Finite Group Databasebeta

← #13280223

Subgroups — #13280223

Order 1792.

1926 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6435C211yesmaximal, characteristic
2C2×#89759C211yesmaximal, characteristic
3C2×#89759C211yesmaximal, characteristic
4C2×#89757C211yesmaximal, characteristic, complemented
5C2×#89700C211yesmaximal, characteristic, complemented
6C7×C4⋊#95C211yesmaximal, characteristic, complemented
7#11729317C211yesmaximal, characteristic, complemented
8#11727182C212yesmaximal
9#11727181C212yesmaximal
10#11727174C212yesmaximal, complemented
11#11727167C212yesmaximal, complemented
12C23×C4×D7C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×(C2×D7)⋊C4C2211yescharacteristic
17C22×(C2×D7)⋊C4C2211yescharacteristic
18C22×(C2×D7)⋊C4C2212yes—
19C22×(C2×D7)⋊C4C2212yes—
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×C4⋊Dic7C2212yes—
23C22×Dic7⋊C4C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×Dic7⋊C4C2212yes—
26C22×C4×Dic7C2211yescharacteristic
27C2×#6435—24no—
28C2×#6435—24no—
29C2×#6435—24no—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38#89759—24no—
39#89759C418yescomplemented
40#89757—24no—
41#89700—24no—
42#14264—71nomaximal, Sylow
43C24×D7C2311yescharacteristic
44C23×C4×C7C2312yes—
45C23×C4×C7C2312yes—
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×Dic7C2312yes—
50C23×Dic7C2312yes—
51C23×Dic7C2311yescharacteristic
52C23×Dic7C2311yescharacteristic
53C23×Dic7C2311yescharacteristic
54C22×C4×D7—22no—
55C22×C4×D7—22no—
56C22×C4×D7—22no—
57C22×C4×D7—22no—
58C22×C4×D7C2×C414yes—
59C22×C4×D7D414yes—
60C22×C4×D7Q814yes—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4C2×C414yes—
67C2×C42×C7—22no—
68C2×C42×C7—22no—
69C2×C42×C7D414yes—
70C2×(C2×D7)⋊C4—22no—
71C2×(C2×D7)⋊C4—22no—
72C2×(C2×D7)⋊C4—22no—
73C2×(C2×D7)⋊C4—22no—
74C2×(C2×D7)⋊C4—22no—
75C2×(C2×D7)⋊C4—22no—
76C2×(C2×D7)⋊C4—24no—
77C2×(C2×D7)⋊C4—42no—
78C2×(C2×D7)⋊C4—42no—
79C2×(C2×D7)⋊C4—42no—
80C2×(C2×D7)⋊C4—42no—
81C2×(C2×D7)⋊C4C2×C418yes—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7—22no—
84C2×C4⋊Dic7—22no—
85C2×C4⋊Dic7—22no—
86C2×C4⋊Dic7—22no—
87C2×C4⋊Dic7—24no—
88C2×C4⋊Dic7—42no—
89C2×C4⋊Dic7—42no—
90C2×C4⋊Dic7C2×C414yes—
91C2×Dic7⋊C4—22no—
92C2×Dic7⋊C4—22no—
93C2×Dic7⋊C4—22no—
94C2×Dic7⋊C4—22no—
95C2×Dic7⋊C4—22no—
96C2×Dic7⋊C4—22no—
97C2×Dic7⋊C4—24no—
98C2×Dic7⋊C4—42no—
99C2×Dic7⋊C4—42no—
100C2×C4×Dic7—22no—
101C2×C4×Dic7—22no—
102C2×C4×Dic7D414yes—
103#6435—232no—
104C7×#95—42no—
105C7×#95—42no—
106C7⋊#95—24no—
107C7⋊#95—24no—
108C7⋊#95—24no—
109C7⋊#95—42no—
110C7⋊#95—42no—
111C7⋊#95C2×C418yes—
112C22×#117—71no—
113C2×#389—71no—
114C2×#389—71no—
115C2×#380—71no—
116C2×#380—71no—
117#1444—72no—
118#1442—72no—
119#1439—72no—
120#1439—72no—
121C4⋊#95—71no—
122C4⋊#95D711yescharacteristic, complemented
123C24×C7C2411yescharacteristic
124C23×D7—21no—
125C23×D7—21no—
126C23×D7—21no—
127C23×D7—21no—
128C23×D7—21no—
129C23×D7—21no—
130C23×D7—21no—
131C23×D7—21no—
132C23×D7—21no—
133C23×D7—21no—
134C23×D7—21no—
135C23×D7—21no—
136C23×D7C22×C412yes—
137C23×D7C2×D412yes—
138C23×D7C2×Q812yes—
139C22×C4×C7—22no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—22no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7C22×C414yes—
165C22×C4×C7C22×C412yes—
166C22×C4×C7C2×D412yes—
167C22×C4×C7C2×D412yes—
168C22×C4×C7C2×D412yes—
169C22×C4×C7C2×D412yes—
170C22×C4×C7C2×D412yes—
171C22×C4×C7C2×Q812yes—
172C22×C4×C7#4112yes—
173C22×C4×C7#4112yes—
174C22×Dic7—21no—
175C22×Dic7—21no—
176C22×Dic7—21no—
177C22×Dic7—21no—
178C22×Dic7—22no—
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—22no—
184C22×Dic7—21no—
185C22×Dic7—21no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—21no—
190C22×Dic7—21no—
191C22×Dic7—22no—
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7C22×C414yes—
204C22×Dic7C22×C412yes—
205C22×Dic7C2×D412yes—
206C22×Dic7C2×D412yes—
207C22×Dic7C2×D412yes—
208C22×Dic7C2×Q812yes—
209C2×C4×D7—28no—
210C2×C4×D7—28no—
211C2×C4×D7—28no—
212C2×C4×D7—28no—
213C2×C4×D7—28no—
214C2×C4×D7—28no—
215C2×C4×D7C4⋊C4116yescomplemented
216C7×C4⋊C4—28no—
217C7×C4⋊C4—44no—
218C42×C7—28no—
219(C2×D7)⋊C4—28no—
220(C2×D7)⋊C4—28no—
221(C2×D7)⋊C4—48no—
222(C2×D7)⋊C4—48no—
223C4⋊Dic7—28no—
224C4⋊Dic7—48no—
225C4⋊Dic7—44no—
226Dic7⋊C4—28no—
227Dic7⋊C4—28no—
228Dic7⋊C4—48no—
229C4×Dic7—28no—
230C24×C4—71no—
231C2×#117—144no—
232C2×#117—144no—
233C2×#117—144no—
234C22×C4⋊C4—71no—
235C22×C4⋊C4—71no—
236C22×C4⋊C4—71no—
237C22×C4⋊C4—71no—
238C22×C4⋊C4—72no—
239C22×C4⋊C4—72no—
240C22×C4⋊C4C2×D711yescharacteristic
241C22×C4⋊C4C2×D711yescharacteristic
242C22×C22⋊C4—72no—
243C22×C22⋊C4—71no—
244C22×C22⋊C4—71no—
245C22×C22⋊C4—72no—
246C22×C42—71no—
247C22×C42C2×D711yescharacteristic
248#389—144no—
249#389—144no—
250#380—78no—
251#380—144no—
252C2×#95—72no—
253C2×#95—72no—
254C2×#95—72no—
255C2×#95—72no—
256C2×#95—72no—
257C2×#95—72no—
258C2×#95C2×D712yes—
259C2×#95C2×D712yes—
260C23×C7C23×C411yescharacteristic
261C23×C7C22×D411yescharacteristic
262C23×C7C22×D411yescharacteristic
263C23×C7C22×D411yescharacteristic
264C23×C7C22×Q811yescharacteristic
265C23×C7C2×#4111yescharacteristic
266C23×C7C2×#4111yescharacteristic
267C23×C7H(5,𝔽2)11yescharacteristic
268C23×C7H(5,𝔽2)11yescharacteristic
269C23×C7H(5,𝔽2)11yescharacteristic
270C23×C7H(5,𝔽2)11yescharacteristic
271C23×C72−1+411yescharacteristic
272C23×C72−1+411yescharacteristic
273C23×C72−1+411yescharacteristic
274C23×C72−1+411yescharacteristic
275C22×D7—22no—
276C22×D7—22no—
277C22×D7—22no—
278C22×D7—22no—
279C22×D7—22no—
280C22×D7—22no—
281C22×D7—22no—
282C22×D7—22no—
283C22×D7—22no—
284C22×D7—22no—
285C22×D7—22no—
286C22×D7—22no—
287C22×D7—22no—
288C22×D7—22no—
289C22×D7—22no—
290C22×D7—22no—
291C22×D7—22no—
292C22×D7—22no—
293C22×D7—41no—
294C22×D7—41no—
295C22×D7—41no—
296C22×D7—41no—
297C22×D7—41no—
298C22×D7—41no—
299C22×D7—41no—
300C22×D7—41no—
301C22×D7—41no—
302C22×D7—41no—
303C22×D7—41no—
304C22×D7—41no—
305C22×D7—41no—
306C22×D7—41no—
307C22×D7—41no—
308C22×D7—41no—
309C22×D7C2×C4⋊C414yes—
310C2×C4×C7—24no—
311C2×C4×C7—24no—
312C2×C4×C7—24no—
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—42no—
320C2×C4×C7—41no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—41no—
324C2×C4×C7—42no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
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—42no—
338C2×C4×C7C2×C4⋊C414yes—
339C2×C4×C7C4×D414yes—
340C2×C4×C7C4×D414yes—
341C2×C4×C7#12014yes—
342C2×C4×C7C22⋊Q814yes—
343C2×C4×C7C22⋊Q814yes—
344C2×C4×C7#12314yes—
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—42no—
361C2×Dic7—41no—
362C2×Dic7—41no—
363C2×Dic7—41no—
364C2×Dic7—41no—
365C2×Dic7—42no—
366C2×Dic7—41no—
367C2×Dic7—41no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—42no—
371C2×Dic7—42no—
372C2×Dic7—42no—
373C2×Dic7—42no—
374C2×Dic7—42no—
375C2×Dic7—42no—
376C2×Dic7—42no—
377C2×Dic7—42no—
378C2×Dic7—42no—
379C2×Dic7C2×C4⋊C414yes—
380C4×D7—232no—
381C25—71no—
382C23×C4—71no—
383C23×C4—74no—
384C23×C4—74no—
385C23×C4—74no—
386C23×C4—71no—
387C23×C4—72no—
388C23×C4—71no—
389C23×C4—72no—
390C23×C4—142no—
391C23×C4—142no—
392C23×C4—142no—
393C23×C4—142no—
394C23×C4C22×D712yes—
395C23×C4C22×D712yes—
396C23×C4C22×D711yescharacteristic
397C23×C4C22×D711yescharacteristic
398C23×C4C22×D711yescharacteristic
399#117—1432no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
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⋊C4—142no—
414C2×C4⋊C4—144no—
415C2×C4⋊C4—144no—
416C2×C4⋊C4—142no—
417C2×C4⋊C4—142no—
418C2×C4⋊C4—142no—
419C2×C4⋊C4—282no—
420C2×C4⋊C4—282no—
421C2×C4⋊C4—282no—
422C2×C4⋊C4—282no—
423C2×C4⋊C4C4×D714yes—
424C2×C22⋊C4—78no—
425C2×C22⋊C4—142no—
426C2×C22⋊C4—142no—
427C2×C22⋊C4—142no—
428C2×C22⋊C4—142no—
429C2×C22⋊C4—142no—
430C2×C22⋊C4—142no—
431C2×C22⋊C4—144no—
432C2×C22⋊C4—282no—
433C2×C22⋊C4—282no—
434C2×C22⋊C4—282no—
435C2×C22⋊C4—282no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—74no—
439C2×C42—142no—
440C2×C42—142no—
441C2×C42D2814yes—
442#95—42no—
443#95—42no—
444#95—78no—
445#95—144no—
446#95—144no—
447#95—144no—
448#95—282no—
449#95—282no—
450C22×C7C22×C4⋊C411yescharacteristic
451C22×C7C2×C4×D411yescharacteristic
452C22×C7C2×C4×D411yescharacteristic
453C22×C7#51811yescharacteristic
454C22×C7#51911yescharacteristic
455C22×C7#52011yescharacteristic
456C22×C7#52011yescharacteristic
457C22×C7C2×#12011yescharacteristic
458C22×C7C2×C22⋊Q811yescharacteristic
459C22×C7C2×C22⋊Q811yescharacteristic
460C22×C7C2×#12311yescharacteristic
461C22×C7#53511yescharacteristic
462C22×C7#53511yescharacteristic
463C22×C7#53511yescharacteristic
464C22×C7#53611yescharacteristic
465C22×C7#53611yescharacteristic
466C22×C7#53611yescharacteristic
467C22×C7#53711yescharacteristic
468C22×C7#53711yescharacteristic
469C22×C7#53711yescharacteristic
470C22×C7#53711yescharacteristic
471C22×C7#53711yescharacteristic
472C22×C7#53711yescharacteristic
473C22×C7#54011yescharacteristic
474C22×C7#54011yescharacteristic
475C22×C7#54111yescharacteristic
476C22×C7#54111yescharacteristic
477C22×C7#54211yescharacteristic
478C22×C7#54211yescharacteristic
479C22×C7#54211yescharacteristic
480C22×C7#54211yescharacteristic
481C22×C7#54411yescharacteristic
482C22×C7#54411yescharacteristic
483C22×C7#54411yescharacteristic
484C22×C7#54411yescharacteristic
485C2×D7—24no—
486C2×D7—24no—
487C2×D7—24no—
488C2×D7—42no—
489C2×D7—42no—
490C2×D7—42no—
491C2×D7—42no—
492C2×D7—42no—
493C2×D7—42no—
494C2×D7—42no—
495C2×D7—42no—
496C2×D7—42no—
497C2×D7—42no—
498C2×D7—42no—
499C2×D7—42no—
500C4×C7—44no—
501C4×C7—42no—
502C4×C7—42no—
503C4×C7—82no—
504C4×C7#38518yes—
505Dic7—24no—
506Dic7—44no—
507Dic7—42no—
508Dic7—42no—
509Dic7—82no—
510C24—72no—
511C24—72no—
512C24—72no—
513C24—141no—
514C24—141no—
515C24—141no—
516C24—141no—
517C24—141no—
518C24—141no—
519C24—141no—
520C24—141no—
521C24—141no—
522C24—141no—
523C24—141no—
524C24—141no—
525C24C23×D711yescharacteristic
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—72no—
552C22×C4—72no—
553C22×C4—72no—
554C22×C4—716no—
555C22×C4—74no—
556C22×C4—72no—
557C22×C4—72no—
558C22×C4—141no—
559C22×C4—141no—
560C22×C4—141no—
561C22×C4—141no—
562C22×C4—148no—
563C22×C4—148no—
564C22×C4—148no—
565C22×C4—148no—
566C22×C4—148no—
567C22×C4—148no—
568C22×C4—142no—
569C22×C4—141no—
570C22×C4—141no—
571C22×C4—142no—
572C22×C4—141no—
573C22×C4—141no—
574C22×C4—141no—
575C22×C4—142no—
576C22×C4—141no—
577C22×C4—142no—
578C22×C4—141no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—142no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—142no—
593C22×C4C2×C4×D714yes—
594C22×C4C2×C4×D712yes—
595C22×C4C2×D2812yes—
596C22×C4C2×D2812yes—
597C22×C4C2×D2812yes—
598C22×C4#115712yes—
599C22×C4D4×D712yes—
600C22×C4D4×D712yes—
601C22×C4#115912yes—
602C22×C4Q8×D712yes—
603C4⋊C4—28no—
604C4⋊C4—44no—
605C4⋊C4—148no—
606C4⋊C4—148no—
607C4⋊C4—148no—
608C4⋊C4—288no—
609C4⋊C4—288no—
610C4⋊C4—284no—
611C22⋊C4—148no—
612C22⋊C4—148no—
613C22⋊C4—288no—
614C22⋊C4—288no—
615C42—28no—
616C42—148no—
617C2×C7C2×#38511yescharacteristic
618C2×C7#231611yescharacteristic
619C2×C7#231711yescharacteristic
620C2×C7#232311yescharacteristic
621C2×C7#232311yescharacteristic
622C2×C7#232411yescharacteristic
623C2×C7#232411yescharacteristic
624C2×C7#261511yescharacteristic
625C2×C7#261611yescharacteristic
626C2×C7#262411yescharacteristic
627C2×C7#262511yescharacteristic
628C2×C7#262811yescharacteristic
629C2×C7#262811yescharacteristic
630C2×C7#262911yescharacteristic
631C2×C7#262911yescharacteristic
632D7—44no—
633C23—74no—
634C23—142no—
635C23—142no—
636C23—142no—
637C23—142no—
638C23—142no—
639C23—142no—
640C23—142no—
641C23—142no—
642C23—142no—
643C23—142no—
644C23—142no—
645C23—142no—
646C23—142no—
647C23—142no—
648C23—142no—
649C23—142no—
650C23—142no—
651C23—142no—
652C23—281no—
653C23—281no—
654C23—281no—
655C23—281no—
656C23—281no—
657C23—281no—
658C23—281no—
659C23—281no—
660C23—281no—
661C23—281no—
662C23—281no—
663C23—281no—
664C23—281no—
665C23—281no—
666C23—281no—
667C23—281no—
668C23C22×C4×D711yescharacteristic
669C23C22×D2811yescharacteristic
670C23C2×#115711yescharacteristic
671C23C2×D4×D711yescharacteristic
672C23C2×D4×D711yescharacteristic
673C23C2×#115911yescharacteristic
674C23#654811yescharacteristic
675C23#654811yescharacteristic
676C23C2×Q8×D711yescharacteristic
677C23#655111yescharacteristic
678C23#655111yescharacteristic
679C23#655311yescharacteristic
680C23#655311yescharacteristic
681C23#655411yescharacteristic
682C23#655411yescharacteristic
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—74no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—1432no—
719C2×C4—144no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—144no—
723C2×C4—144no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—282no—
729C2×C4—281no—
730C2×C4—281no—
731C2×C4—282no—
732C2×C4—281no—
733C2×C4—281no—
734C2×C4—282no—
735C2×C4—282no—
736C2×C4—281no—
737C2×C4—281no—
738C2×C4—281no—
739C2×C4—281no—
740C2×C4—282no—
741C2×C4—282no—
742C2×C4—282no—
743C2×C4—282no—
744C2×C4—282no—
745C2×C4—282no—
746C2×C4—282no—
747C2×C4C4×D2814yes—
748C2×C4(C22⋊D7)⋊C414yes—
749C2×C4#644514yes—
750C2×C4#644614yes—
751C2×C4D7×C4⋊C414yes—
752C2×C4#645914yes—
753C2×C4#646014yes—
754C7#1426411yescharacteristic, complemented, Sylow
755C22—144no—
756C22—144no—
757C22—144no—
758C22—282no—
759C22—282no—
760C22—282no—
761C22—282no—
762C22—282no—
763C22—282no—
764C22—282no—
765C22—282no—
766C22—282no—
767C22—282no—
768C22—282no—
769C22—282no—
770C22C2×C4×D2811yescharacteristic
771C22C2×(C22⋊D7)⋊C411yescharacteristic
772C22C2×#644511yescharacteristic
773C22C2×#644611yescharacteristic
774C22C2×D7×C4⋊C411yescharacteristic
775C22C2×#645911yescharacteristic
776C22C2×#646011yescharacteristic
777C22#9020111yescharacteristic
778C22#9020111yescharacteristic
779C22#9021611yescharacteristic
780C22#9021711yescharacteristic
781C22#9023611yescharacteristic
782C22#9023711yescharacteristic
783C22#9025211yescharacteristic
784C22#9025311yescharacteristic
785C22#9026311yescharacteristic
786C22#9026511yescharacteristic
787C22#9027311yescharacteristic
788C22#9027411yescharacteristic
789C22#9029811yescharacteristic
790C22#9029811yescharacteristic
791C22#9029911yescharacteristic
792C22#9029911yescharacteristic
793C22#9031911yescharacteristic
794C22#9031911yescharacteristic
795C22#9032011yescharacteristic
796C22#9032011yescharacteristic
797C22#9037311yescharacteristic
798C22#9037311yescharacteristic
799C22#9038011yescharacteristic
800C22#9038011yescharacteristic
801C22#9041011yescharacteristic
802C22#9042011yescharacteristic
803C22#9042011yescharacteristic
804C22#9042211yescharacteristic
805C4—42no—
806C4—44no—
807C4—42no—
808C4—82no—
809C4—144no—
810C4—284no—
811C4—282no—
812C4—282no—
813C4—562no—
814C4#8944018yes—
815C2—284no—
816C2C2×#8944011yescharacteristic
817C2#1173120711yescharacteristic
818C2#1173120811yescharacteristic
819C2#1173139511yescharacteristic
820C2#1173147511yescharacteristic
821C2#1173163911yescharacteristic
822C2#1173178911yescharacteristic
823C2#1173341311yescharacteristic
824C2#1173364011yescharacteristic
825C2#1173369511yescharacteristic
826C2#1173369611yescharacteristic
827C2#1173387511yescharacteristic
828C2#1173390311yescharacteristic
829C2#1173405611yescharacteristic
830C2#1173408711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC4⋊#95D7
hypocenterC7#14264
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#89757C2semidirect
5. C2×#89700C2semidirect
6. C7×C4⋊#95C2semidirect
7. #11729317C2semidirect
10. #11727174C2semidirect
11. #11727167C2semidirect
39. #89759C4semidirect
122. C4⋊#95D7semidirect
215. C2×C4×D7C4⋊C4semidirect
754. C7#14264semidirect

Maximal subgroups

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

subgroupindex
C22×#64352
C2×#897592
C2×#897572
C2×#897002
C7×C4⋊#952
#117293172
#117271822
#117271812
#117271742
#117271672
#142647