Finite Group Databasebeta

← #33010079

Subgroups — #33010079

Order 18688.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556550C211yesmaximal, characteristic
2C2×#17988486C211yesmaximal, characteristic, complemented
3C2×#17988480C211yesmaximal, characteristic
4C2×#17988473C211yesmaximal, characteristic, complemented
5#22608188C211yesmaximal, characteristic, complemented
6#22608184C211yesmaximal, characteristic, complemented
7#22608180C211yesmaximal, characteristic
8#22608176C211yesmaximal, characteristic
9#22608168C211yesmaximal, characteristic
10#22608165C211yesmaximal, characteristic, complemented
11#22608165C211yesmaximal, characteristic, complemented
12#22608163C211yesmaximal, characteristic, complemented
13#22608154C211yesmaximal, characteristic
14#95×Dic73C211yesmaximal, characteristic, complemented
15C2×#385×C73C211yesmaximal, characteristic
16C2×#14556550—24no—
17C2×#14556550—24no—
18C2×#14556550—24no—
19C22×C4⋊Dic73C2211yescharacteristic
20C22×C4⋊Dic73C2211yescharacteristic
21C22×C4⋊Dic73C2211yescharacteristic
22C22×C4⋊Dic73C2211yescharacteristic
23C22×C22⋊Dic73C2211yescharacteristic
24C22×C22⋊Dic73C2211yescharacteristic
25C22×C22⋊Dic73C2211yescharacteristic
26C22×C22⋊Dic73C2211yescharacteristic
27C22×C4×Dic73C2211yescharacteristic
28C22×C4×Dic73C2211yescharacteristic
29C22×C4×Dic73C2211yescharacteristic
30C22×C4×Dic73C2211yescharacteristic
31#17988486—24no—
32#17988480—24no—
33#17988473—24no—
34C2×#14556498C2211yescharacteristic
35C2×#14556498C2211yescharacteristic
36C2×#14556498C2211yescharacteristic
37C2×#14556498C2211yescharacteristic
38C2×#14556498C2211yescharacteristic
39C2×#14556498C2211yescharacteristic
40C2×#14556498C2211yescharacteristic
41C2×#14556498C2211yescharacteristic
42C2×#14556498C2211yescharacteristic
43C2×#14556498C2211yescharacteristic
44C2×#14556498C2211yescharacteristic
45C2×#14556498C2211yescharacteristic
46C2×#14556498C2211yescharacteristic
47C2×#14556498C2211yescharacteristic
48C2×#14556498C2211yescharacteristic
49C2×#14556498C2211yescharacteristic
50C24×C4×C73C2211yescharacteristic
51C22×C4⋊C4×C73C2211yescharacteristic
52C22×C4⋊C4×C73C2211yescharacteristic
53C22×C22⋊C4×C73C2211yescharacteristic
54C22×C22⋊C4×C73C2211yescharacteristic
55#385×C73C418yescomplemented
56C2×#95×C73C2211yescharacteristic
57C2×#95×C73C2211yescharacteristic
58C23×Dic73C2311yescharacteristic
59C23×Dic73C2311yescharacteristic
60C23×Dic73C2311yescharacteristic
61C23×Dic73C2311yescharacteristic
62C23×Dic73C2311yescharacteristic
63C23×Dic73C2311yescharacteristic
64C23×Dic73C2311yescharacteristic
65C23×Dic73C2311yescharacteristic
66#14556550—232no—
67C2×C4⋊Dic73—22no—
68C2×C4⋊Dic73—22no—
69C2×C4⋊Dic73—22no—
70C2×C4⋊Dic73—22no—
71C2×C4⋊Dic73—22no—
72C2×C4⋊Dic73—22no—
73C2×C4⋊Dic73—22no—
74C2×C4⋊Dic73—22no—
75C2×C4⋊Dic73—22no—
76C2×C4⋊Dic73—22no—
77C2×C4⋊Dic73—41no—
78C2×C4⋊Dic73D414yes—
79C2×C22⋊Dic73—22no—
80C2×C22⋊Dic73—22no—
81C2×C22⋊Dic73—22no—
82C2×C22⋊Dic73—22no—
83C2×C22⋊Dic73—22no—
84C2×C22⋊Dic73—22no—
85C2×C22⋊Dic73—22no—
86C2×C22⋊Dic73—22no—
87C2×C22⋊Dic73—22no—
88C2×C22⋊Dic73—41no—
89C2×C22⋊Dic73—41no—
90C2×C22⋊Dic73D414yes—
91C2×C4×Dic73—22no—
92C2×C4×Dic73—22no—
93C2×C4×Dic73—22no—
94C2×C4×Dic73—22no—
95C2×C4×Dic73—22no—
96C2×C4×Dic73—22no—
97C2×C4×Dic73—22no—
98C2×C4×Dic73—22no—
99C2×C4×Dic73—22no—
100C2×C4×Dic73—41no—
101C2×C4×Dic73—41no—
102C2×C4×Dic73D414yes—
103#14556498—22no—
104#14556498—22no—
105#14556498—22no—
106#14556498—22no—
107#14556498—22no—
108#14556498—22no—
109#14556498—22no—
110#14556498—22no—
111#14556498—22no—
112#14556498—22no—
113#14556498—22no—
114#14556498—22no—
115#14556498—22no—
116#14556498—22no—
117#14556498—22no—
118#14556498—41no—
119C25×C73C2311yescharacteristic
120C23×C4×C73—22no—
121C23×C4×C73—22no—
122C23×C4×C73—22no—
123C23×C4×C73—22no—
124C23×C4×C73—22no—
125C23×C4×C73—22no—
126C23×C4×C73C2×C414yes—
127C23×C4×C73C2311yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C2×C4⋊C4×C73—22no—
134C2×C4⋊C4×C73—22no—
135C2×C4⋊C4×C73—22no—
136C2×C4⋊C4×C73—22no—
137C2×C4⋊C4×C73C2×C414yes—
138C2×C4⋊C4×C73C2×C414yes—
139C2×C22⋊C4×C73—22no—
140C2×C22⋊C4×C73—22no—
141C2×C22⋊C4×C73—22no—
142C2×C22⋊C4×C73—22no—
143C2×C22⋊C4×C73C2×C414yes—
144C2×C22⋊C4×C73C2×C414yes—
145#95×C73C2×C414yes—
146#95×C73C2×C414yes—
147C22×Dic73—21no—
148C22×Dic73—21no—
149C22×Dic73—21no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73—21no—
154C22×Dic73—21no—
155C22×Dic73—21no—
156C22×Dic73—21no—
157C22×Dic73—21no—
158C22×Dic73—21no—
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73—21no—
170C22×Dic73—21no—
171C22×Dic73—21no—
172C22×Dic73—21no—
173C22×Dic73—21no—
174C22×Dic73—21no—
175C22×Dic73—21no—
176C22×Dic73—21no—
177C22×Dic73—21no—
178C22×Dic73—21no—
179C22×Dic73—21no—
180C22×Dic73—21no—
181C22×Dic73—21no—
182C22×Dic73—21no—
183C22×Dic73—21no—
184C22×Dic73—21no—
185C22×Dic73—21no—
186C22×Dic73—21no—
187C22×Dic73—21no—
188C22×Dic73—21no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73C2×D412yes—
196C22×Dic73C2×D412yes—
197C22×Dic73C2×D412yes—
198C22×Dic73C2×D412yes—
199C22×Dic73C2×D412yes—
200C22×Dic73C2×D412yes—
201C22×Dic73#4112yes—
202C22×Dic73#4112yes—
203C4⋊Dic73—28no—
204C4⋊Dic73—28no—
205C4⋊Dic73—44no—
206C4⋊Dic73—44no—
207C22⋊Dic73—28no—
208C22⋊Dic73—28no—
209C22⋊Dic73—44no—
210C22⋊Dic73—44no—
211C4×Dic73—28no—
212C4×Dic73—28no—
213C4×Dic73—44no—
214C4×Dic73—44no—
215C24×C73—21no—
216C24×C73—21no—
217C24×C73—21no—
218C24×C73—21no—
219C24×C73—21no—
220C24×C73—21no—
221C24×C73—21no—
222C24×C73—21no—
223C24×C73—21no—
224C24×C73—21no—
225C24×C73—21no—
226C24×C73—21no—
227C24×C73C22×C412yes—
228C24×C73C2×D412yes—
229C24×C73#4112yes—
230C24×C73C2411yescharacteristic
231C22×C4×C73—28no—
232C22×C4×C73—28no—
233C22×C4×C73—28no—
234C22×C4×C73—28no—
235C22×C4×C73—28no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—28no—
249C22×C4×C73—28no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73C22×C412yes—
269C22×C4×C73C22×C412yes—
270C22×C4×C73C22×C412yes—
271C22×C4×C73C22×C412yes—
272C22×C4×C73C22×C412yes—
273C22×C4×C73C22×C412yes—
274C22×C4×C73C2×D412yes—
275C22×C4×C73C2×D412yes—
276C22×C4×C73#4112yes—
277C22×C4×C73#4112yes—
278C22×C4×C73#4112yes—
279C22×C4×C73#4112yes—
280C4⋊C4×C73—28no—
281C4⋊C4×C73—28no—
282C22⋊C4×C73—28no—
283C22⋊C4×C73—28no—
284C23×C73—22no—
285C23×C73—22no—
286C23×C73—22no—
287C23×C73—22no—
288C23×C73—22no—
289C23×C73—22no—
290C23×C73—22no—
291C23×C73—22no—
292C23×C73—22no—
293C23×C73—22no—
294C23×C73—22no—
295C23×C73—22no—
296C23×C73—22no—
297C23×C73—22no—
298C23×C73—22no—
299C23×C73—22no—
300C23×C73—22no—
301C23×C73—22no—
302C23×C73—41no—
303C23×C73—41no—
304C23×C73—41no—
305C23×C73—41no—
306C23×C73—41no—
307C23×C73—41no—
308C23×C73—41no—
309C23×C73—41no—
310C23×C73—41no—
311C23×C73—41no—
312C23×C73—41no—
313C23×C73—41no—
314C23×C73—41no—
315C23×C73—41no—
316C23×C73—41no—
317C23×C73—41no—
318C23×C73C4×D414yes—
319C23×C73C23×C411yescharacteristic
320C23×C73C22×D411yescharacteristic
321C23×C73C22×D411yescharacteristic
322C23×C73C22×D411yescharacteristic
323C23×C73C2×#4111yescharacteristic
324C23×C73C2×#4111yescharacteristic
325C23×C73C2×#4111yescharacteristic
326C23×C73C2×#4111yescharacteristic
327C23×C73C2×#4111yescharacteristic
328C23×C73C2×#4111yescharacteristic
329C23×C73C2×#4111yescharacteristic
330C23×C73H(5,𝔽2)11yescharacteristic
331C23×C732−1+411yescharacteristic
332C23×C732−1+411yescharacteristic
333C23×C732−1+411yescharacteristic
334C2×C4×C73—232no—
335C2×C4×C73—22no—
336C2×C4×C73—22no—
337C2×C4×C73—22no—
338C2×C4×C73—22no—
339C2×C4×C73—22no—
340C2×C4×C73—22no—
341C2×C4×C73—22no—
342C2×C4×C73—22no—
343C2×C4×C73—22no—
344C2×C4×C73—22no—
345C2×C4×C73—22no—
346C2×C4×C73—22no—
347C2×C4×C73—22no—
348C2×C4×C73—22no—
349C2×C4×C73—22no—
350C2×C4×C73—22no—
351C2×C4×C73—22no—
352C2×C4×C73—22no—
353C2×C4×C73—22no—
354C2×C4×C73—22no—
355C2×C4×C73—22no—
356C2×C4×C73—22no—
357C2×C4×C73—22no—
358C2×C4×C73—22no—
359C2×C4×C73—22no—
360C2×C4×C73—22no—
361C2×C4×C73—22no—
362C2×C4×C73—41no—
363C2×C4×C73—41no—
364C2×C4×C73—41no—
365C2×C4×C73—41no—
366C2×C4×C73—41no—
367C2×C4×C73—41no—
368C2×C4×C73—41no—
369C2×C4×C73—41no—
370C2×C4×C73—41no—
371C2×C4×C73—41no—
372C2×C4×C73—41no—
373C2×C4×C73—41no—
374C2×C4×C73#11714yescomplemented
375C2×C4×C73C4×D414yes—
376C2×C4×C73C4×D414yes—
377C2×Dic73—22no—
378C2×Dic73—22no—
379C2×Dic73—22no—
380C2×Dic73—22no—
381C2×Dic73—22no—
382C2×Dic73—22no—
383C2×Dic73—22no—
384C2×Dic73—22no—
385C2×Dic73—22no—
386C2×Dic73—22no—
387C2×Dic73—22no—
388C2×Dic73—22no—
389C2×Dic73—22no—
390C2×Dic73—22no—
391C2×Dic73—22no—
392C2×Dic73—22no—
393C2×Dic73—22no—
394C2×Dic73—22no—
395C2×Dic73—22no—
396C2×Dic73—22no—
397C2×Dic73—22no—
398C2×Dic73—41no—
399C2×Dic73—41no—
400C2×Dic73—41no—
401C2×Dic73—41no—
402C2×Dic73—41no—
403C2×Dic73—41no—
404C2×Dic73—41no—
405C2×Dic73—41no—
406C2×Dic73—41no—
407C2×Dic73—41no—
408C2×Dic73—41no—
409C2×Dic73—41no—
410C2×Dic73—41no—
411C2×Dic73—41no—
412C2×Dic73—41no—
413C2×Dic73—41no—
414C2×Dic73—41no—
415C2×Dic73—41no—
416C2×Dic73—41no—
417C2×Dic73—41no—
418C2×Dic73—41no—
419C2×Dic73—41no—
420C2×Dic73—41no—
421C2×Dic73—41no—
422C2×Dic73—41no—
423C2×Dic73—41no—
424C2×Dic73—41no—
425C2×Dic73—41no—
426C2×Dic73—41no—
427C2×Dic73—41no—
428C2×Dic73—41no—
429C2×Dic73—41no—
430C2×Dic73—41no—
431C2×Dic73—41no—
432C2×Dic73#12014yes—
433C22×C73—24no—
434C22×C73—24no—
435C22×C73—24no—
436C22×C73—42no—
437C22×C73—42no—
438C22×C73—42no—
439C22×C73—42no—
440C22×C73—42no—
441C22×C73—42no—
442C22×C73—42no—
443C22×C73—42no—
444C22×C73—42no—
445C22×C73—42no—
446C22×C73—42no—
447C22×C73—42no—
448C22×C73C2×#11711yescharacteristic
449C22×C73C2×C4×D411yescharacteristic
450C22×C73C2×C4×D411yescharacteristic
451C22×C73C2×C4×D411yescharacteristic
452C22×C73C4×#4111yescharacteristic
453C22×C73#51911yescharacteristic
454C22×C73#52011yescharacteristic
455C22×C73C2×#12011yescharacteristic
456C22×C73#52511yescharacteristic
457C22×C73#52511yescharacteristic
458C22×C73#52511yescharacteristic
459C22×C73#52911yescharacteristic
460C22×C73#52911yescharacteristic
461C22×C73#53211yescharacteristic
462C22×C73#53211yescharacteristic
463C22×C73#53611yescharacteristic
464C22×C73#53711yescharacteristic
465C22×C73#54111yescharacteristic
466C22×C73#54211yescharacteristic
467C22×C73#54611yescharacteristic
468C22×C73#54611yescharacteristic
469C22×C73#54711yescharacteristic
470C22×C73#54711yescharacteristic
471C22×C73#54711yescharacteristic
472C22×C73#54711yescharacteristic
473C22×C73#54811yescharacteristic
474C22×C73#54811yescharacteristic
475C22×C73#55111yescharacteristic
476C22×C73#55211yescharacteristic
477C22×C73#55211yescharacteristic
478C22×C73#55211yescharacteristic
479C22×C73#55211yescharacteristic
480C22×C73#55211yescharacteristic
481C22×C73#55311yescharacteristic
482C22×C73#55611yescharacteristic
483C4×C73—24no—
484C4×C73—24no—
485C4×C73—24no—
486C4×C73—42no—
487C4×C73—42no—
488C4×C73—42no—
489Dic73—24no—
490Dic73—42no—
491Dic73—42no—
492Dic73—42no—
493Dic73—42no—
494Dic73—42no—
495Dic73—81no—
496Dic73—81no—
497#14072—731nomaximal, Sylow
498C2×C73—44no—
499C2×C73#229311yescharacteristic
500C2×C73C4×#12011yescharacteristic
501C2×C73#232311yescharacteristic
502C2×C73#234411yescharacteristic
503C2×C73#235211yescharacteristic
504C2×C73#235911yescharacteristic
505C2×C73#236211yescharacteristic
506C2×C73#243011yescharacteristic
507C2×C73#243211yescharacteristic
508C2×C73#247011yescharacteristic
509C2×C73#247511yescharacteristic
510C2×C73#247711yescharacteristic
511C2×C73#247811yescharacteristic
512C2×C73#260111yescharacteristic
513C2×C73#261111yescharacteristic
514C22×#117—731no—
515C2×#389—731no—
516C2×#388—731no—
517C2×#387—731no—
518C2×#385D7311yescharacteristic
519#1442—731no—
520#1441—731no—
521#1440—731no—
522#1439—731no—
523#1437—731no—
524#1436—731no—
525#1436—731no—
526#1436—731no—
527C22⋊#95—731no—
528C4×#95—731no—
529C73#1407211yescharacteristic, complemented, Sylow
530C24×C4C2×D7311yescharacteristic
531C2×#117—1464no—
532C2×#117—1464no—
533C2×#117—1464no—
534C22×C4⋊C4—731no—
535C22×C4⋊C4—731no—
536C22×C4⋊C4—731no—
537C22×C4⋊C4—731no—
538C22×C4⋊C4C2×D7311yescharacteristic
539C22×C4⋊C4C2×D7311yescharacteristic
540C22×C22⋊C4—731no—
541C22×C22⋊C4—731no—
542C22×C22⋊C4—731no—
543C22×C22⋊C4—731no—
544C22×C22⋊C4C2×D7311yescharacteristic
545C22×C22⋊C4C2×D7311yescharacteristic
546C22×C42—731no—
547C22×C42—731no—
548C22×C42—731no—
549C22×C42—731no—
550#389—1464no—
551#388—1464no—
552#387—1464no—
553#385Dic7318yescomplemented
554C2×#95—731no—
555C2×#95—731no—
556C2×#95—731no—
557C2×#95—731no—
558C2×#95—731no—
559C2×#95—731no—
560C2×#95—731no—
561C2×#95—731no—
562C2×#95—731no—
563C2×#95—731no—
564C2×#95—731no—
565C2×#95—731no—
566C2×#95—731no—
567C2×#95—731no—
568C2×#95—731no—
569C2×#95—731no—
570C2×#95C2×D7311yescharacteristic
571C2×#95C2×D7311yescharacteristic
572C25C22×D7311yescharacteristic
573C23×C4—22no—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—731no—
580C23×C4—731no—
581C23×C4—731no—
582C23×C4—731no—
583C23×C4—731no—
584C23×C4—731no—
585C23×C4—731no—
586C23×C4—731no—
587C23×C4C2×Dic7314yes—
588C23×C4C22×D7311yescharacteristic
589C23×C4C22×D7311yescharacteristic
590C23×C4C22×D7311yescharacteristic
591C23×C4C22×D7311yescharacteristic
592C23×C4C22×D7311yescharacteristic
593C23×C4C22×D7311yescharacteristic
594#117—14632no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—2921no—
600C2×C4⋊C4—734no—
601C2×C4⋊C4—1462no—
602C2×C4⋊C4—1462no—
603C2×C4⋊C4—1462no—
604C2×C4⋊C4—1462no—
605C2×C4⋊C4—1462no—
606C2×C4⋊C4—1462no—
607C2×C4⋊C4—1462no—
608C2×C4⋊C4—1462no—
609C2×C4⋊C4—1462no—
610C2×C4⋊C4—1462no—
611C2×C4⋊C4C2×Dic7314yes—
612C2×C4⋊C4C2×Dic7314yes—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—2921no—
618C2×C22⋊C4—2921no—
619C2×C22⋊C4—734no—
620C2×C22⋊C4—1462no—
621C2×C22⋊C4—1462no—
622C2×C22⋊C4—1462no—
623C2×C22⋊C4—1462no—
624C2×C22⋊C4—1462no—
625C2×C22⋊C4—1462no—
626C2×C22⋊C4—1462no—
627C2×C22⋊C4—1462no—
628C2×C22⋊C4—1462no—
629C2×C22⋊C4C2×Dic7314yes—
630C2×C22⋊C4C2×Dic7314yes—
631C2×C42—2921no—
632C2×C42—2921no—
633C2×C42—734no—
634C2×C42—1462no—
635C2×C42—1462no—
636C2×C42—1462no—
637C2×C42—1462no—
638C2×C42—1462no—
639C2×C42—1462no—
640C2×C42—1462no—
641C2×C42—1462no—
642C2×C42—1462no—
643#95—2921no—
644#95—1462no—
645#95—1462no—
646#95—1462no—
647#95—1462no—
648#95—1462no—
649#95—1462no—
650#95—1462no—
651#95—1462no—
652#95—1462no—
653#95—1462no—
654#95—1462no—
655#95—1462no—
656#95—1462no—
657#95—1462no—
658#95—1462no—
659#95C2×Dic7314yes—
660#95C2×Dic7314yes—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24C22×Dic7312yes—
674C24D4×D7312yes—
675C24#1192402712yes—
676C24C23×D7311yescharacteristic
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—28no—
695C22×C4—28no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—732no—
715C22×C4—732no—
716C22×C4—732no—
717C22×C4—732no—
718C22×C4—732no—
719C22×C4—732no—
720C22×C4—732no—
721C22×C4—732no—
722C22×C4—1461no—
723C22×C4—1461no—
724C22×C4—1461no—
725C22×C4—1461no—
726C22×C4—1461no—
727C22×C4—1461no—
728C22×C4—1461no—
729C22×C4—1461no—
730C22×C4—1461no—
731C22×C4—1461no—
732C22×C4—1461no—
733C22×C4—1461no—
734C22×C4—1461no—
735C22×C4—1461no—
736C22×C4—1461no—
737C22×C4—1461no—
738C22×C4—1461no—
739C22×C4—1461no—
740C22×C4—1461no—
741C22×C4—1461no—
742C22×C4—1461no—
743C22×C4—1461no—
744C22×C4—1461no—
745C22×C4—1461no—
746C22×C4—1461no—
747C22×C4—1461no—
748C22×C4—1461no—
749C22×C4—1461no—
750C22×C4—1461no—
751C22×C4—1461no—
752C22×C4—1461no—
753C22×C4—1461no—
754C22×C4—1461no—
755C22×C4—1461no—
756C22×C4—1461no—
757C22×C4—1461no—
758C22×C4—1461no—
759C22×C4—1461no—
760C22×C4—1461no—
761C22×C4—1461no—
762C22×C4—1461no—
763C22×C4—1461no—
764C22×C4—1461no—
765C22×C4—1461no—
766C22×C4—1461no—
767C22×C4—1461no—
768C22×C4—1461no—
769C22×C4—1461no—
770C22×C4C22×Dic7312yes—
771C22×C4C22×Dic7312yes—
772C22×C4C22×Dic7312yes—
773C22×C4C22×Dic7312yes—
774C22×C4C22×Dic7312yes—
775C22×C4C22×Dic7312yes—
776C22×C4D4×D7312yes—
777C22×C4D4×D7312yes—
778C22×C4#1192402712yes—
779C22×C4#1192402712yes—
780C22×C4#1192402812yes—
781C22×C4#1192402812yes—
782C4⋊C4—28no—
783C4⋊C4—28no—
784C4⋊C4—2924no—
785C4⋊C4—2924no—
786C4⋊C4—1468no—
787C4⋊C4—1468no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—2924no—
791C22⋊C4—2924no—
792C22⋊C4—1468no—
793C22⋊C4—1468no—
794C42—2924no—
795C42—2924no—
796C42—1468no—
797C42—1468no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23D4×Dic7314yes—
833C23C23×Dic7311yescharacteristic
834C23C2×D4×D7311yescharacteristic
835C23C2×D4×D7311yescharacteristic
836C23C2×D4×D7311yescharacteristic
837C23#41×D7311yescharacteristic
838C23#41×D7311yescharacteristic
839C23C2×#1192402711yescharacteristic
840C23C2×#1192402711yescharacteristic
841C23C2×#1192402711yescharacteristic
842C23C2×#1192402811yescharacteristic
843C23C2×#1192402811yescharacteristic
844C23#1455663711yescharacteristic
845C23#1455663811yescharacteristic
846C23#1455663911yescharacteristic
847C23#1455663911yescharacteristic
848C2×C4—232no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—2921no—
889C2×C4—2921no—
890C2×C4—2921no—
891C2×C4—2921no—
892C2×C4—2921no—
893C2×C4—2921no—
894C2×C4—2921no—
895C2×C4—2921no—
896C2×C4—2921no—
897C2×C4—2921no—
898C2×C4—2921no—
899C2×C4—2921no—
900C2×C4—2921no—
901C2×C4—2921no—
902C2×C4—2921no—
903C2×C4—2921no—
904C2×C4—2921no—
905C2×C4—2921no—
906C2×C4—2921no—
907C2×C4—2921no—
908C2×C4—2921no—
909C2×C4—2921no—
910C2×C4—2921no—
911C2×C4—2921no—
912C2×C4—2921no—
913C2×C4—2921no—
914C2×C4—2921no—
915C2×C4—2921no—
916C2×C4—2921no—
917C2×C4—2921no—
918C2×C4—2921no—
919C2×C4—2921no—
920C2×C4—2921no—
921C2×C4—2921no—
922C2×C4—734no—
923C2×C4—1462no—
924C2×C4—1462no—
925C2×C4—1462no—
926C2×C4—1462no—
927C2×C4—1462no—
928C2×C4—1462no—
929C2×C4—1462no—
930C2×C4—1462no—
931C2×C4—1462no—
932C2×C4—1462no—
933C2×C4—1462no—
934C2×C4—1462no—
935C2×C4—1462no—
936C2×C4—1462no—
937C2×C4—1462no—
938C2×C4—1462no—
939C2×C4—1462no—
940C2×C4—1462no—
941C2×C4—1462no—
942C2×C4—1462no—
943C2×C4—1462no—
944C2×C4#1455655014yescomplemented
945C2×C4D4×Dic7314yes—
946C2×C4D4×Dic7314yes—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22C2×#1455655011yescharacteristic
963C22C2×D4×Dic7311yescharacteristic
964C22C2×D4×Dic7311yescharacteristic
965C22C2×D4×Dic7311yescharacteristic
966C22#41×Dic7311yescharacteristic
967C22#1798906511yescharacteristic
968C22#1798907011yescharacteristic
969C22#120×D7311yescharacteristic
970C22#1798909311yescharacteristic
971C22#1798909311yescharacteristic
972C22#1798909311yescharacteristic
973C22#1798911911yescharacteristic
974C22#1798911911yescharacteristic
975C22#1798913411yescharacteristic
976C22#1798913411yescharacteristic
977C22#1798916011yescharacteristic
978C22#1798916711yescharacteristic
979C22#1798919711yescharacteristic
980C22#1798921011yescharacteristic
981C22#1798922911yescharacteristic
982C22#1798923311yescharacteristic
983C22#1798923511yescharacteristic
984C22#1798923811yescharacteristic
985C22#1798923811yescharacteristic
986C22#1798923911yescharacteristic
987C22#1798924611yescharacteristic
988C22#1798924711yescharacteristic
989C22#1798926011yescharacteristic
990C22#1798927111yescharacteristic
991C22#1798927211yescharacteristic
992C22#1798927211yescharacteristic
993C22#1798927411yescharacteristic
994C22#1798927711yescharacteristic
995C22#1798928311yescharacteristic
996C22#1798930811yescharacteristic
997C4—24no—
998C4—24no—
999C4—24no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—2922no—
1004C4—2922no—
1005C4—2922no—
1006C4—2922no—
1007C4—2922no—
1008C4—5841no—
1009C4—5841no—
1010C4—1464no—
1011C2—44no—
1012C2#2261239611yescharacteristic
1013C2#120×Dic7311yescharacteristic
1014C2#2261261511yescharacteristic
1015C2#2261280011yescharacteristic
1016C2#2261286011yescharacteristic
1017C2#2261292711yescharacteristic
1018C2#2261296211yescharacteristic
1019C2#2261354011yescharacteristic
1020C2#2261355711yescharacteristic
1021C2#2261402611yescharacteristic
1022C2#2261410111yescharacteristic
1023C2#2261413111yescharacteristic
1024C2#2261414611yescharacteristic
1025C2#2261553211yescharacteristic
1026C2#2261562511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×#385×C73C2
socle, cosocleC24×C73C24
prime radicalC25×C73C23
hypercenterC2×#385D73
hypocenterC73#14072
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#17988486C2semidirect
4. C2×#17988473C2semidirect
5. #22608188C2semidirect
6. #22608184C2semidirect
10. #22608165C2semidirect
11. #22608165C2semidirect
12. #22608163C2semidirect
14. #95×Dic73C2semidirect
55. #385×C73C4semidirect
374. C2×C4×C73#117semidirect
529. C73#14072semidirect
553. #385Dic73semidirect
944. C2×C4#14556550semidirect

Maximal subgroups

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

subgroupindex
C22×#145565502
C2×#179884862
C2×#179884802
C2×#179884732
#226081882
#226081842
#226081802
#226081762
#226081682
#226081652
#226081632
#226081542
#95×Dic732
C2×#385×C732
#1407273