Finite Group Databasebeta

← #13359556

Subgroups — #13359556

Order 1792.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90214C211yesmaximal, characteristic
2C7×#2323C211yesmaximal, characteristic, complemented
3C2×#89819C211yesmaximal, characteristic
4C2×#89802C211yesmaximal, characteristic, complemented
5C2×C4×#1143C211yesmaximal, characteristic, complemented
6#11729446C211yesmaximal, characteristic, complemented
7#11729336C211yesmaximal, characteristic, complemented
8#11727444C211yesmaximal, characteristic, complemented
9#11727441C211yesmaximal, characteristic, complemented
10#11727386C211yesmaximal, characteristic, complemented
11#11727380C211yesmaximal, characteristic, complemented
12#11727276C211yesmaximal, characteristic
13#11727259C211yesmaximal, characteristic, complemented
14#11727228C211yesmaximal, characteristic, complemented
15C4×#6384C211yesmaximal, characteristic, complemented
16C22×#1157C2211yescharacteristic
17C2×C7×C22⋊Q8C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C2×C7×#117C2211yescharacteristic
20C22×#1144C2211yescharacteristic
21C22×#1143C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23#90214—24no—
24#90214—24no—
25C2×#6455—21no—
26C2×D7×C4⋊C4—21no—
27C2×(C22⋊D7)⋊C4—21no—
28C2×(C22⋊D7)⋊C4—21no—
29C2×C4×D28C2211yescharacteristic
30C2×C4×D28C2211yescharacteristic
31C2×C4×Dic14C2211yescharacteristic
32C2×C4×Dic14C2211yescharacteristic
33C7×#391C2211yescharacteristic
34C7×#389—21no—
35C7×#389C2211yescharacteristic
36C7×#388—21no—
37C7×#388—21no—
38C7×#387—21no—
39C7×#380C2211yescharacteristic
40C4×C7×C4⋊C4C2211yescharacteristic
41C2×#6409C2211yescharacteristic
42C2×#6409C2211yescharacteristic
43C2×C22⋊(C7⋊C8)C2211yescharacteristic
44C2×C22⋊(C7⋊C8)C2211yescharacteristic
45#89819C418yescomplemented
46#89802—24no—
47C4×#1143—24no—
48C2×#6384C2211yescharacteristic
49C2×#6384C2211yescharacteristic
50C2×#6384C2211yescharacteristic
51C2×#6383C2211yescharacteristic
52C2×#6383C2211yescharacteristic
53C2×#6383C2211yescharacteristic
54C2×#6382C2211yescharacteristic
55C2×#6382C2211yescharacteristic
56C2×#6377C2211yescharacteristic
57C2×C4×C7⋊C8C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#89319C2211yescharacteristic
63#89319C2211yescharacteristic
64#21461—71nomaximal, Sylow
65C22×C7×Q8C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C22×C22⋊D7—21no—
68C23×Dic7—21no—
69C2×#1157—22no—
70C2×#1157—22no—
71C2×#1157—22no—
72C2×#1157—22no—
73C2×#1157—22no—
74C2×#1157C2×C414yes—
75C22×D28C2311yescharacteristic
76C22×C4×D7—21no—
77C22×C4×D7—21no—
78C22×C4×D7—21no—
79C22×Dic14C2311yescharacteristic
80C7×C22⋊Q8—22no—
81C7×C22⋊Q8C2×C414yescomplemented
82C4×C7×Q8—22no—
83C4×C7×Q8—22no—
84C7×#117—22no—
85C7×#117—22no—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—21no—
88C2×C7×C4⋊C4—21no—
89C2×C7×C4⋊C4D411yescharacteristic
90C2×C7×C4⋊C4D411yescharacteristic
91C2×C7×C4⋊C4C2311yescharacteristic
92C2×C7×C4⋊C4C2311yescharacteristic
93C2×C7×C4⋊C4C2311yescharacteristic
94C2×C7×C22⋊C4—21no—
95C2×C7×C22⋊C4—21no—
96C2×C7×C22⋊C4D411yescharacteristic
97C2×C7×C22⋊C4D411yescharacteristic
98C2×C42×C7—21no—
99C2×C42×C7—21no—
100C2×C42×C7C2311yescharacteristic
101C2×C42×C7C2311yescharacteristic
102C2×#1144—22no—
103C2×#1144—22no—
104C2×#1144C2×C414yescomplemented
105C2×#1143—22no—
106C2×#1143—22no—
107C2×#1143C2×C414yescomplemented
108C2×(C2×D7)⋊C4—21no—
109C2×(C2×D7)⋊C4—21no—
110C2×C4⋊Dic7—21no—
111C2×C4⋊Dic7—22no—
112C2×C4⋊Dic7—22no—
113C2×C4⋊Dic7C2311yescharacteristic
114C2×C4⋊Dic7C2311yescharacteristic
115C2×Dic7⋊C4—21no—
116C2×Dic7⋊C4—21no—
117C2×C4×Dic7—21no—
118C2×C4×Dic7—21no—
119C22×C7⋊C8C2311yescharacteristic
120C22×C7⋊C8C2311yescharacteristic
121C22×C7⋊C8C2311yescharacteristic
122C22×C7⋊C8C2311yescharacteristic
123#6455—28no—
124D7×C4⋊C4—28no—
125(C22⋊D7)⋊C4—28no—
126(C22⋊D7)⋊C4—28no—
127C4×D28—22no—
128C4×D28—22no—
129C4×D28—22no—
130C4×D28D414yes—
131C4×Dic14—22no—
132C4×Dic14—22no—
133C4×Dic14—22no—
134C4×Dic14D414yes—
135C7×#95—21no—
136C7×#95—21no—
137C7×#95—21no—
138C7×#95—21no—
139C7×#95—21no—
140#6409—22no—
141#6409—22no—
142C22⋊(C7⋊C8)—22no—
143C22⋊(C7⋊C8)C2×C414yescomplemented
144#6384—22no—
145#6384—22no—
146#6384C2×C414yescomplemented
147#6383—22no—
148#6383—22no—
149#6383C2×C414yescomplemented
150#6382—22no—
151#6382—22no—
152#6377—22no—
153C4×C7⋊C8—22no—
154C2×#520—71no—
155C2×#452—71no—
156C2×#441—71no—
157C2×C4×SD16—71no—
158#2323D711yescharacteristic, complemented
159#1878—71no—
160#1877—71no—
161#1872—71no—
162#1865—71no—
163#1864—71no—
164#1853—71no—
165#1788—71no—
166#1762—71no—
167C4×#103—71no—
168#1750—71no—
169C24×C7C2×D411yescharacteristic
170C23×D7—21no—
171C2×C7×Q8—21no—
172C2×C7×Q8—21no—
173C2×C7×Q8—21no—
174C2×C7×Q8—21no—
175C2×C7×Q8—21no—
176C2×C7×Q8C22×C412yes—
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×C7C22×C412yes—
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7C2×D411yescharacteristic
188C22×C4×C7C2×D411yescharacteristic
189C22×C4×C7C2×D411yescharacteristic
190C22×C4×C7C2×D411yescharacteristic
191C22×C4×C7#4112yes—
192C22×C4×C7C2411yescharacteristic
193C2×C22⋊D7—24no—
194C2×C22⋊D7—24no—
195C2×C22⋊D7—24no—
196C22×Dic7—21no—
197C22×Dic7—21no—
198C22×Dic7—21no—
199C22×Dic7—24no—
200C22×Dic7—81no—
201C22×Dic7—81no—
202#1157—28no—
203#1157—28no—
204#1157—28no—
205#1157—28no—
206C2×D28—21no—
207C2×D28—21no—
208C2×D28—21no—
209C2×D28C22×C412yes—
210C2×D28C2×D412yes—
211C2×D28#4112yes—
212C2×C4×D7—24no—
213C2×C4×D7—24no—
214C2×C4×D7—24no—
215C2×C4×D7—24no—
216C2×C4×D7—24no—
217C2×C4×D7—81no—
218C2×C4×D7—81no—
219C2×C4×D7—81no—
220C2×C4×D7—81no—
221C2×Dic14—21no—
222C2×Dic14—21no—
223C2×Dic14—21no—
224C2×Dic14C22×C412yes—
225C2×Dic14C2×D412yes—
226C2×Dic14#4112yes—
227C7×C4⋊C4—24no—
228C7×C4⋊C4—22no—
229C7×C4⋊C4—22no—
230C7×C4⋊C4—21no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4—21no—
233C7×C4⋊C4—21no—
234C7×C4⋊C4—21no—
235C7×C4⋊C4—42no—
236C7×C4⋊C4—81no—
237C7×C4⋊C4C22×C412yes—
238C7×C22⋊C4—24no—
239C7×C22⋊C4—22no—
240C7×C22⋊C4—22no—
241C7×C22⋊C4—81no—
242C42×C7—21no—
243C42×C7—21no—
244C42×C7—42no—
245C42×C7—81no—
246C42×C7C2×D412yes—
247C42×C7C2×D412yes—
248#1144—28no—
249#1143—28no—
250(C2×D7)⋊C4—24no—
251(C2×D7)⋊C4—24no—
252C4⋊Dic7—24no—
253C4⋊Dic7—21no—
254C4⋊Dic7—21no—
255C4⋊Dic7C2×D412yes—
256C4⋊Dic7C2×D412yes—
257Dic7⋊C4—24no—
258Dic7⋊C4—24no—
259C4×Dic7—24no—
260C4×Dic7—24no—
261C2×C7⋊C8—21no—
262C2×C7⋊C8—21no—
263C2×C7⋊C8—21no—
264C2×C7⋊C8—21no—
265C2×C7⋊C8—21no—
266C2×C7⋊C8—21no—
267C2×C7⋊C8—21no—
268C2×C7⋊C8—21no—
269C2×C7⋊C8—21no—
270C2×C7⋊C8—21no—
271C2×C7⋊C8C22×C412yes—
272C2×C7⋊C8C22×C412yes—
273C22×#41—71no—
274C22×Q16—71no—
275C22×SD16—71no—
276C2×C22⋊Q8C2×D711yescharacteristic
277#520—144no—
278#520—144no—
279C2×C4×Q8—71no—
280C2×C4×Q8—71no—
281C2×C4×Q8C2×D711yescharacteristic
282C2×C4×D4—71no—
283C2×C4×D4—71no—
284C2×C4×D4—141no—
285C2×C4×D4—141no—
286C2×#117—141no—
287C2×#117C2×D711yescharacteristic
288C22×C4⋊C4—71no—
289C22×C4⋊C4—141no—
290#452—78no—
291#441—144no—
292C4×SD16—144no—
293C2×#106—71no—
294C2×#106—71no—
295C2×#103—71no—
296C2×#103—71no—
297C2×#103—71no—
298C2×#103—71no—
299C2×#103—71no—
300C2×#102—71no—
301C2×#102—71no—
302C2×#102—71no—
303C2×C22⋊C8—71no—
304C2×C22⋊C8—71no—
305C2×#97—71no—
306C2×C4×C8—71no—
307#391C2×D711yescharacteristic
308#389—21no—
309#389C2×D711yescharacteristic
310#388—21no—
311#388—21no—
312#387—21no—
313#380C2×D711yescharacteristic
314C4×C4⋊C4C2×D711yescharacteristic
315#340—71no—
316#340—71no—
317#340—71no—
318#340—71no—
319#336—71no—
320#336—71no—
321C23×C7—21no—
322C23×C7—21no—
323C23×C7—21no—
324C23×C7—21no—
325C23×C7—21no—
326C23×C7—21no—
327C23×C7C4×D412yes—
328C23×C7C22×D411yescharacteristic
329C22×D7—22no—
330C22×D7—22no—
331C22×D7—22no—
332C22×D7—41no—
333C22×D7—41no—
334C22×D7—41no—
335C22×D7—41no—
336C7×Q8—22no—
337C7×Q8—22no—
338C7×Q8—41no—
339C7×Q8—41no—
340C2×C4×C7—21no—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—21no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—21no—
353C2×C4×C7—21no—
354C2×C4×C7—21no—
355C2×C4×C7—21no—
356C2×C4×C7—21no—
357C2×C4×C7—21no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7C4×D412yes—
369C2×C4×C7#12012yes—
370C2×C4×C7#12012yes—
371C2×C4×C7C23×C411yescharacteristic
372C2×C4×C7C22×D411yescharacteristic
373C2×C4×C7C22×D411yescharacteristic
374C2×C4×C7C2×#4111yescharacteristic
375C2×C4×C7C2×#4111yescharacteristic
376C2×C4×C7C2×#4111yescharacteristic
377C22⋊D7—216no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—41no—
384C2×Dic7—41no—
385C2×Dic7—41no—
386C2×Dic7—41no—
387C2×Dic7—84no—
388D28—22no—
389D28—22no—
390D28—22no—
391D28C4×D414yes—
392C4×D7—216no—
393C4×D7—84no—
394C4×D7—84no—
395Dic14—22no—
396Dic14—22no—
397Dic14—22no—
398Dic14C4×D414yes—
399C7⋊C8—22no—
400C7⋊C8—22no—
401C7⋊C8—41no—
402C7⋊C8—41no—
403C2×#41—74no—
404C2×#41—142no—
405C2×#41—142no—
406C2×#41—142no—
407C2×#41—142no—
408C2×#41—142no—
409C22×Q8—71no—
410C22×Q8C22×D711yescharacteristic
411C22×D4—71no—
412C22×D4—141no—
413C23×C4—141no—
414C23×C4—141no—
415C23×C4—141no—
416C23×C4—141no—
417C23×C4C22×D711yescharacteristic
418C2×Q16—74no—
419C2×Q16—142no—
420C2×Q16—142no—
421C2×SD16—74no—
422C2×SD16—142no—
423C2×SD16—142no—
424C22×C8—71no—
425C22×C8—71no—
426C22×C8—71no—
427C22×C8—71no—
428C22⋊Q8—22no—
429C22⋊Q8C4×D714yescomplemented
430C4×Q8—22no—
431C4×Q8—22no—
432C4×Q8—74no—
433C4×Q8—142no—
434C4×Q8—142no—
435C4×Q8—142no—
436C4×D4—74no—
437C4×D4—142no—
438C4×D4—142no—
439C4×D4—148no—
440C4×D4—148no—
441C4×D4—142no—
442#117—22no—
443#117—22no—
444#117—148no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—71no—
449C2×C4⋊C4—71no—
450C2×C4⋊C4—148no—
451C2×C4⋊C4—142no—
452C2×C4⋊C4—142no—
453C2×C4⋊C4—141no—
454C2×C4⋊C4—141no—
455C2×C4⋊C4—141no—
456C2×C4⋊C4C22⋊D711yescharacteristic
457C2×C4⋊C4C22⋊D711yescharacteristic
458C2×C4⋊C4C22×D711yescharacteristic
459C2×C4⋊C4C22×D711yescharacteristic
460C2×C4⋊C4C22×D711yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—141no—
464C2×C22⋊C4—141no—
465C2×C22⋊C4C22⋊D711yescharacteristic
466C2×C22⋊C4C22⋊D711yescharacteristic
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—141no—
470C2×C42—141no—
471C2×C42C22×D711yescharacteristic
472C2×C42C22×D711yescharacteristic
473#106—142no—
474#106—142no—
475#103—74no—
476#103—142no—
477#103—142no—
478#103—142no—
479#103—142no—
480#102—74no—
481#102—142no—
482#102—142no—
483C22⋊C8—74no—
484C22⋊C8—142no—
485#97—142no—
486C4×C8—142no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492C22×C7—22no—
493C22×C7—22no—
494C22×C7—22no—
495C22×C7—41no—
496C22×C7—41no—
497C22×C7—41no—
498C22×C7—41no—
499C22×C7C2×C4×D411yescharacteristic
500C22×C7C2×#12011yescharacteristic
501C22×C7#52511yescharacteristic
502C22×C7#57711yescharacteristic
503C22×C7#57711yescharacteristic
504C22×C7#57711yescharacteristic
505C22×C7#57811yescharacteristic
506C2×D7—24no—
507C2×D7—42no—
508C2×D7—42no—
509C2×D7—42no—
510C2×D7—42no—
511C2×D7—42no—
512C2×D7—42no—
513C4×C7—22no—
514C4×C7—22no—
515C4×C7—22no—
516C4×C7—42no—
517C4×C7—41no—
518C4×C7—41no—
519C4×C7—42no—
520C4×C7—81no—
521C4×C7—81no—
522C4×C7C2×C4×D411yescharacteristic
523C4×C7C2×C4×D411yescharacteristic
524C4×C7#52511yescharacteristic
525C4×C7#52511yescharacteristic
526Dic7—24no—
527Dic7—42no—
528Dic7—42no—
529C24—141no—
530C24C2×C22⋊D711yescharacteristic
531#41—148no—
532#41—148no—
533#41—148no—
534#41—148no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—72no—
541C2×Q8—72no—
542C2×Q8—72no—
543C2×Q8—141no—
544C2×Q8—141no—
545C2×Q8—141no—
546C2×Q8C2×C4×D712yes—
547C2×D4—72no—
548C2×D4—72no—
549C2×D4—72no—
550C2×D4—144no—
551C2×D4—144no—
552C2×D4—144no—
553C2×D4—141no—
554C2×D4—141no—
555C2×D4—141no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—144no—
565C22×C4—144no—
566C22×C4—144no—
567C22×C4—141no—
568C22×C4—144no—
569C22×C4—141no—
570C22×C4—141no—
571C22×C4—144no—
572C22×C4—144no—
573C22×C4—561no—
574C22×C4—561no—
575C22×C4—561no—
576C22×C4—561no—
577C22×C4—561no—
578C22×C4—561no—
579C22×C4C2×C4×D712yes—
580C22×C4#115712yes—
581C22×C4C2×C22⋊D711yescharacteristic
582C22×C4C2×C22⋊D711yescharacteristic
583C22×C4C2×C22⋊D711yescharacteristic
584C22×C4C2×C22⋊D711yescharacteristic
585C22×C4C2×C22⋊D711yescharacteristic
586C22×C4C23×D711yescharacteristic
587Q16—148no—
588SD16—148no—
589C2×C8—72no—
590C2×C8—72no—
591C2×C8—141no—
592C2×C8—141no—
593C2×C8—141no—
594C2×C8—141no—
595C2×C8—141no—
596C2×C8—141no—
597C2×C8—141no—
598C2×C8—141no—
599C2×C8—141no—
600C2×C8—141no—
601C4⋊C4—24no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—72no—
611C4⋊C4—72no—
612C4⋊C4—81no—
613C4⋊C4—144no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—141no—
617C4⋊C4—141no—
618C4⋊C4C2×C4×D712yes—
619C22⋊C4—24no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—81no—
623C22⋊C4—144no—
624C22⋊C4—144no—
625C42—21no—
626C42—21no—
627C42—42no—
628C42—81no—
629C42—144no—
630C42—144no—
631C42D4×D712yes—
632C42D4×D712yes—
633C2×C7—42no—
634C2×C7C4×#12011yescharacteristic
635C2×C7#294711yescharacteristic
636C2×C7#295211yescharacteristic
637C2×C7#300911yescharacteristic
638C2×C7#301311yescharacteristic
639C2×C7#312011yescharacteristic
640C2×C7#312511yescharacteristic
641D7—44no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—142no—
649C23—142no—
650C23—142no—
651C23—281no—
652C23—281no—
653C23—281no—
654C23—281no—
655C23C4×C22⋊D712yes—
656C23C22×C22⋊D711yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661Q8—74no—
662Q8—142no—
663Q8—142no—
664Q8—142no—
665D4—74no—
666D4—1416no—
667D4—142no—
668D4—142no—
669D4—142no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—1416no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—281no—
705C2×C4—281no—
706C2×C4—281no—
707C2×C4—281no—
708C2×C4—564no—
709C2×C4—564no—
710C2×C4—564no—
711C2×C4C4×C22⋊D712yes—
712C2×C4#650012yes—
713C2×C4#650012yes—
714C2×C4C22×C4×D711yescharacteristic
715C2×C4C2×#115711yescharacteristic
716C2×C4C2×D4×D711yescharacteristic
717C2×C4C2×D4×D711yescharacteristic
718C2×C4D7×#4111yescharacteristic
719C2×C4D7×#4111yescharacteristic
720C8—142no—
721C8—142no—
722C8—281no—
723C8—281no—
724C7#2146111yescharacteristic, complemented, Sylow
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—144no—
733C22—282no—
734C22—282no—
735C22—282no—
736C22—282no—
737C22—282no—
738C22—282no—
739C22C2×C4×C22⋊D711yescharacteristic
740C22C2×#650011yescharacteristic
741C22#9051911yescharacteristic
742C22#9052711yescharacteristic
743C22#9052811yescharacteristic
744C22#9052811yescharacteristic
745C22#9052911yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—42no—
750C4—41no—
751C4—42no—
752C4—41no—
753C4—81no—
754C4—81no—
755C4—144no—
756C4—282no—
757C4—282no—
758C4C4×D4×D711yescharacteristic
759C4C4×D4×D711yescharacteristic
760C4#9023811yescharacteristic
761C4#9023811yescharacteristic
762C2—42no—
763C2—284no—
764C2C4×#650011yescharacteristic
765C2#1173999211yescharacteristic
766C2#1174000311yescharacteristic
767C2#1174084911yescharacteristic
768C2#1174087211yescharacteristic
769C2#1174089111yescharacteristic
770C2#1174090711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2323C2
socleC23×C7C22×D4
prime radicalC22×#1157C22
cosocleC22×C4×C7C24
hypercenter#2323D7
hypocenterC7#21461
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C7×#2323C2semidirect
4. C2×#89802C2semidirect
5. C2×C4×#1143C2semidirect
6. #11729446C2semidirect
7. #11729336C2semidirect
8. #11727444C2semidirect
9. #11727441C2semidirect
10. #11727386C2semidirect
11. #11727380C2semidirect
13. #11727259C2semidirect
14. #11727228C2semidirect
15. C4×#6384C2semidirect
45. #89819C4semidirect
81. C7×C22⋊Q8C2×C4semidirect
104. C2×#1144C2×C4semidirect
107. C2×#1143C2×C4semidirect
143. C22⋊(C7⋊C8)C2×C4semidirect
146. #6384C2×C4semidirect
149. #6383C2×C4semidirect
158. #2323D7semidirect
429. C22⋊Q8C4×D7semidirect
724. C7#21461semidirect

Maximal subgroups

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

subgroupindex
C2×#902142
C7×#23232
C2×#898192
C2×#898022
C2×C4×#11432
#117294462
#117293362
#117274442
#117274412
#117273862
#117273802
#117272762
#117272592
#117272282
C4×#63842
#214617