7#4112yes—
171C22×C4×C7#4112yes—
172C22×C4×C7#4112yes—
173C22×C4×C7#4112yes—
174C22×Dic7—21no—
175C22×Dic7—21no—
176C22×Dic7—21no—
177C22×Dic7—21no—
178C22×Dic7—21no—
179C22×Dic7—22no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—22no—
183C22×Dic7—21no—
184C22×Dic7—21no—
185C22×Dic7—21no—
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—22no—
189C22×Dic7—21no—
190C22×Dic7—21no—
191C22×Dic7—21no—
192C22×Dic7—21no—
193C22×Dic7—22no—
194C22×Dic7—21no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—21no—
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7C22×C414yes—
203C22×Dic7C2×D412yes—
204C22×Dic7C2×D412yes—
205C22×Dic7C2×D412yes—
206C22×Dic7C2×D412yes—
207C22×Dic7#4112yes—
208C22×Dic7#4112yes—
209C2×D28—28no—
210C2×D28—28no—
211C2×D28—28no—
212C2×D28—44no—
213C2×D28—44no—
214C2×D28—44no—
215C2×D28—44no—
216C7×C4⋊C4—28no—
217C7×C4⋊C4—44no—
218C42×C7—28no—
219(C2×D7)⋊C4—216no—
220(C2×D7)⋊C4—48no—
221(C2×D7)⋊C4—48no—
222(C2×D7)⋊C4—48no—
223(C2×D7)⋊C4—48no—
224(C2×D7)⋊C4—48no—
225C4⋊Dic7—28no—
226C4⋊Dic7—28no—
227C4⋊Dic7—28no—
228C4×Dic7—28no—
229C4×Dic7—48no—
230C4×Dic7—44no—
231C23×D4—71no—
232C22×C4⋊C4—71no—
233C22×C4⋊C4—71no—
234C22×C4⋊C4—71no—
235C22×C4⋊C4C2×D711yescharacteristic
236C22×C4⋊C4C2×D711yescharacteristic
237C22×C22⋊C4—72no—
238C22×C22⋊C4—72no—
239C22×C22⋊C4—72no—
240C22×C22⋊C4—72no—
241C22×C22⋊C4—72no—
242C22×C22⋊C4—72no—
243C22×C42—71no—
244C22×C42—71no—
245C22×C42—72no—
246C22×C42C2×D711yescharacteristic
247#390—78no—
248#390—144no—
249#390—144no—
250#388—148no—
251C4×C4⋊C4—144no—
252C4×C4⋊C4—144no—
253C2×#95—72no—
254C2×#95—71no—
255C2×#95—72no—
256C2×#95—71no—
257C2×#95—72no—
258C2×#95C2×D712yes—
259C2×#95C2×D712yes—
260C23×C7C23×C411yescharacteristic
261C23×C7C22×D411yescharacteristic
262C23×C7C22×D411yescharacteristic
263C23×C7C22×D411yescharacteristic
264C23×C7C2×#4111yescharacteristic
265C23×C7C2×#4111yescharacteristic
266C23×C7C2×#4111yescharacteristic
267C23×C7C2×#4111yescharacteristic
268C23×C7C2×#4111yescharacteristic
269C23×C7C2×#4111yescharacteristic
270C23×C7C2×#4111yescharacteristic
271C23×C7H(5,𝔽2)11yescharacteristic
272C23×C7H(5,𝔽2)11yescharacteristic
273C23×C7H(5,𝔽2)11yescharacteristic
274C23×C72−1+411yescharacteristic
275C22×D7—24no—
276C22×D7—24no—
277C22×D7—24no—
278C22×D7—24no—
279C22×D7—24no—
280C22×D7—24no—
281C22×D7—24no—
282C22×D7—42no—
283C22×D7—42no—
284C22×D7—42no—
285C22×D7—42no—
286C22×D7—42no—
287C22×D7—42no—
288C22×D7—42no—
289C22×D7—42no—
290C22×D7—42no—
291C22×D7—42no—
292C22×D7—42no—
293C22×D7—42no—
294C22×D7—42no—
295C22×D7—42no—
296C22×D7—42no—
297C22×D7—42no—
298C22×D7—42no—
299C22×D7—42no—
300C22×D7—42no—
301C22×D7—42no—
302C22×D7—42no—
303C22×D7—42no—
304C22×D7—42no—
305C22×D7—42no—
306C22×D7—42no—
307C22×D7—42no—
308C22×D7—42no—
309C22×D7—42no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—24no—
320C2×C4×C7—24no—
321C2×C4×C7—24no—
322C2×C4×C7—42no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—42no—
327C2×C4×C7—41no—
328C2×C4×C7—42no—
329C2×C4×C7—42no—
330C2×C4×C7—42no—
331C2×C4×C7—42no—
332C2×C4×C7—42no—
333C2×C4×C7—42no—
334C2×C4×C7—42no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7#11714yes—
338C2×C4×C7C4×D414yes—
339C2×C4×C7C4×D414yes—
340C2×C4×C7C4×D414yes—
341C2×C4×C7#12114yes—
342C2×C4×C7#12314yes—
343C2×C4×C7#12414yes—
344C2×C4×C7#12614yes—
345C2×Dic7—22no—
346C2×Dic7—22no—
347C2×Dic7—22no—
348C2×Dic7—22no—
349C2×Dic7—22no—
350C2×Dic7—22no—
351C2×Dic7—24no—
352C2×Dic7—24no—
353C2×Dic7—24no—
354C2×Dic7—22no—
355C2×Dic7—22no—
356C2×Dic7—22no—
357C2×Dic7—22no—
358C2×Dic7—22no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—41no—
364C2×Dic7—41no—
365C2×Dic7—41no—
366C2×Dic7—41no—
367C2×Dic7—42no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—42no—
371C2×Dic7—42no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—42no—
379C2×Dic7#12114yes—
380D28—416no—
381C25—72no—
382C22×D4—74no—
383C22×D4—142no—
384C22×D4—142no—
385C22×D4—142no—
386C22×D4—142no—
387C22×D4—142no—
388C22×D4—142no—
389C23×C4—71no—
390C23×C4—72no—
391C23×C4—71no—
392C23×C4—71no—
393C23×C4—71no—
394C23×C4C22×D712yes—
395C23×C4C22×D711yescharacteristic
396C23×C4C22×D712yes—
397C23×C4C22×D711yescharacteristic
398C23×C4C22×D711yescharacteristic
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—74no—
405C2×C4⋊C4—74no—
406C2×C4⋊C4—142no—
407C2×C4⋊C4—142no—
408C2×C4⋊C4—142no—
409C2×C4⋊C4—142no—
410C2×C4⋊C4—142no—
411C2×C4⋊C4—142no—
412C2×C4⋊C4—142no—
413C2×C4⋊C4D2814yes—
414C2×C22⋊C4—78no—
415C2×C22⋊C4—78no—
416C2×C22⋊C4—144no—
417C2×C22⋊C4—144no—
418C2×C22⋊C4—144no—
419C2×C22⋊C4—144no—
420C2×C22⋊C4—144no—
421C2×C22⋊C4—144no—
422C2×C22⋊C4—144no—
423C2×C22⋊C4—144no—
424C2×C22⋊C4—144no—
425C2×C22⋊C4—144no—
426C2×C22⋊C4—282no—
427C2×C22⋊C4—282no—
428C2×C22⋊C4—282no—
429C2×C22⋊C4—282no—
430C2×C22⋊C4—282no—
431C2×C22⋊C4—282no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—74no—
435C2×C42—142no—
436C2×C42—142no—
437C2×C42—144no—
438C2×C42—144no—
439C2×C42—142no—
440C2×C42—142no—
441C2×C42—142no—
442C2×C42—282no—
443C2×C42C4×D714yes—
444#95—24no—
445#95—42no—
446#95—142no—
447#95—142no—
448#95—144no—
449#95—144no—
450#95—282no—
451C22×C7C2×#11711yescharacteristic
452C22×C7C2×C4×D411yescharacteristic
453C22×C7C2×C4×D411yescharacteristic
454C22×C7C2×C4×D411yescharacteristic
455C22×C7C4×#4111yescharacteristic
456C22×C7#51811yescharacteristic
457C22×C7#52011yescharacteristic
458C22×C7C2×#12111yescharacteristic
459C22×C7C2×#12111yescharacteristic
460C22×C7C2×#12311yescharacteristic
461C22×C7#52511yescharacteristic
462C22×C7C2×#12411yescharacteristic
463C22×C7C2×#12611yescharacteristic
464C22×C7#52911yescharacteristic
465C22×C7#53211yescharacteristic
466C22×C7#53511yescharacteristic
467C22×C7#53711yescharacteristic
468C22×C7#54011yescharacteristic
469C22×C7#54211yescharacteristic
470C22×C7D4211yescharacteristic
471C22×C7#54611yescharacteristic
472C22×C7#54711yescharacteristic
473C22×C7#54811yescharacteristic
474C22×C7#55011yescharacteristic
475C22×C7#55011yescharacteristic
476C22×C7#55011yescharacteristic
477C22×C7#55311yescharacteristic
478C22×C7#55311yescharacteristic
479C22×C7#55511yescharacteristic
480C22×C7#55611yescharacteristic
481C22×C7#55611yescharacteristic
482C22×C7#55911yescharacteristic
483C22×C7#55911yescharacteristic
484C22×C7#55911yescharacteristic
485C22×C7#55911yescharacteristic
486C2×D7—44no—
487C2×D7—44no—
488C2×D7—44no—
489C2×D7—44no—
490C2×D7—44no—
491C2×D7—44no—
492C2×D7—44no—
493C2×D7—82no—
494C2×D7—82no—
495C2×D7—82no—
496C2×D7—82no—
497C2×D7—82no—
498C2×D7—82no—
499C2×D7—82no—
500C2×D7—82no—
501C4×C7—24no—
502C4×C7—42no—
503C4×C7—44no—
504C4×C7—82no—
505C4×C7#38818yescomplemented
506Dic7—24no—
507Dic7—44no—
508Dic7—42no—
509Dic7—42no—
510Dic7—42no—
511C24—74no—
512C24—142no—
513C24—142no—
514C24—142no—
515C24—142no—
516C24—142no—
517C24—142no—
518C24—142no—
519C24—142no—
520C24—142no—
521C24—142no—
522C24—142no—
523C24—142no—
524C24—142no—
525C24—142no—
526C24C23×D711yescharacteristic
527C2×D4—148no—
528C2×D4—148no—
529C2×D4—148no—
530C2×D4—284no—
531C2×D4—284no—
532C2×D4—284no—
533C2×D4—284no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—72no—
558C22×C4—72no—
559C22×C4—72no—
560C22×C4—74no—
561C22×C4—72no—
562C22×C4—72no—
563C22×C4—72no—
564C22×C4—141no—
565C22×C4—141no—
566C22×C4—141no—
567C22×C4—141no—
568C22×C4—141no—
569C22×C4—142no—
570C22×C4—141no—
571C22×C4—141no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—141no—
575C22×C4—141no—
576C22×C4—141no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—142no—
582C22×C4—141no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—141no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4C2×C4×D712yes—
593C22×C4C2×C4×D712yes—
594C22×C4C2×C4×D712yes—
595C22×C4C2×D2814yes—
596C22×C4C2×D2812yes—
597C22×C4#115712yes—
598C22×C4D4×D712yes—
599C22×C4D4×D712yes—
600C22×C4#115912yes—
601C22×C4#115912yes—
602C22×C4#116112yes—
603C22×C4#116112yes—
604C4⋊C4—28no—
605C4⋊C4—44no—
606C4⋊C4—148no—
607C4⋊C4—148no—
608C4⋊C4—148no—
609C22⋊C4—1416no—
610C22⋊C4—288no—
611C22⋊C4—288no—
612C22⋊C4—288no—
613C22⋊C4—288no—
614C22⋊C4—288no—
615C42—28no—
616C42—148no—
617C42—288no—
618C42—284no—
619C2×C7C2×#38811yescharacteristic
620C2×C7C4×#12111yescharacteristic
621C2×C7#232411yescharacteristic
622C2×C7#235411yescharacteristic
623C2×C7#235711yescharacteristic
624C2×C7#236611yescharacteristic
625C2×C7#236711yescharacteristic
626C2×C7#241411yescharacteristic
627C2×C7#241611yescharacteristic
628C2×C7#244511yescharacteristic
629C2×C7#244811yescharacteristic
630C2×C7#251211yescharacteristic
631C2×C7#251311yescharacteristic
632C2×C7#254811yescharacteristic
633C2×C7#259211yescharacteristic
634D7—84no—
635C23—144no—
636C23—144no—
637C23—144no—
638C23—144no—
639C23—144no—
640C23—144no—
641C23—144no—
642C23—282no—
643C23—282no—
644C23—282no—
645C23—282no—
646C23—282no—
647C23—282no—
648C23—282no—
649C23—282no—
650C23—282no—
651C23—282no—
652C23—282no—
653C23—282no—
654C23—282no—
655C23—282no—
656C23—282no—
657C23—282no—
658C23—282no—
659C23—282no—
660C23—282no—
661C23—282no—
662C23—282no—
663C23—282no—
664C23—282no—
665C23—282no—
666C23—282no—
667C23—282no—
668C23—282no—
669C23—282no—
670C23C22×C4×D711yescharacteristic
671C23C22×D2811yescharacteristic
672C23C2×#115711yescharacteristic
673C23C2×D4×D711yescharacteristic
674C23C2×D4×D711yescharacteristic
675C23C2×#115911yescharacteristic
676C23C2×#115911yescharacteristic
677C23#654811yescharacteristic
678C23C2×#116111yescharacteristic
679C23C2×#116111yescharacteristic
680C23#655111yescharacteristic
681C23D7×#4111yescharacteristic
682C23D7×#4111yescharacteristic
683C23#655311yescharacteristic
684C23#655311yescharacteristic
685D4—2816no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—74no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—144no—
723C2×C4—144no—
724C2×C4—142no—
725C2×C4—144no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—281no—
733C2×C4—281no—
734C2×C4—281no—
735C2×C4—281no—
736C2×C4—281no—
737C2×C4—281no—
738C2×C4—282no—
739C2×C4—282no—
740C2×C4—281no—
741C2×C4—281no—
742C2×C4—281no—
743C2×C4—281no—
744C2×C4—282no—
745C2×C4—282no—
746C2×C4—281no—
747C2×C4—281no—
748C2×C4C4×D2814yes—
749C2×C4(C22⋊D7)⋊C414yes—
750C2×C4#644814yes—
751C2×C4#644914yes—
752C2×C4#645514yes—
753C2×C4#645614yes—
754C2×C4#645814yes—
755C2×C4#646114yes—
756C7#1402211yescharacteristic, complemented, Sylow
757C22—284no—
758C22—284no—
759C22—284no—
760C22—284no—
761C22—284no—
762C22—284no—
763C22—284no—
764C22—562no—
765C22—562no—
766C22—562no—
767C22—562no—
768C22—562no—
769C22—562no—
770C22—562no—
771C22—562no—
772C22C2×C4×D2811yescharacteristic
773C22C2×(C22⋊D7)⋊C411yescharacteristic
774C22C2×#644811yescharacteristic
775C22C2×#644911yescharacteristic
776C22C2×#645511yescharacteristic
777C22C2×#645611yescharacteristic
778C22#9019511yescharacteristic
779C22C2×#645811yescharacteristic
780C22C2×#646111yescharacteristic
781C22#9021211yescharacteristic
782C22#9021311yescharacteristic
783C22D4×D2811yescharacteristic
784C22#9024411yescharacteristic
785C22#9024511yescharacteristic
786C22#9025011yescharacteristic
787C22#9025911yescharacteristic
788C22#9026711yescharacteristic
789C22#9026811yescharacteristic
790C22#9027611yescharacteristic
791C22#9028711yescharacteristic
792C22D7×#12111yescharacteristic
793C22#9029811yescharacteristic
794C22#9031011yescharacteristic
795C22#9031511yescharacteristic
796C22#9031811yescharacteristic
797C22#9032011yescharacteristic
798C22#9033411yescharacteristic
799C22#9037211yescharacteristic
800C22#9037211yescharacteristic
801C22#9038611yescharacteristic
802C22#9038611yescharacteristic
803C22#9040911yescharacteristic
804C22#9041711yescharacteristic
805C22#9042311yescharacteristic
806C22#9042511yescharacteristic
807C4—24no—
808C4—44no—
809C4—42no—
810C4—82no—
811C4—144no—
812C4—282no—
813C4—282no—
814C4—282no—
815C4—284no—
816C4#8944218yescomplemented
817C2—564no—
818C2C2×#8944211yescharacteristic
819C2#1173109811yescharacteristic
820C2#1173109911yescharacteristic
821C2#1173131011yescharacteristic
822C2#1173131711yescharacteristic
823C2#1173160511yescharacteristic
824C2#1173176911yescharacteristic
825C2#1173349211yescharacteristic
826C2#1173349311yescharacteristic
827C2#1173365411yescharacteristic
828C2#1173365611yescharacteristic
829C2#1173376211yescharacteristic
830C2#1173379811yescharacteristic
831C2#1173395211yescharacteristic
832C2#1173400011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, cosocleC24×C7C24
prime radicalC23×D28C22
hypercenterC4⋊#95D7
hypocenterC7#14022
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic7C2semidirect
5. C2×C4×C4⋊Dic7C2semidirect
6. C2×#89442C2semidirect
7. C7×C4⋊#95C2semidirect
8. #11729317C2semidirect
9. #11727183C2semidirect
10. #11727181C2semidirect
11. #11727162C2semidirect
38. #89711C4semidirect
95. C2×C4⋊Dic7D4semidirect
122. C4⋊#95D7semidirect
505. C4×C7#388semidirect
756. C7#14022semidirect
816. C4#89442semidirect

Maximal subgroups

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

subgroupindex
C2×#897602
C2×C4⋊C4×Dic72
C2×#897112
C2×C4×C4⋊Dic72
C2×#894422
C7×C4⋊#952
#117293172
#117271832
#117271812
#117271622
#140227