Finite Group Databasebeta

← #33009031

Subgroups — #33009031

Order 18688.

1586 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988475C211yesmaximal, characteristic
2C2×#17988454C211yesmaximal, characteristic, complemented
3#22608197C211yesmaximal, characteristic, complemented
4#22608186C211yesmaximal, characteristic, complemented
5#22608178C211yesmaximal, characteristic
6#22608174C211yesmaximal, characteristic
7#22608168C211yesmaximal, characteristic
8#22608164C211yesmaximal, characteristic, complemented
9#22608164C211yesmaximal, characteristic, complemented
10#22608158C211yesmaximal, characteristic, complemented
11#22608156C211yesmaximal, characteristic, complemented
12#22608154C211yesmaximal, characteristic
13#22608154C211yesmaximal, characteristic
14C4×#14556498C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C73C211yesmaximal, characteristic
16C22×#11924007C2211yescharacteristic
17C22×#11924007C2211yescharacteristic
18C22×C22⋊Dic73C2211yescharacteristic
19C22×C22⋊Dic73C2211yescharacteristic
20C22×C22⋊Dic73C2211yescharacteristic
21C22×C22⋊Dic73C2211yescharacteristic
22C22×C4×Dic73C2211yescharacteristic
23C22×C4×Dic73C2211yescharacteristic
24#17988475C418yescomplemented
25#17988454—24no—
26C2×#14556498C2211yescharacteristic
27C2×#14556498C2211yescharacteristic
28C2×#14556498C2211yescharacteristic
29C2×#14556498C2211yescharacteristic
30C2×#14556498C2211yescharacteristic
31C2×#14556498C2211yescharacteristic
32C2×#14556498C2211yescharacteristic
33C2×#14556498C2211yescharacteristic
34C2×#14556498C2211yescharacteristic
35C2×#14556498C2211yescharacteristic
36C2×#14556498C2211yescharacteristic
37C2×#14556498C2211yescharacteristic
38C2×#14556498C2211yescharacteristic
39C2×#14556498C2211yescharacteristic
40C2×#14556498C2211yescharacteristic
41C2×#14556498C2211yescharacteristic
42C2×#14556498C2211yescharacteristic
43C2×#14556498C2211yescharacteristic
44C2×#14556498C2211yescharacteristic
45C2×#14556498C2211yescharacteristic
46C24×C4×C73C2211yescharacteristic
47C22×C22⋊C4×C73C2211yescharacteristic
48C22×C22⋊C4×C73C2211yescharacteristic
49C22×C42×C73C2211yescharacteristic
50C22×C42×C73C2211yescharacteristic
51C4×C22⋊C4×C73—24no—
52C2×#95×C73C2211yescharacteristic
53C2×#95×C73C2211yescharacteristic
54C23×Dic73C2311yescharacteristic
55C23×Dic73C2311yescharacteristic
56C23×Dic73C2311yescharacteristic
57C23×Dic73C2311yescharacteristic
58C23×Dic73C2311yescharacteristic
59C23×Dic73C2311yescharacteristic
60C23×Dic73C2311yescharacteristic
61C23×Dic73C2311yescharacteristic
62C2×#11924007—22no—
63C2×#11924007—41no—
64C2×#11924007—41no—
65C2×#11924007—41no—
66C2×#11924007—41no—
67C2×#11924007C2×C414yescomplemented
68C2×C22⋊Dic73—22no—
69C2×C22⋊Dic73—22no—
70C2×C22⋊Dic73—22no—
71C2×C22⋊Dic73—22no—
72C2×C22⋊Dic73—22no—
73C2×C22⋊Dic73—22no—
74C2×C22⋊Dic73—41no—
75C2×C22⋊Dic73—41no—
76C2×C22⋊Dic73—41no—
77C2×C22⋊Dic73—41no—
78C2×C22⋊Dic73C2×C414yes—
79C2×C22⋊Dic73C2×C414yes—
80C2×C4×Dic73—22no—
81C2×C4×Dic73—22no—
82C2×C4×Dic73—22no—
83C2×C4×Dic73—22no—
84C2×C4×Dic73—41no—
85C2×C4×Dic73C2×C414yescomplemented
86#14556498—22no—
87#14556498—22no—
88#14556498—22no—
89#14556498—22no—
90#14556498—22no—
91#14556498—22no—
92#14556498—22no—
93#14556498—22no—
94#14556498—22no—
95#14556498—22no—
96#14556498—22no—
97#14556498—22no—
98#14556498—22no—
99#14556498—41no—
100#14556498—41no—
101#14556498—41no—
102#14556498—41no—
103#14556498—41no—
104#14556498C2×C414yescomplemented
105#14556498C2×C414yescomplemented
106C25×C73C2311yescharacteristic
107C23×C4×C73—22no—
108C23×C4×C73—22no—
109C23×C4×C73—22no—
110C23×C4×C73—22no—
111C23×C4×C73—22no—
112C23×C4×C73—41no—
113C23×C4×C73—41no—
114C23×C4×C73C2311yescharacteristic
115C23×C4×C73C2311yescharacteristic
116C23×C4×C73C2311yescharacteristic
117C23×C4×C73C2311yescharacteristic
118C23×C4×C73C2311yescharacteristic
119C23×C4×C73C2311yescharacteristic
120C2×C22⋊C4×C73—22no—
121C2×C22⋊C4×C73—22no—
122C2×C22⋊C4×C73—22no—
123C2×C22⋊C4×C73—22no—
124C2×C22⋊C4×C73—22no—
125C2×C22⋊C4×C73C2×C414yes—
126C2×C42×C73—22no—
127C2×C42×C73—22no—
128C2×C42×C73—22no—
129C2×C42×C73—22no—
130C2×C42×C73—41no—
131C2×C42×C73—41no—
132#95×C73—22no—
133#95×C73D414yes—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C22×Dic73—21no—
137C22×Dic73—21no—
138C22×Dic73—21no—
139C22×Dic73—21no—
140C22×Dic73—21no—
141C22×Dic73—21no—
142C22×Dic73—21no—
143C22×Dic73—21no—
144C22×Dic73—21no—
145C22×Dic73—21no—
146C22×Dic73—21no—
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×Dic73C22×C412yes—
185C22×Dic73C22×C412yes—
186C22×Dic73C22×C412yes—
187C22×Dic73C22×C412yes—
188C22×Dic73#4112yes—
189C22×Dic73#4112yes—
190#11924007—44no—
191#11924007—44no—
192C22⋊Dic73—28no—
193C22⋊Dic73—44no—
194C22⋊Dic73—44no—
195C22⋊Dic73—44no—
196C4×Dic73—28no—
197C4×Dic73—44no—
198C24×C73—21no—
199C24×C73—21no—
200C24×C73—21no—
201C24×C73—21no—
202C24×C73—21no—
203C24×C73—21no—
204C24×C73—21no—
205C24×C73—21no—
206C24×C73—21no—
207C24×C73—21no—
208C24×C73—21no—
209C24×C73—21no—
210C24×C73C22×C412yes—
211C24×C73#4112yes—
212C24×C73#4112yes—
213C24×C73C2411yescharacteristic
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—28no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
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—44no—
248C22×C4×C73—44no—
249C22×C4×C73—44no—
250C22×C4×C73—44no—
251C22×C4×C73—44no—
252C22×C4×C73—44no—
253C22×C4×C73C22×C412yes—
254C22×C4×C73C22×C412yes—
255C22×C4×C73C2×D412yes—
256C22×C4×C73C2×D412yes—
257C22×C4×C73C2×D412yes—
258C22×C4×C73#4112yes—
259C22×C4×C73#4112yes—
260C22×C4×C73#4112yes—
261C22×C4×C73#4112yes—
262C22×C4×C73#4112yes—
263C22⋊C4×C73—28no—
264C22⋊C4×C73—28no—
265C42×C73—44no—
266C42×C73—44no—
267C23×C73—22no—
268C23×C73—22no—
269C23×C73—22no—
270C23×C73—22no—
271C23×C73—22no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73—22no—
277C23×C73—22no—
278C23×C73—22no—
279C23×C73—22no—
280C23×C73—22no—
281C23×C73—22no—
282C23×C73—22no—
283C23×C73—22no—
284C23×C73—22no—
285C23×C73—41no—
286C23×C73—41no—
287C23×C73—41no—
288C23×C73—41no—
289C23×C73—41no—
290C23×C73—41no—
291C23×C73—41no—
292C23×C73—41no—
293C23×C73—41no—
294C23×C73—41no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—41no—
298C23×C73—41no—
299C23×C73—41no—
300C23×C73—41no—
301C23×C73#11714yes—
302C23×C73C23×C411yescharacteristic
303C23×C73C22×D411yescharacteristic
304C23×C73C2×#4111yescharacteristic
305C23×C73C2×#4111yescharacteristic
306C23×C73C2×#4111yescharacteristic
307C23×C73C2×#4111yescharacteristic
308C23×C73C2×#4111yescharacteristic
309C23×C73C2×#4111yescharacteristic
310C23×C73C2×#4111yescharacteristic
311C23×C73C2×#4111yescharacteristic
312C23×C73C2×#4111yescharacteristic
313C23×C73H(5,𝔽2)11yescharacteristic
314C23×C73H(5,𝔽2)11yescharacteristic
315C23×C73H(5,𝔽2)11yescharacteristic
316C23×C732−1+411yescharacteristic
317C2×C4×C73—22no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73—22no—
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—416no—
342C2×C4×C73—41no—
343C2×C4×C73—41no—
344C2×C4×C73—41no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
347C2×C4×C73—41no—
348C2×C4×C73—41no—
349C2×C4×C73—41no—
350C2×C4×C73—41no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—41no—
354C2×C4×C73—41no—
355C2×C4×C73—41no—
356C2×C4×C73—41no—
357C2×C4×C73—41no—
358C2×C4×C73C4×D414yes—
359C2×C4×C73#12614yes—
360C2×Dic73—22no—
361C2×Dic73—22no—
362C2×Dic73—22no—
363C2×Dic73—22no—
364C2×Dic73—22no—
365C2×Dic73—22no—
366C2×Dic73—22no—
367C2×Dic73—22no—
368C2×Dic73—22no—
369C2×Dic73—22no—
370C2×Dic73—22no—
371C2×Dic73—22no—
372C2×Dic73—22no—
373C2×Dic73—22no—
374C2×Dic73—22no—
375C2×Dic73—22no—
376C2×Dic73—22no—
377C2×Dic73—22no—
378C2×Dic73—41no—
379C2×Dic73—41no—
380C2×Dic73—41no—
381C2×Dic73—41no—
382C2×Dic73—41no—
383C2×Dic73—41no—
384C2×Dic73—41no—
385C2×Dic73—41no—
386C2×Dic73—41no—
387C2×Dic73—41no—
388C2×Dic73—41no—
389C2×Dic73—41no—
390C2×Dic73—41no—
391C2×Dic73—41no—
392C2×Dic73—41no—
393C2×Dic73—41no—
394C2×Dic73—41no—
395C2×Dic73—41no—
396C2×Dic73—41no—
397C2×Dic73—41no—
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—
416C22×C73—24no—
417C22×C73—24no—
418C22×C73—24no—
419C22×C73—42no—
420C22×C73—42no—
421C22×C73—42no—
422C22×C73—42no—
423C22×C73—42no—
424C22×C73—42no—
425C22×C73—42no—
426C22×C73—42no—
427C22×C73—42no—
428C22×C73—42no—
429C22×C73—42no—
430C22×C73—42no—
431C22×C73C2×#11711yescharacteristic
432C22×C73C2×C4×D411yescharacteristic
433C22×C73C4×#4111yescharacteristic
434C22×C73C4×#4111yescharacteristic
435C22×C73C4×#4111yescharacteristic
436C22×C73#51811yescharacteristic
437C22×C73#52011yescharacteristic
438C22×C73#52511yescharacteristic
439C22×C73#52511yescharacteristic
440C22×C73C2×#12611yescharacteristic
441C22×C73#52911yescharacteristic
442C22×C73#52911yescharacteristic
443C22×C73#52911yescharacteristic
444C22×C73#52911yescharacteristic
445C22×C73#52911yescharacteristic
446C22×C73#53811yescharacteristic
447C22×C73#53811yescharacteristic
448C22×C73#54211yescharacteristic
449C22×C73#54211yescharacteristic
450C22×C73#54611yescharacteristic
451C22×C73#54611yescharacteristic
452C22×C73#54711yescharacteristic
453C22×C73#55011yescharacteristic
454C22×C73#55111yescharacteristic
455C22×C73#55111yescharacteristic
456C22×C73#55111yescharacteristic
457C22×C73#55111yescharacteristic
458C22×C73#55111yescharacteristic
459C22×C73#55211yescharacteristic
460C22×C73#55211yescharacteristic
461C22×C73#55211yescharacteristic
462C22×C73#55311yescharacteristic
463C22×C73#55311yescharacteristic
464C22×C73#55311yescharacteristic
465C22×C73#55511yescharacteristic
466C4×C73—24no—
467C4×C73—24no—
468C4×C73—42no—
469C4×C73—42no—
470C4×C73—42no—
471C4×C73—42no—
472Dic73—42no—
473Dic73—42no—
474Dic73—42no—
475Dic73—42no—
476Dic73—42no—
477Dic73—42no—
478Dic73—81no—
479Dic73—81no—
480#13990—731nomaximal, Sylow
481C2×C73—44no—
482C2×C73#229011yescharacteristic
483C2×C73C4×#12611yescharacteristic
484C2×C73#233711yescharacteristic
485C2×C73#234311yescharacteristic
486C2×C73#235311yescharacteristic
487C2×C73#235911yescharacteristic
488C2×C73#236311yescharacteristic
489C2×C73#246711yescharacteristic
490C2×C73#246811yescharacteristic
491C2×C73#247911yescharacteristic
492C2×C73#248011yescharacteristic
493C2×C73#249511yescharacteristic
494C2×C73#251511yescharacteristic
495C2×C73#257211yescharacteristic
496C2×C73#257811yescharacteristic
497C2×#388—731no—
498C2×#383—731no—
499C2×C4×C22⋊C4D7311yescharacteristic
500#1445—731no—
501#1442—731no—
502#1440—731no—
503#1439—731no—
504#1437—731no—
505#1436—731no—
506#1436—731no—
507#1434—731no—
508#1434—731no—
509C22⋊#95—731no—
510C22⋊#95—731no—
511C4×#95—731no—
512C73#1399011yescharacteristic, complemented, Sylow
513C24×C4C2×D7311yescharacteristic
514C22×C4⋊C4—731no—
515C22×C4⋊C4—731no—
516C22×C22⋊C4—731no—
517C22×C22⋊C4—731no—
518C22×C22⋊C4—731no—
519C22×C22⋊C4—731no—
520C22×C22⋊C4C2×D7311yescharacteristic
521C22×C22⋊C4C2×D7311yescharacteristic
522C22×C42—731no—
523C22×C42—731no—
524C22×C42C2×D7311yescharacteristic
525C22×C42C2×D7311yescharacteristic
526#388—738no—
527#383—1464no—
528C4×C22⋊C4—24no—
529C2×#95—731no—
530C2×#95—731no—
531C2×#95—731no—
532C2×#95—731no—
533C2×#95—731no—
534C2×#95—731no—
535C2×#95—731no—
536C2×#95—731no—
537C2×#95—731no—
538C2×#95—731no—
539C2×#95—731no—
540C2×#95—731no—
541C2×#95—731no—
542C2×#95—731no—
543C2×#95—731no—
544C2×#95—731no—
545C2×#95—731no—
546C2×#95—731no—
547C2×#95—731no—
548C2×#95—731no—
549C2×#95C2×D7311yescharacteristic
550C2×#95C2×D7311yescharacteristic
551C25C22×D7311yescharacteristic
552C23×C4—22no—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—22no—
556C23×C4—22no—
557C23×C4—41no—
558C23×C4—41no—
559C23×C4—731no—
560C23×C4—731no—
561C23×C4—731no—
562C23×C4—731no—
563C23×C4—731no—
564C23×C4—731no—
565C23×C4—731no—
566C23×C4—731no—
567C23×C4C22×D7311yescharacteristic
568C23×C4C22×D7311yescharacteristic
569C23×C4C22×D7311yescharacteristic
570C23×C4C22×D7311yescharacteristic
571C23×C4C22×D7311yescharacteristic
572C23×C4C22×D7311yescharacteristic
573C2×C4⋊C4—2921no—
574C2×C4⋊C4—2921no—
575C2×C4⋊C4—2921no—
576C2×C4⋊C4—2921no—
577C2×C4⋊C4—734no—
578C2×C4⋊C4—1462no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—2921no—
585C2×C22⋊C4—2921no—
586C2×C22⋊C4—2921no—
587C2×C22⋊C4—2921no—
588C2×C22⋊C4—734no—
589C2×C22⋊C4—734no—
590C2×C22⋊C4—1462no—
591C2×C22⋊C4—1462no—
592C2×C22⋊C4—1462no—
593C2×C22⋊C4—1462no—
594C2×C22⋊C4—1462no—
595C2×C22⋊C4—1462no—
596C2×C22⋊C4C4×D7314yes—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—41no—
602C2×C42—41no—
603C2×C42—2921no—
604C2×C42—734no—
605C2×C42—1462no—
606C2×C42—1462no—
607C2×C42—1462no—
608C2×C42—1462no—
609#95—22no—
610#95—2921no—
611#95—2921no—
612#95—2921no—
613#95—2921no—
614#95—2921no—
615#95—734no—
616#95—734no—
617#95—1462no—
618#95—1462no—
619#95—1462no—
620#95—1462no—
621#95—1462no—
622#95—1462no—
623#95—1462no—
624#95—1462no—
625#95—1462no—
626#95—1462no—
627#95—1462no—
628#95—1462no—
629#95—1462no—
630#95C22⋊D7314yes—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24C2×C4×D7312yes—
644C24#1192402812yes—
645C24#1192402812yes—
646C24C23×D7311yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—28no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—732no—
687C22×C4—732no—
688C22×C4—732no—
689C22×C4—732no—
690C22×C4—732no—
691C22×C4—732no—
692C22×C4—1461no—
693C22×C4—1461no—
694C22×C4—1461no—
695C22×C4—1461no—
696C22×C4—1461no—
697C22×C4—1461no—
698C22×C4—1461no—
699C22×C4—1461no—
700C22×C4—1461no—
701C22×C4—1461no—
702C22×C4—1461no—
703C22×C4—1461no—
704C22×C4—1461no—
705C22×C4—1461no—
706C22×C4—1461no—
707C22×C4—1461no—
708C22×C4—1461no—
709C22×C4—1461no—
710C22×C4—1461no—
711C22×C4—1461no—
712C22×C4—1461no—
713C22×C4—1461no—
714C22×C4—1461no—
715C22×C4—1461no—
716C22×C4—1461no—
717C22×C4—1461no—
718C22×C4—1461no—
719C22×C4—1461no—
720C22×C4—1461no—
721C22×C4—1461no—
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×C4C2×C4×D7312yes—
743C22×C4C2×C4×D7312yes—
744C22×C4C2×C22⋊D7312yes—
745C22×C4C2×C22⋊D7312yes—
746C22×C4C2×C22⋊D7312yes—
747C22×C4#1192402712yes—
748C22×C4#1192402712yes—
749C22×C4#1192402812yes—
750C22×C4#1192402812yes—
751C22×C4#1192402812yes—
752C4⋊C4—2924no—
753C4⋊C4—2924no—
754C22⋊C4—28no—
755C22⋊C4—28no—
756C22⋊C4—2924no—
757C22⋊C4—2924no—
758C22⋊C4—2924no—
759C22⋊C4—1468no—
760C42—44no—
761C42—44no—
762C42—2924no—
763C42—1468no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23#1455654814yes—
799C23C22×C4×D7311yescharacteristic
800C23C22×C22⋊D7311yescharacteristic
801C23#41×D7311yescharacteristic
802C23#41×D7311yescharacteristic
803C23C2×#1192402711yescharacteristic
804C23C2×#1192402711yescharacteristic
805C23C2×#1192402811yescharacteristic
806C23C2×#1192402811yescharacteristic
807C23C2×#1192402811yescharacteristic
808C23C2×#1192402811yescharacteristic
809C23C2×#1192402811yescharacteristic
810C23#1455663611yescharacteristic
811C23#1455663611yescharacteristic
812C23#1455663711yescharacteristic
813C23#1455663811yescharacteristic
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—416no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—2921no—
856C2×C4—2921no—
857C2×C4—2921no—
858C2×C4—2921no—
859C2×C4—2921no—
860C2×C4—2921no—
861C2×C4—2921no—
862C2×C4—2921no—
863C2×C4—2921no—
864C2×C4—2921no—
865C2×C4—2921no—
866C2×C4—2921no—
867C2×C4—2921no—
868C2×C4—2921no—
869C2×C4—2921no—
870C2×C4—2921no—
871C2×C4—2921no—
872C2×C4—2921no—
873C2×C4—2921no—
874C2×C4—2921no—
875C2×C4—2921no—
876C2×C4—2921no—
877C2×C4—2921no—
878C2×C4—2921no—
879C2×C4—2921no—
880C2×C4—2921no—
881C2×C4—2921no—
882C2×C4—2921no—
883C2×C4—2921no—
884C2×C4—2921no—
885C2×C4—2921no—
886C2×C4—2921no—
887C2×C4—2921no—
888C2×C4—2921no—
889C2×C4—2921no—
890C2×C4—2921no—
891C2×C4—2921no—
892C2×C4—2921no—
893C2×C4—1462no—
894C2×C4—1462no—
895C2×C4—1462no—
896C2×C4—1462no—
897C2×C4—1462no—
898C2×C4—1462no—
899C2×C4—1462no—
900C2×C4—1462no—
901C2×C4—1462no—
902C2×C4—1462no—
903C2×C4—1462no—
904C2×C4—1462no—
905C2×C4—1462no—
906C2×C4—1462no—
907C2×C4—1462no—
908C2×C4—1462no—
909C2×C4—1462no—
910C2×C4—1462no—
911C2×C4C4×C22⋊D7314yes—
912C2×C4#1455658414yes—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×#1455654811yescharacteristic
929C22C2×C4×C22⋊D7311yescharacteristic
930C22C4×#1192402711yescharacteristic
931C22C4×#1192402711yescharacteristic
932C22C4×#1192402811yescharacteristic
933C22#1798905911yescharacteristic
934C22#1798906611yescharacteristic
935C22#1798909811yescharacteristic
936C22#1798909811yescharacteristic
937C22C2×#1455658411yescharacteristic
938C22#1798911511yescharacteristic
939C22#1798911711yescharacteristic
940C22#1798911911yescharacteristic
941C22#1798912111yescharacteristic
942C22#1798912111yescharacteristic
943C22#1798917011yescharacteristic
944C22#1798917511yescharacteristic
945C22#1798920211yescharacteristic
946C22#1798920811yescharacteristic
947C22#1798923111yescharacteristic
948C22#1798923111yescharacteristic
949C22#1798923611yescharacteristic
950C22#1798925611yescharacteristic
951C22#1798926111yescharacteristic
952C22#1798926311yescharacteristic
953C22#1798926311yescharacteristic
954C22#1798926611yescharacteristic
955C22#1798926611yescharacteristic
956C22#1798927011yescharacteristic
957C22#1798927711yescharacteristic
958C22#1798927711yescharacteristic
959C22#1798928311yescharacteristic
960C22#1798928611yescharacteristic
961C22#1798928711yescharacteristic
962C22#1798930211yescharacteristic
963C4—24no—
964C4—24no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—2922no—
970C4—2922no—
971C4—2922no—
972C4—2922no—
973C4—2922no—
974C4—2922no—
975C4—5841no—
976C4—5841no—
977C2—44no—
978C2#2261237411yescharacteristic
979C2C4×#1455658411yescharacteristic
980C2#2261273911yescharacteristic
981C2#2261278511yescharacteristic
982C2#2261286511yescharacteristic
983C2#2261291711yescharacteristic
984C2#2261296511yescharacteristic
985C2#2261397611yescharacteristic
986C2#2261399111yescharacteristic
987C2#2261415611yescharacteristic
988C2#2261417111yescharacteristic
989C2#2261434211yescharacteristic
990C2#2261455011yescharacteristic
991C2#2261517511yescharacteristic
992C2#2261525911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×C4×C22⋊C4×C73C2
socle, cosocleC24×C73C24
prime radicalC25×C73C23
hypercenterC2×C4×C22⋊C4D73
hypocenterC73#13990
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#17988454C2semidirect
3. #22608197C2semidirect
4. #22608186C2semidirect
8. #22608164C2semidirect
9. #22608164C2semidirect
10. #22608158C2semidirect
11. #22608156C2semidirect
14. C4×#14556498C2semidirect
24. #17988475C4semidirect
67. C2×#11924007C2×C4semidirect
85. C2×C4×Dic73C2×C4semidirect
104. #14556498C2×C4semidirect
105. #14556498C2×C4semidirect
512. C73#13990semidirect

Maximal subgroups

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

subgroupindex
C2×#179884752
C2×#179884542
#226081972
#226081862
#226081782
#226081742
#226081682
#226081642
#226081582
#226081562
#226081542
C4×#145564982
C2×C4×C22⋊C4×C732
#1399073