Finite Group Databasebeta

← #33010147

Subgroups — #33010147

Order 18688.

1578 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988485C211yesmaximal, characteristic, complemented
2C2×#17988481C211yesmaximal, characteristic
3C2×#17988481C211yesmaximal, characteristic
4C2×#17988480C211yesmaximal, characteristic
5C2×#17988438C211yesmaximal, characteristic, complemented
6#22608192C211yesmaximal, characteristic, complemented
7#22608183C211yesmaximal, characteristic, complemented
8#22608176C211yesmaximal, characteristic
9#22608174C211yesmaximal, characteristic
10#22608168C211yesmaximal, characteristic
11#22608166C211yesmaximal, characteristic, complemented
12#22608165C211yesmaximal, characteristic, complemented
13#22608156C211yesmaximal, characteristic, complemented
14C4×#14556498C211yesmaximal, characteristic, complemented
15C73×#1437C211yesmaximal, characteristic
16C22×C4⋊Dic73C2211yescharacteristic
17C22×C4⋊Dic73C2211yescharacteristic
18C22×#11924007C2211yescharacteristic
19C22×#11924007C2211yescharacteristic
20C22×#11924007C2211yescharacteristic
21C22×C22⋊Dic73C2211yescharacteristic
22C22×C22⋊Dic73C2211yescharacteristic
23C22×C22⋊Dic73C2211yescharacteristic
24C22×C22⋊Dic73C2211yescharacteristic
25C22×C4×Dic73C2211yescharacteristic
26C22×C4×Dic73C2211yescharacteristic
27C22×C4×Dic73C2211yescharacteristic
28C22×C4×Dic73C2211yescharacteristic
29#17988485—24no—
30#17988481—24no—
31#17988481—24no—
32#17988480C418yescomplemented
33#17988438—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
49C22×C22⋊C4×C73C2211yescharacteristic
50C22×C22⋊C4×C73C2211yescharacteristic
51C22×C22⋊C4×C73C2211yescharacteristic
52C22×C42×C73C2211yescharacteristic
53C2×#95×C73C2211yescharacteristic
54C2×#95×C73C2211yescharacteristic
55C2×#95×C73C2211yescharacteristic
56C23×Dic73C2311yescharacteristic
57C23×Dic73C2311yescharacteristic
58C23×Dic73C2311yescharacteristic
59C23×Dic73C2311yescharacteristic
60C23×Dic73C2311yescharacteristic
61C23×Dic73C2311yescharacteristic
62C23×Dic73C2311yescharacteristic
63C23×Dic73C2311yescharacteristic
64C2×C4⋊Dic73—22no—
65C2×C4⋊Dic73—22no—
66C2×C4⋊Dic73—22no—
67C2×C4⋊Dic73—22no—
68C2×C4⋊Dic73—41no—
69C2×C4⋊Dic73C2×C414yes—
70C2×#11924007—22no—
71C2×#11924007—22no—
72C2×#11924007—22no—
73C2×#11924007—22no—
74C2×#11924007—22no—
75C2×#11924007—22no—
76C2×#11924007—22no—
77C2×#11924007—22no—
78C2×#11924007D414yes—
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—41no—
87C2×C22⋊Dic73—41no—
88C2×C22⋊Dic73—41no—
89C2×C22⋊Dic73C2×C414yes—
90C2×C22⋊Dic73C2×C414yes—
91C2×C4×Dic73—22no—
92C2×C4×Dic73—22no—
93C2×C4×Dic73—22no—
94C2×C4×Dic73—22no—
95C2×C4×Dic73—22no—
96C2×C4×Dic73—41no—
97C2×C4×Dic73—41no—
98C2×C4×Dic73—41no—
99C2×C4×Dic73—41no—
100C2×C4×Dic73—41no—
101C2×C4×Dic73C2×C414yes—
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—41no—
116#14556498C2×C414yes—
117#14556498C2×C414yes—
118C25×C73C2311yescharacteristic
119C23×C4×C73C2311yescharacteristic
120C23×C4×C73C2311yescharacteristic
121C23×C4×C73C2311yescharacteristic
122C23×C4×C73C2311yescharacteristic
123C23×C4×C73C2311yescharacteristic
124C23×C4×C73C2311yescharacteristic
125C2×C22⋊C4×C73—22no—
126C2×C22⋊C4×C73—22no—
127C2×C22⋊C4×C73—22no—
128C2×C22⋊C4×C73—22no—
129C2×C22⋊C4×C73—22no—
130C2×C22⋊C4×C73—22no—
131C2×C22⋊C4×C73—22no—
132C2×C22⋊C4×C73—41no—
133C2×C22⋊C4×C73C2×C414yes—
134C2×C42×C73—22no—
135C2×C42×C73—22no—
136C2×C42×C73—41no—
137#95×C73—22no—
138#95×C73—22no—
139#95×C73—22no—
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×Dic73—21no—
185C22×Dic73C22×C412yes—
186C22×Dic73C22×C412yes—
187C22×Dic73C22×C412yes—
188C22×Dic73C22×C412yes—
189C22×Dic73C2×D412yes—
190C22×Dic73C2×D412yes—
191C22×Dic73C2×D412yes—
192C22×Dic73C2×D412yes—
193C22×Dic73#4112yes—
194C22×Dic73#4112yes—
195C22×Dic73#4112yes—
196C4⋊Dic73—28no—
197C4⋊Dic73—44no—
198#11924007—28no—
199#11924007—28no—
200#11924007—44no—
201C22⋊Dic73—28no—
202C22⋊Dic73—28no—
203C22⋊Dic73—44no—
204C22⋊Dic73—44no—
205C4×Dic73—28no—
206C4×Dic73—44no—
207C4×Dic73—44no—
208C4×Dic73—44no—
209C24×C73—21no—
210C24×C73—21no—
211C24×C73—21no—
212C24×C73—21no—
213C24×C73—21no—
214C24×C73—21no—
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×C73C22×C412yes—
224C24×C73C2411yescharacteristic
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—21no—
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×C73C22×C412yes—
259C22×C4×C73C22×C412yes—
260C22×C4×C73C2×D412yes—
261C22×C4×C73C2×D412yes—
262C22×C4×C73#4112yes—
263C22×C4×C73#4112yes—
264C22×C4×C73#4112yes—
265C22×C4×C73#4112yes—
266C22×C4×C73#4112yes—
267C22⋊C4×C73—28no—
268C22⋊C4×C73—44no—
269C22⋊C4×C73—44no—
270C42×C73—44no—
271C23×C73—22no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73—22no—
277C23×C73—22no—
278C23×C73—41no—
279C23×C73—41no—
280C23×C73—41no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—41no—
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—41no—
302C23×C73—41no—
303C23×C73—41no—
304C23×C73—41no—
305C23×C73—41no—
306C23×C73C23×C411yescharacteristic
307C23×C73C22×D411yescharacteristic
308C23×C73C22×D411yescharacteristic
309C23×C73C2×#4111yescharacteristic
310C23×C73C2×#4111yescharacteristic
311C23×C73C2×#4111yescharacteristic
312C23×C73C2×#4111yescharacteristic
313C23×C73C2×#4111yescharacteristic
314C23×C73C2×#4111yescharacteristic
315C23×C73C2×#4111yescharacteristic
316C23×C73C2×#4111yescharacteristic
317C23×C73H(5,𝔽2)11yescharacteristic
318C23×C73H(5,𝔽2)11yescharacteristic
319C23×C732−1+411yescharacteristic
320C23×C732−1+411yescharacteristic
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—22no—
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×C73—41no—
359C2×C4×C73—41no—
360C2×C4×C73—41no—
361C2×C4×C73#11714yes—
362C2×C4×C73#12114yes—
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—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—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—
416C2×Dic73—41no—
417C2×Dic73C4×D414yes—
418C2×Dic73C4×D414yes—
419C22×C73—42no—
420C22×C73—42no—
421C22×C73—42no—
422C22×C73—42no—
423C22×C73—42no—
424C22×C73—42no—
425C22×C73—42no—
426C22×C73—81no—
427C22×C73—81no—
428C22×C73—81no—
429C22×C73—81no—
430C22×C73—81no—
431C22×C73—81no—
432C22×C73—81no—
433C22×C73—81no—
434C22×C73C2×#11711yescharacteristic
435C22×C73C2×C4×D411yescharacteristic
436C22×C73C2×C4×D411yescharacteristic
437C22×C73C4×#4111yescharacteristic
438C22×C73C4×#4111yescharacteristic
439C22×C73#52011yescharacteristic
440C22×C73#52011yescharacteristic
441C22×C73C2×#12111yescharacteristic
442C22×C73#52511yescharacteristic
443C22×C73#52911yescharacteristic
444C22×C73#52911yescharacteristic
445C22×C73#52911yescharacteristic
446C22×C73#53211yescharacteristic
447C22×C73#53211yescharacteristic
448C22×C73#53211yescharacteristic
449C22×C73#53411yescharacteristic
450C22×C73#53611yescharacteristic
451C22×C73#53911yescharacteristic
452C22×C73#53911yescharacteristic
453C22×C73#54611yescharacteristic
454C22×C73#54611yescharacteristic
455C22×C73#54811yescharacteristic
456C22×C73#54811yescharacteristic
457C22×C73#55111yescharacteristic
458C22×C73#55211yescharacteristic
459C22×C73#55211yescharacteristic
460C22×C73#55311yescharacteristic
461C22×C73#55311yescharacteristic
462C22×C73#55311yescharacteristic
463C22×C73#55311yescharacteristic
464C22×C73#55611yescharacteristic
465C22×C73#55611yescharacteristic
466C22×C73#55611yescharacteristic
467C22×C73#55611yescharacteristic
468C22×C73#55911yescharacteristic
469C4×C73—24no—
470C4×C73—24no—
471C4×C73—42no—
472C4×C73—42no—
473C4×C73—42no—
474C4×C73—81no—
475Dic73—24no—
476Dic73—24no—
477Dic73—42no—
478Dic73—42no—
479Dic73—42no—
480Dic73—42no—
481Dic73—42no—
482Dic73—81no—
483#14077—731nomaximal, Sylow
484C2×C73—82no—
485C2×C73#229311yescharacteristic
486C2×C73C4×#12111yescharacteristic
487C2×C73#232211yescharacteristic
488C2×C73#234711yescharacteristic
489C2×C73#235211yescharacteristic
490C2×C73#236711yescharacteristic
491C2×C73#237311yescharacteristic
492C2×C73#254311yescharacteristic
493C2×C73#254511yescharacteristic
494C2×C73#255811yescharacteristic
495C2×C73#256011yescharacteristic
496C2×C73#259411yescharacteristic
497C2×C73#259611yescharacteristic
498C2×C73#260211yescharacteristic
499C2×C73#260411yescharacteristic
500C2×#389—731no—
501C2×#388—731no—
502C2×#388—731no—
503C2×#388—731no—
504C2×C4×C4⋊C4—731no—
505#1443—731no—
506#1441—731no—
507#1439—731no—
508#1439—731no—
509#1437—731no—
510#1437D7311yescharacteristic
511#1436—731no—
512#1436—731no—
513#1434—731no—
514C4×#95—731no—
515C73#1407711yescharacteristic, complemented, Sylow
516C22×C4⋊C4—731no—
517C22×C4⋊C4—731no—
518C22×C4⋊C4—731no—
519C22×C4⋊C4—731no—
520C22×C4⋊C4—731no—
521C22×C22⋊C4—731no—
522C22×C22⋊C4—731no—
523C22×C22⋊C4—731no—
524C22×C22⋊C4—731no—
525C22×C22⋊C4C2×D7311yescharacteristic
526C22×C22⋊C4C2×D7311yescharacteristic
527C22×C22⋊C4C2×D7311yescharacteristic
528C22×C42—731no—
529C22×C42—731no—
530C22×C42—731no—
531C22×C42—731no—
532C22×C42C2×D7311yescharacteristic
533#389—1464no—
534#388—738no—
535#388—1464no—
536#388—1464no—
537C4×C4⋊C4—1464no—
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×#95—731no—
550C2×#95—731no—
551C2×#95—731no—
552C2×#95—731no—
553C2×#95C2×D7311yescharacteristic
554C2×#95C2×D7311yescharacteristic
555C2×#95C2×D7311yescharacteristic
556C25C22×D7311yescharacteristic
557C23×C4—731no—
558C23×C4—731no—
559C23×C4—731no—
560C23×C4—731no—
561C23×C4—731no—
562C23×C4—731no—
563C23×C4—731no—
564C23×C4—731no—
565C23×C4C22×D7311yescharacteristic
566C23×C4C22×D7311yescharacteristic
567C23×C4C22×D7311yescharacteristic
568C23×C4C22×D7311yescharacteristic
569C23×C4C22×D7311yescharacteristic
570C23×C4C22×D7311yescharacteristic
571C2×C4⋊C4—2921no—
572C2×C4⋊C4—734no—
573C2×C4⋊C4—734no—
574C2×C4⋊C4—1462no—
575C2×C4⋊C4—1462no—
576C2×C4⋊C4—1462no—
577C2×C4⋊C4—1462no—
578C2×C4⋊C4—1462no—
579C2×C4⋊C4—1462no—
580C2×C4⋊C4—1462no—
581C2×C4⋊C4—1462no—
582C2×C4⋊C4—1462no—
583C2×C4⋊C4—1462no—
584C2×C4⋊C4—1462no—
585C2×C4⋊C4—1462no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—41no—
594C2×C22⋊C4—2921no—
595C2×C22⋊C4—2921no—
596C2×C22⋊C4—2921no—
597C2×C22⋊C4—734no—
598C2×C22⋊C4—734no—
599C2×C22⋊C4—1462no—
600C2×C22⋊C4—1462no—
601C2×C22⋊C4—1462no—
602C2×C22⋊C4—1462no—
603C2×C22⋊C4—1462no—
604C2×C22⋊C4—1462no—
605C2×C22⋊C4—1462no—
606C2×C22⋊C4C4×D7314yes—
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—41no—
610C2×C42—2921no—
611C2×C42—2921no—
612C2×C42—2921no—
613C2×C42—2921no—
614C2×C42—2921no—
615C2×C42—734no—
616C2×C42—734no—
617C2×C42—1462no—
618C2×C42—1462no—
619C2×C42—1462no—
620C2×C42—1462no—
621C2×C42—1462no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—2921no—
626#95—734no—
627#95—734no—
628#95—1462no—
629#95—1462no—
630#95—1462no—
631#95—1462no—
632#95—1462no—
633#95—1462no—
634#95—1462no—
635#95—1462no—
636#95—1462no—
637#95—1462no—
638#95—1462no—
639#95—1462no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24C2×C4×D7312yes—
655C24C23×D7311yescharacteristic
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—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—732no—
690C22×C4—732no—
691C22×C4—732no—
692C22×C4—732no—
693C22×C4—732no—
694C22×C4—732no—
695C22×C4—732no—
696C22×C4—732no—
697C22×C4—732no—
698C22×C4—732no—
699C22×C4—732no—
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×C4—1461no—
743C22×C4—1461no—
744C22×C4—1461no—
745C22×C4C2×C4×D7312yes—
746C22×C4C2×C4×D7312yes—
747C22×C4D4×D7312yes—
748C22×C4D4×D7312yes—
749C22×C4#1192402712yes—
750C22×C4#1192402712yes—
751C22×C4#1192402712yes—
752C22×C4#1192402812yes—
753C22×C4#1192402812yes—
754C4⋊C4—2924no—
755C4⋊C4—2924no—
756C4⋊C4—1468no—
757C4⋊C4—1468no—
758C4⋊C4—1468no—
759C22⋊C4—28no—
760C22⋊C4—44no—
761C22⋊C4—44no—
762C22⋊C4—2924no—
763C22⋊C4—2924no—
764C22⋊C4—1468no—
765C22⋊C4—1468no—
766C42—44no—
767C42—2924no—
768C42—2924no—
769C42—2924no—
770C42—1468no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
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—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23C22×C4×D7311yescharacteristic
807C23C2×D4×D7311yescharacteristic
808C23C2×D4×D7311yescharacteristic
809C23#41×D7311yescharacteristic
810C23#41×D7311yescharacteristic
811C23#41×D7311yescharacteristic
812C23C2×#1192402711yescharacteristic
813C23C2×#1192402711yescharacteristic
814C23C2×#1192402711yescharacteristic
815C23C2×#1192402811yescharacteristic
816C23C2×#1192402811yescharacteristic
817C23#1455663611yescharacteristic
818C23#1455663711yescharacteristic
819C23#1455663811yescharacteristic
820C23#1455663811yescharacteristic
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—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
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—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
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—734no—
889C2×C4—734no—
890C2×C4—1462no—
891C2×C4—1462no—
892C2×C4—1462no—
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×C4—1462no—
912C2×C4—1462no—
913C2×C4—1462no—
914C2×C4—1462no—
915C2×C4—1462no—
916C2×C4—1462no—
917C2×C4#1455654714yes—
918C2×C4#1455656414yes—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22C2×#1455654711yescharacteristic
935C22C4×D4×D7311yescharacteristic
936C22C4×D4×D7311yescharacteristic
937C22C4×#1192402711yescharacteristic
938C22C4×#1192402811yescharacteristic
939C22#1798906611yescharacteristic
940C22#1798906711yescharacteristic
941C22C2×#1455656411yescharacteristic
942C22#1798909611yescharacteristic
943C22#1798911511yescharacteristic
944C22#1798911611yescharacteristic
945C22#1798911811yescharacteristic
946C22#1798913211yescharacteristic
947C22#1798913411yescharacteristic
948C22#1798913511yescharacteristic
949C22#1798914511yescharacteristic
950C22#1798915711yescharacteristic
951C22#1798917811yescharacteristic
952C22#1798918011yescharacteristic
953C22#1798922411yescharacteristic
954C22#1798922911yescharacteristic
955C22#1798924311yescharacteristic
956C22#1798924311yescharacteristic
957C22#1798926311yescharacteristic
958C22#1798927411yescharacteristic
959C22#1798927611yescharacteristic
960C22#1798928011yescharacteristic
961C22#1798928311yescharacteristic
962C22#1798928311yescharacteristic
963C22#1798928611yescharacteristic
964C22#1798930411yescharacteristic
965C22#1798930711yescharacteristic
966C22#1798930711yescharacteristic
967C22#1798930711yescharacteristic
968C22#1798931911yescharacteristic
969C4—24no—
970C4—24no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—81no—
975C4—2922no—
976C4—2922no—
977C4—2922no—
978C4—2922no—
979C4—2922no—
980C4—5841no—
981C4—1464no—
982C4—1464no—
983C2—82no—
984C2#2261239311yescharacteristic
985C2C4×#1455656411yescharacteristic
986C2#2261260111yescharacteristic
987C2#2261282211yescharacteristic
988C2#2261285811yescharacteristic
989C2#2261300511yescharacteristic
990C2#2261305211yescharacteristic
991C2#2261489511yescharacteristic
992C2#2261491311yescharacteristic
993C2#2261505111yescharacteristic
994C2#2261507911yescharacteristic
995C2#2261543511yescharacteristic
996C2#2261546311yescharacteristic
997C2#2261554011yescharacteristic
998C2#2261556711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×#1437C2
socle, cosocleC24×C73C24
prime radicalC25×C73C23
hypercenter#1437D73
hypocenterC73#14077
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
1. C2×#17988485C2semidirect
5. C2×#17988438C2semidirect
6. #22608192C2semidirect
7. #22608183C2semidirect
11. #22608166C2semidirect
12. #22608165C2semidirect
13. #22608156C2semidirect
14. C4×#14556498C2semidirect
32. #17988480C4semidirect
515. C73#14077semidirect

Maximal subgroups

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

subgroupindex
C2×#179884852
C2×#179884812
C2×#179884802
C2×#179884382
#226081922
#226081832
#226081762
#226081742
#226081682
#226081662
#226081652
#226081562
C4×#145564982
C73×#14372
#1407773