Finite Group Databasebeta

← #33022585

Subgroups — #33022585

Order 18688.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988510C211yesmaximal, characteristic
2C2×#17988482C211yesmaximal, characteristic, complemented
3C2×#17988482C211yesmaximal, characteristic, complemented
4C2×#17988456C211yesmaximal, characteristic, complemented
5C2×#17988445C211yesmaximal, characteristic
6C2×#17988445C211yesmaximal, characteristic
7C2×C22⋊C4×Dic73C211yesmaximal, characteristic
8#22608184C211yesmaximal, characteristic, complemented
9#22608182C211yesmaximal, characteristic, complemented
10#22608181C211yesmaximal, characteristic, complemented
11#22608181C211yesmaximal, characteristic, complemented
12#22608174C211yesmaximal, characteristic
13#22608174C211yesmaximal, characteristic
14#22608159C211yesmaximal, characteristic, complemented
15C2×#396×C73C211yesmaximal, characteristic
16C24×Dic73C2211yescharacteristic
17C22×C4⋊Dic73C2211yescharacteristic
18C22×#11924007C2211yescharacteristic
19C22×#11924007C2211yescharacteristic
20C22×#11924007C2211yescharacteristic
21C22×#11924007C2211yescharacteristic
22C22×#11924007C2211yescharacteristic
23C22×#11924007C2211yescharacteristic
24C22×#11924007C2211yescharacteristic
25C22×#11924007C2211yescharacteristic
26C22×C22⋊Dic73C2211yescharacteristic
27C22×C22⋊Dic73C2211yescharacteristic
28C22×C22⋊Dic73C2211yescharacteristic
29C22×C4×Dic73C2211yescharacteristic
30C22×C4×Dic73C2211yescharacteristic
31#17988510—24no—
32#17988482—24no—
33#17988482—24no—
34#17988456—24no—
35#17988445—24no—
36#17988445—24no—
37C22⋊C4×Dic73—24no—
38C2×#14556498C2211yescharacteristic
39C2×#14556498C2211yescharacteristic
40C2×#14556498C2211yescharacteristic
41C2×#14556498C2211yescharacteristic
42C2×#14556498C2211yescharacteristic
43C2×#14556498C2211yescharacteristic
44C2×#14556498C2211yescharacteristic
45C2×#14556498C2211yescharacteristic
46C2×#14556498C2211yescharacteristic
47C2×#14556498C2211yescharacteristic
48C2×#14556498C2211yescharacteristic
49C2×#14556498C2211yescharacteristic
50C2×#14556498C2211yescharacteristic
51C22×C4⋊C4×C73C2211yescharacteristic
52C22×C4⋊C4×C73C2211yescharacteristic
53C22×C4⋊C4×C73C2211yescharacteristic
54C22×C22⋊C4×C73C2211yescharacteristic
55C22×C22⋊C4×C73C2211yescharacteristic
56C22×C22⋊C4×C73C2211yescharacteristic
57#396×C73—24no—
58C2×#95×C73C2211yescharacteristic
59C23×Dic73—22no—
60C23×Dic73—22no—
61C23×Dic73—22no—
62C23×Dic73—22no—
63C23×Dic73—22no—
64C23×Dic73—22no—
65C23×Dic73Q814yes—
66C23×Dic73C2311yescharacteristic
67C23×Dic73C2311yescharacteristic
68C23×Dic73C2311yescharacteristic
69C23×Dic73C2311yescharacteristic
70C23×Dic73C2311yescharacteristic
71C23×Dic73C2311yescharacteristic
72C23×Dic73C2311yescharacteristic
73C23×Dic73C2311yescharacteristic
74C2×C4⋊Dic73—22no—
75C2×C4⋊Dic73—22no—
76C2×C4⋊Dic73—41no—
77C2×#11924007—22no—
78C2×#11924007—22no—
79C2×#11924007—22no—
80C2×#11924007—22no—
81C2×#11924007—22no—
82C2×#11924007—22no—
83C2×#11924007—22no—
84C2×#11924007—22no—
85C2×#11924007—22no—
86C2×#11924007—22no—
87C2×#11924007—22no—
88C2×#11924007—22no—
89C2×#11924007—22no—
90C2×#11924007—22no—
91C2×#11924007—22no—
92C2×#11924007—22no—
93C2×#11924007—22no—
94C2×#11924007—22no—
95C2×#11924007—22no—
96C2×#11924007—41no—
97C2×#11924007—41no—
98C2×#11924007—41no—
99C2×#11924007D414yes—
100C2×#11924007D414yes—
101C2×C22⋊Dic73—22no—
102C2×C22⋊Dic73—22no—
103C2×C22⋊Dic73—22no—
104C2×C22⋊Dic73—22no—
105C2×C22⋊Dic73—22no—
106C2×C22⋊Dic73—22no—
107C2×C22⋊Dic73—41no—
108C2×C22⋊Dic73—41no—
109C2×C22⋊Dic73Q814yes—
110C2×C4×Dic73—22no—
111C2×C4×Dic73—22no—
112C2×C4×Dic73—22no—
113C2×C4×Dic73—22no—
114C2×C4×Dic73—22no—
115C2×C4×Dic73D414yes—
116#14556498—22no—
117#14556498—22no—
118#14556498—22no—
119#14556498—22no—
120#14556498—22no—
121#14556498—22no—
122#14556498—22no—
123#14556498—22no—
124#14556498—22no—
125#14556498—22no—
126#14556498—22no—
127#14556498—41no—
128#14556498—41no—
129C25×C73C2311yescharacteristic
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C23×C4×C73C2311yescharacteristic
135C23×C4×C73C2311yescharacteristic
136C2×C4⋊C4×C73—22no—
137C2×C4⋊C4×C73—22no—
138C2×C4⋊C4×C73—22no—
139C2×C4⋊C4×C73—22no—
140C2×C4⋊C4×C73—22no—
141C2×C4⋊C4×C73—22no—
142C2×C4⋊C4×C73—22no—
143C2×C4⋊C4×C73—41no—
144C2×C4⋊C4×C73—41no—
145C2×C22⋊C4×C73—22no—
146C2×C22⋊C4×C73—22no—
147C2×C22⋊C4×C73—22no—
148C2×C22⋊C4×C73—22no—
149C2×C22⋊C4×C73—22no—
150C2×C22⋊C4×C73—22no—
151C2×C22⋊C4×C73—41no—
152C2×C22⋊C4×C73—41no—
153C2×C22⋊C4×C73D414yes—
154#95×C73—22no—
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—28no—
184C22×Dic73—28no—
185C22×Dic73—28no—
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×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73—21no—
200C22×Dic73—44no—
201C22×Dic73—44no—
202C22×Dic73—44no—
203C22×Dic73—44no—
204C22×Dic73C2×D412yes—
205C22×Dic73C2×D412yes—
206C22×Dic73C2×D412yes—
207C22×Dic73C2×D412yes—
208C22×Dic73C2×D412yes—
209C22×Dic73C2×D412yes—
210C22×Dic73C2×Q812yes—
211C22×Dic73C2×Q812yes—
212C22×Dic73C2×Q812yes—
213C22×Dic73C2×Q812yes—
214C22×Dic73#4112yes—
215C22×Dic73#4112yes—
216C22×Dic73#4112yes—
217C22×Dic73#4112yes—
218C4⋊Dic73—44no—
219#11924007—28no—
220#11924007—28no—
221#11924007—44no—
222#11924007—44no—
223#11924007—44no—
224#11924007—44no—
225#11924007—44no—
226#11924007—44no—
227C22⋊Dic73—28no—
228C22⋊Dic73—44no—
229C22⋊Dic73—44no—
230C4×Dic73—28no—
231C4×Dic73—44no—
232C24×C73—21no—
233C24×C73—21no—
234C24×C73—21no—
235C24×C73—21no—
236C24×C73—21no—
237C24×C73—21no—
238C24×C73—21no—
239C24×C73—21no—
240C24×C73—21no—
241C24×C73—21no—
242C24×C73—21no—
243C24×C73—21no—
244C24×C73C2×D412yes—
245C24×C73C2×Q812yes—
246C24×C73C2×Q812yes—
247C24×C73C2411yescharacteristic
248C22×C4×C73—21no—
249C22×C4×C73—21no—
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×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—21no—
276C22×C4×C73—21no—
277C22×C4×C73—21no—
278C22×C4×C73—21no—
279C22×C4×C73—21no—
280C22×C4×C73—21no—
281C22×C4×C73—21no—
282C22×C4×C73—21no—
283C22×C4×C73—21no—
284C22×C4×C73C2×D412yes—
285C22×C4×C73C2×D412yes—
286C22×C4×C73C2×D412yes—
287C22×C4×C73C2×D412yes—
288C22×C4×C73C2×D412yes—
289C22×C4×C73#4112yes—
290C4⋊C4×C73—44no—
291C4⋊C4×C73—44no—
292C4⋊C4×C73—44no—
293C22⋊C4×C73—28no—
294C22⋊C4×C73—44no—
295C22⋊C4×C73—44no—
296C23×C73—22no—
297C23×C73—22no—
298C23×C73—22no—
299C23×C73—22no—
300C23×C73—22no—
301C23×C73—22no—
302C23×C73—22no—
303C23×C73—22no—
304C23×C73—22no—
305C23×C73—22no—
306C23×C73—22no—
307C23×C73—22no—
308C23×C73—22no—
309C23×C73—22no—
310C23×C73—22no—
311C23×C73—22no—
312C23×C73—22no—
313C23×C73—22no—
314C23×C73—41no—
315C23×C73—41no—
316C23×C73—41no—
317C23×C73—41no—
318C23×C73—41no—
319C23×C73—41no—
320C23×C73—41no—
321C23×C73—41no—
322C23×C73—41no—
323C23×C73—41no—
324C23×C73—41no—
325C23×C73—41no—
326C23×C73—41no—
327C23×C73—41no—
328C23×C73—41no—
329C23×C73—41no—
330C23×C73C4⋊Q814yes—
331C23×C73C22×D411yescharacteristic
332C23×C73C22×D411yescharacteristic
333C23×C73C22×D411yescharacteristic
334C23×C73C22×D411yescharacteristic
335C23×C73C22×Q811yescharacteristic
336C23×C73C22×Q811yescharacteristic
337C23×C73C2×#4111yescharacteristic
338C23×C73C2×#4111yescharacteristic
339C23×C73C2×#4111yescharacteristic
340C23×C73C2×#4111yescharacteristic
341C23×C73C2×#4111yescharacteristic
342C23×C73H(5,𝔽2)11yescharacteristic
343C23×C73H(5,𝔽2)11yescharacteristic
344C23×C732−1+411yescharacteristic
345C23×C732−1+411yescharacteristic
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—41no—
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—41no—
375C2×C4×C73—41no—
376C2×C4×C73—41no—
377C2×C4×C73—41no—
378C2×C4×C73—41no—
379C2×C4×C73—41no—
380C2×C4×C73—41no—
381C2×C4×C73—41no—
382C2×C4×C73—41no—
383C2×C4×C73—41no—
384C2×C4×C73—41no—
385C2×C4×C73—41no—
386C2×C4×C73—41no—
387C2×C4×C73#12114yes—
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—22no—
399C2×Dic73—22no—
400C2×Dic73—22no—
401C2×Dic73—22no—
402C2×Dic73—22no—
403C2×Dic73—22no—
404C2×Dic73—22no—
405C2×Dic73—22no—
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—416no—
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—41no—
433C2×Dic73—41no—
434C2×Dic73—41no—
435C2×Dic73—41no—
436C2×Dic73—41no—
437C2×Dic73#12114yes—
438C2×Dic73#12114yes—
439C2×Dic73#12114yes—
440C2×Dic73C22⋊Q814yes—
441C2×Dic73C22⋊Q814yes—
442C2×Dic73C22⋊Q814yes—
443C2×Dic73C22⋊Q814yes—
444C2×Dic73#12614yes—
445C22×C73—24no—
446C22×C73—24no—
447C22×C73—24no—
448C22×C73—42no—
449C22×C73—42no—
450C22×C73—42no—
451C22×C73—42no—
452C22×C73—42no—
453C22×C73—42no—
454C22×C73—42no—
455C22×C73—42no—
456C22×C73—42no—
457C22×C73—42no—
458C22×C73—42no—
459C22×C73—42no—
460C22×C73C2×#12111yescharacteristic
461C22×C73C2×#12111yescharacteristic
462C22×C73C2×#12111yescharacteristic
463C22×C73C2×#12111yescharacteristic
464C22×C73C2×C22⋊Q811yescharacteristic
465C22×C73C2×C22⋊Q811yescharacteristic
466C22×C73C2×C22⋊Q811yescharacteristic
467C22×C73C2×C22⋊Q811yescharacteristic
468C22×C73C2×#12611yescharacteristic
469C22×C73C2×C4⋊Q811yescharacteristic
470C22×C73#53211yescharacteristic
471C22×C73#53311yescharacteristic
472C22×C73#53311yescharacteristic
473C22×C73#53711yescharacteristic
474C22×C73#53711yescharacteristic
475C22×C73#54011yescharacteristic
476C22×C73#54111yescharacteristic
477C22×C73#54411yescharacteristic
478C22×C73#54411yescharacteristic
479C22×C73D4211yescharacteristic
480C22×C73D4211yescharacteristic
481C22×C73#54611yescharacteristic
482C22×C73#54711yescharacteristic
483C22×C73#54711yescharacteristic
484C22×C73#54711yescharacteristic
485C22×C73#54811yescharacteristic
486C22×C73D4×Q811yescharacteristic
487C22×C73D4×Q811yescharacteristic
488C22×C73#55011yescharacteristic
489C22×C73#55211yescharacteristic
490C22×C73#55311yescharacteristic
491C22×C73#55411yescharacteristic
492C22×C73#55411yescharacteristic
493C22×C73#55511yescharacteristic
494C22×C73#55611yescharacteristic
495C4×C73—24no—
496C4×C73—42no—
497C4×C73—42no—
498C4×C73—42no—
499C4×C73—81no—
500C4×C73—81no—
501Dic73—24no—
502Dic73—42no—
503Dic73—42no—
504Dic73—42no—
505Dic73—42no—
506Dic73—81no—
507Dic73—81no—
508Dic73#39618yescomplemented
509#15131—731nomaximal, Sylow
510C2×C73—44no—
511C2×C73C2×#39611yescharacteristic
512C2×C73#241611yescharacteristic
513C2×C73#241711yescharacteristic
514C2×C73#242811yescharacteristic
515C2×C73#242911yescharacteristic
516C2×C73#243911yescharacteristic
517C2×C73#244011yescharacteristic
518C2×C73#244011yescharacteristic
519C2×C73#244111yescharacteristic
520C2×C73#249611yescharacteristic
521C2×C73#249711yescharacteristic
522C2×C73#253711yescharacteristic
523C2×C73#253811yescharacteristic
524C2×C73#262911yescharacteristic
525C2×C73#285711yescharacteristic
526C2×#396—731no—
527C2×#396D7311yescharacteristic
528C2×#389—731no—
529C2×#389—731no—
530C2×#384—731no—
531C2×#380—731no—
532C2×#380—731no—
533C2×C4×C22⋊C4—731no—
534#1441—731no—
535#1441—731no—
536#1441—731no—
537#1441—731no—
538#1439—731no—
539#1439—731no—
540C4⋊#95—731no—
541C73#1513111yescharacteristic, complemented, Sylow
542C24×C4—731no—
543C22×C4⋊C4—731no—
544C22×C4⋊C4—731no—
545C22×C4⋊C4—731no—
546C22×C4⋊C4—731no—
547C22×C4⋊C4—731no—
548C22×C4⋊C4—731no—
549C22×C4⋊C4—731no—
550C22×C4⋊C4—731no—
551C22×C4⋊C4—731no—
552C22×C4⋊C4C2×D7311yescharacteristic
553C22×C4⋊C4C2×D7311yescharacteristic
554C22×C4⋊C4C2×D7311yescharacteristic
555C22×C22⋊C4—731no—
556C22×C22⋊C4—731no—
557C22×C22⋊C4—731no—
558C22×C22⋊C4C2×D7311yescharacteristic
559C22×C22⋊C4C2×D7311yescharacteristic
560C22×C22⋊C4C2×D7311yescharacteristic
561C22×C42—731no—
562C22×C42—731no—
563#396—24no—
564#396—1464no—
565#389—1464no—
566#389—1464no—
567#384—1464no—
568#380—1464no—
569#380—1464no—
570C4×C22⋊C4—1464no—
571C2×#95—731no—
572C2×#95—731no—
573C2×#95—731no—
574C2×#95—731no—
575C2×#95—731no—
576C2×#95—731no—
577C2×#95—731no—
578C2×#95—731no—
579C2×#95—731no—
580C2×#95—731no—
581C2×#95—731no—
582C2×#95—731no—
583C2×#95—731no—
584C2×#95C2×D7311yescharacteristic
585C25C22×D7311yescharacteristic
586C23×C4—731no—
587C23×C4—731no—
588C23×C4—734no—
589C23×C4—731no—
590C23×C4—731no—
591C23×C4—731no—
592C23×C4—731no—
593C23×C4—731no—
594C23×C4—731no—
595C23×C4—1462no—
596C23×C4—1462no—
597C23×C4—1462no—
598C23×C4—1462no—
599C23×C4—1462no—
600C23×C4—1462no—
601C23×C4C22×D7311yescharacteristic
602C23×C4C22×D7311yescharacteristic
603C23×C4C22×D7311yescharacteristic
604C23×C4C22×D7311yescharacteristic
605C23×C4C22×D7311yescharacteristic
606C23×C4C22×D7311yescharacteristic
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—41no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—2921no—
617C2×C4⋊C4—2921no—
618C2×C4⋊C4—2921no—
619C2×C4⋊C4—2921no—
620C2×C4⋊C4—734no—
621C2×C4⋊C4—734no—
622C2×C4⋊C4—1462no—
623C2×C4⋊C4—1462no—
624C2×C4⋊C4—1462no—
625C2×C4⋊C4—1462no—
626C2×C4⋊C4—1462no—
627C2×C4⋊C4—1462no—
628C2×C4⋊C4—1462no—
629C2×C4⋊C4—1462no—
630C2×C4⋊C4—1462no—
631C2×C4⋊C4—1462no—
632C2×C4⋊C4—1462no—
633C2×C4⋊C4—1462no—
634C2×C4⋊C4—1462no—
635C2×C4⋊C4—1462no—
636C2×C4⋊C4—1462no—
637C2×C4⋊C4—1462no—
638C2×C4⋊C4—1462no—
639C2×C4⋊C4—1462no—
640C2×C4⋊C4—1462no—
641C2×C4⋊C4—1462no—
642C2×C4⋊C4—1462no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—41no—
650C2×C22⋊C4—41no—
651C2×C22⋊C4—2921no—
652C2×C22⋊C4—2921no—
653C2×C22⋊C4—734no—
654C2×C22⋊C4—1462no—
655C2×C22⋊C4—1462no—
656C2×C22⋊C4—1462no—
657C2×C22⋊C4—1462no—
658C2×C22⋊C4—1462no—
659C2×C22⋊C4—1462no—
660C2×C22⋊C4C22⋊D7314yes—
661C2×C42—734no—
662C2×C42—1462no—
663C2×C42—1462no—
664C2×C42—1462no—
665C2×C42—1462no—
666C2×C42—1462no—
667#95—22no—
668#95—2921no—
669#95—2921no—
670#95—1462no—
671#95—1462no—
672#95—1462no—
673#95—1462no—
674#95—1462no—
675#95—1462no—
676#95—1462no—
677#95—1462no—
678#95—1462no—
679#95—1462no—
680#95—1462no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24C2×C22⋊D7312yes—
694C24Q8×D7312yes—
695C24Q8×D7312yes—
696C24C23×D7311yescharacteristic
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—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—2924no—
734C22×C4—2924no—
735C22×C4—2924no—
736C22×C4—2924no—
737C22×C4—732no—
738C22×C4—732no—
739C22×C4—732no—
740C22×C4—732no—
741C22×C4—732no—
742C22×C4—732no—
743C22×C4—732no—
744C22×C4—732no—
745C22×C4—732no—
746C22×C4—732no—
747C22×C4—732no—
748C22×C4—732no—
749C22×C4—732no—
750C22×C4—732no—
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—1468no—
766C22×C4—1468no—
767C22×C4—1468no—
768C22×C4—1461no—
769C22×C4—1461no—
770C22×C4—1461no—
771C22×C4—1461no—
772C22×C4—1461no—
773C22×C4—1461no—
774C22×C4—1461no—
775C22×C4—1461no—
776C22×C4—1461no—
777C22×C4—1461no—
778C22×C4—1461no—
779C22×C4—1461no—
780C22×C4—1461no—
781C22×C4—1461no—
782C22×C4—1461no—
783C22×C4—1461no—
784C22×C4—1461no—
785C22×C4—1461no—
786C22×C4—1461no—
787C22×C4—1461no—
788C22×C4—1461no—
789C22×C4—1461no—
790C22×C4—1461no—
791C22×C4—1461no—
792C22×C4—1461no—
793C22×C4—1461no—
794C22×C4—1461no—
795C22×C4—1461no—
796C22×C4D4×D7312yes—
797C22×C4D4×D7312yes—
798C22×C4D4×D7312yes—
799C22×C4C2×C22⋊D7312yes—
800C22×C4C2×C22⋊D7312yes—
801C22×C4#1192402712yes—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—2924no—
806C4⋊C4—2924no—
807C4⋊C4—2924no—
808C4⋊C4—2924no—
809C4⋊C4—2924no—
810C4⋊C4—2924no—
811C4⋊C4—2924no—
812C4⋊C4—1468no—
813C4⋊C4—1468no—
814C22⋊C4—28no—
815C22⋊C4—44no—
816C22⋊C4—44no—
817C22⋊C4—2924no—
818C22⋊C4—2924no—
819C22⋊C4—1468no—
820C42—2924no—
821C42—1468no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23#1455658914yes—
857C23C2×D4×D7311yescharacteristic
858C23C2×D4×D7311yescharacteristic
859C23C2×D4×D7311yescharacteristic
860C23C22×C22⋊D7311yescharacteristic
861C23C2×Q8×D7311yescharacteristic
862C23C2×Q8×D7311yescharacteristic
863C23#41×D7311yescharacteristic
864C23#41×D7311yescharacteristic
865C23#41×D7311yescharacteristic
866C23#41×D7311yescharacteristic
867C23C2×#1192402711yescharacteristic
868C23#1455663611yescharacteristic
869C23#1455663611yescharacteristic
870C23#1455663811yescharacteristic
871C23#1455663811yescharacteristic
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
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—2921no—
923C2×C4—2921no—
924C2×C4—2921no—
925C2×C4—2921no—
926C2×C4—2921no—
927C2×C4—2921no—
928C2×C4—2921no—
929C2×C4—29216no—
930C2×C4—2921no—
931C2×C4—2921no—
932C2×C4—2921no—
933C2×C4—2921no—
934C2×C4—2921no—
935C2×C4—2921no—
936C2×C4—2921no—
937C2×C4—2921no—
938C2×C4—2921no—
939C2×C4—2921no—
940C2×C4—2921no—
941C2×C4—2921no—
942C2×C4—2921no—
943C2×C4—2921no—
944C2×C4—734no—
945C2×C4—734no—
946C2×C4—734no—
947C2×C4—734no—
948C2×C4—734no—
949C2×C4—734no—
950C2×C4—734no—
951C2×C4—734no—
952C2×C4—1462no—
953C2×C4—1462no—
954C2×C4—1462no—
955C2×C4—1462no—
956C2×C4—1462no—
957C2×C4—1462no—
958C2×C4—1462no—
959C2×C4—1462no—
960C2×C4—1462no—
961C2×C4—1462no—
962C2×C4—1462no—
963C2×C4—1462no—
964C2×C4—1462no—
965C2×C4—1462no—
966C2×C4—1462no—
967C2×C4—1462no—
968C2×C4—1462no—
969C2×C4—1462no—
970C2×C4#1455656314yes—
971C22—24no—
972C22—24no—
973C22—24no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—42no—
986C22#121×D7311yescharacteristic
987C22#121×D7311yescharacteristic
988C22#121×D7311yescharacteristic
989C22C2×#1455656311yescharacteristic
990C22C22⋊Q8×D7311yescharacteristic
991C22C22⋊Q8×D7311yescharacteristic
992C22C22⋊Q8×D7311yescharacteristic
993C22C22⋊Q8×D7311yescharacteristic
994C22#126×D7311yescharacteristic
995C22C2×#1455658911yescharacteristic
996C22#1798913311yescharacteristic
997C22#1798913911yescharacteristic
998C22#1798913911yescharacteristic
999C22#1798916411yescharacteristic
1000C22#1798916611yescharacteristic
1001C22#1798918711yescharacteristic
1002C22#1798919411yescharacteristic
1003C22#1798921611yescharacteristic
1004C22#1798921611yescharacteristic
1005C22D4×C22⋊D7311yescharacteristic
1006C22D4×C22⋊D7311yescharacteristic
1007C22#1798922611yescharacteristic
1008C22#1798923611yescharacteristic
1009C22#1798923611yescharacteristic
1010C22#1798923711yescharacteristic
1011C22#1798924311yescharacteristic
1012C22#1798925011yescharacteristic
1013C22#1798925011yescharacteristic
1014C22#1798925511yescharacteristic
1015C22#1798927311yescharacteristic
1016C22#1798928011yescharacteristic
1017C22#1798929111yescharacteristic
1018C22#1798929111yescharacteristic
1019C22#1798930111yescharacteristic
1020C22#1798930411yescharacteristic
1021C4—24no—
1022C4—42no—
1023C4—42no—
1024C4—42no—
1025C4—81no—
1026C4—81no—
1027C4—2922no—
1028C4—2922no—
1029C4—2922no—
1030C4—2922no—
1031C4—5841no—
1032C4—5841no—
1033C4—738no—
1034C4—1464no—
1035C2—44no—
1036C2#396×D7311yescharacteristic
1037C2#2261336811yescharacteristic
1038C2#2261337511yescharacteristic
1039C2#2261351611yescharacteristic
1040C2#2261352311yescharacteristic
1041C2#2261361711yescharacteristic
1042C2#2261363011yescharacteristic
1043C2#2261363011yescharacteristic
1044C2#2261363911yescharacteristic
1045C2#2261435011yescharacteristic
1046C2#2261435711yescharacteristic
1047C2#2261484511yescharacteristic
1048C2#2261484811yescharacteristic
1049C2#2261576011yescharacteristic
1050C2#2261827911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutator, socle, cosocleC24×C73C24
FittingC2×#396×C73C2
prime radicalC25×C73C23
hypercenterC2×#396D73
hypocenterC73#15131
LCSG ▷ C24×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
2. C2×#17988482C2semidirect
3. C2×#17988482C2semidirect
4. C2×#17988456C2semidirect
8. #22608184C2semidirect
9. #22608182C2semidirect
10. #22608181C2semidirect
11. #22608181C2semidirect
14. #22608159C2semidirect
508. Dic73#396semidirect
541. C73#15131semidirect

Maximal subgroups

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

subgroupindex
C2×#179885102
C2×#179884822
C2×#179884562
C2×#179884452
C2×C22⋊C4×Dic732
#226081842
#226081822
#226081812
#226081742
#226081592
C2×#396×C732
#1513173