Finite Group Databasebeta

← #33096268

Subgroups — #33096268

Order 18688.

1090 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988549C211yesmaximal, characteristic
2#22612313C211yesmaximal, characteristic
3#22612310C211yesmaximal, characteristic
4#22610133C211yesmaximal, characteristic, complemented
5#22610132C211yesmaximal, characteristic, complemented
6#22610131C211yesmaximal, characteristic, complemented
7#22610130C211yesmaximal, characteristic, complemented
8#22610129C211yesmaximal, characteristic, complemented
9#22610128C211yesmaximal, characteristic, complemented
10#22610127C211yesmaximal, characteristic, complemented
11#22609965C211yesmaximal, characteristic, complemented
12#22609963C211yesmaximal, characteristic, complemented
13#22609963C211yesmaximal, characteristic, complemented
14#22609961C211yesmaximal, characteristic, complemented
15C73×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D73C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19C2×#14556550C2211yescharacteristic
20C2×#14556549C2211yescharacteristic
21C2×#14556549C2211yescharacteristic
22C2×#14556525C2211yescharacteristic, complemented
23C2×#14556524C2211yescharacteristic, complemented
24C2×#14556524C2211yescharacteristic, complemented
25C2×#14556523C2211yescharacteristic, complemented
26C2×#14556522C2211yescharacteristic, complemented
27C2×#14556522C2211yescharacteristic, complemented
28#17988549C418yescomplemented
29C2×C22⋊#10596831C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32#17988449—21no—
33#17988448—21no—
34#17988447C2211yescharacteristic
35#17988444C2211yescharacteristic
36#17988444C2211yescharacteristic
37#17988444C2211yescharacteristic
38#17988444C2211yescharacteristic
39#17988444C2211yescharacteristic
40#17988444C2211yescharacteristic
41#17988442—21no—
42#17988442—21no—
43C22⋊C4×Dic73—21no—
44C4×#11924005—21no—
45C4×#11924005—21no—
46#17988434—21no—
47#17988350C2211yescharacteristic, complemented
48#17988350C2211yescharacteristic, complemented
49#17988349C2211yescharacteristic, complemented
50#17988349C2211yescharacteristic, complemented
51#17988349C2211yescharacteristic, complemented
52#17988349C2211yescharacteristic, complemented
53C2×#117×C73C2211yescharacteristic
54C2×#107×C73C2211yescharacteristic, complemented
55C2×#106×C73C2211yescharacteristic, complemented
56C2×C22⋊C8×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic, complemented
59#340×C73C2211yescharacteristic, complemented
60C24×D73D411yescharacteristic
61C23×Dic73D411yescharacteristic
62C22×C4×D73—41no—
63C22×C4×D73—41no—
64C22×C4×D73—41no—
65C22×C4×D73—41no—
66C22×C4×D73C2×C414yes—
67C22×C4×D73D411yescharacteristic
68C22×C4×D73D411yescharacteristic
69C22×C4×D73Q814yes—
70C22×C4×D73C2311yescharacteristic
71C22×C4×D73C2311yescharacteristic
72C2×#11924011—41no—
73C2×#11924011—41no—
74C2×#11924011—41no—
75C2×#11924011—41no—
76C2×#11924011C2×C414yes—
77C2×#11924011C2×C414yes—
78C22×#10596831C2311yescharacteristic
79C22×#10596831C2311yescharacteristic
80#14556550—41no—
81#14556550—41no—
82#14556549—41no—
83#14556549—41no—
84#14556549—41no—
85#14556549—41no—
86C2×C4⋊Dic73C2311yescharacteristic
87C2×C4⋊Dic73C2311yescharacteristic
88C2×C4⋊Dic73C2311yescharacteristic
89C2×C4⋊Dic73C2311yescharacteristic
90C2×C22⋊Dic73—21no—
91C2×C22⋊Dic73—21no—
92C2×#11924005—21no—
93C2×#11924005—21no—
94C2×#11924005—21no—
95C2×#11924005—21no—
96C2×#11924005—21no—
97C2×#11924005—21no—
98C2×#11924005—21no—
99C2×#11924005—21no—
100C2×C4×Dic73—21no—
101C2×C4×Dic73—21no—
102C2×C4×Dic73—21no—
103#14556525—41no—
104#14556524—41no—
105#14556524—41no—
106#14556523—41no—
107#14556522—41no—
108#14556522—41no—
109C22⋊#10596831C2×C414yes—
110#14556503C2×C414yes—
111#14556503C2×C414yes—
112#14556498—21no—
113#14556498—21no—
114#14556498—21no—
115#14556498—21no—
116#14556498—21no—
117#14556498—21no—
118#14556498—21no—
119C23×C4×C73C2311yescharacteristic
120C22×C8×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122#117×C73—41no—
123#117×C73—41no—
124C2×C4⋊C4×C73C2311yescharacteristic
125C2×C4⋊C4×C73C2311yescharacteristic
126C2×C4⋊C4×C73C2311yescharacteristic
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C42×C73—21no—
131#107×C73—41no—
132#106×C73—41no—
133C22⋊C8×C73C2×C414yes—
134#95×C73—21no—
135C23×D73—41no—
136C23×D73—41no—
137C23×D73—41no—
138C23×D73—41no—
139C23×D73—41no—
140C23×D73—41no—
141C23×D73C4⋊C414yes—
142C23×D73C2×D411yescharacteristic
143C23×D73C2×D411yescharacteristic
144C22×Dic73—21no—
145C22×Dic73—21no—
146C22×Dic73—21no—
147C22×Dic73—21no—
148C22×Dic73—41no—
149C22×Dic73—41no—
150C22×Dic73C4⋊C414yes—
151C22×Dic73C2×D411yescharacteristic
152C22×Dic73C2×D411yescharacteristic
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—21no—
161C2×C4×D73—44no—
162C2×C4×D73—44no—
163C2×C4×D73—44no—
164C2×C4×D73—44no—
165C2×C4×D73—41no—
166C2×C4×D73—41no—
167C2×C4×D73—41no—
168C2×C4×D73—41no—
169C2×C4×D73C4⋊C414yes—
170C2×C4×D73C4⋊C414yes—
171C2×C4×D73C22×C412yes—
172C2×C4×D73C22×C412yes—
173C2×C4×D73C2×Q812yes—
174C2×C4×D73C2×Q812yes—
175#11924011—44no—
176#11924011—44no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—21no—
180C2×#10596831—21no—
181C2×#10596831C22×C412yes—
182C2×#10596831C22×C412yes—
183C4⋊Dic73—21no—
184C4⋊Dic73—21no—
185C4⋊Dic73—21no—
186C4⋊Dic73—21no—
187C4⋊Dic73—21no—
188C4⋊Dic73—21no—
189C4⋊Dic73—21no—
190C4⋊Dic73—21no—
191C22⋊Dic73—42no—
192C22⋊Dic73—42no—
193#11924005—42no—
194#11924005—42no—
195#11924005—42no—
196#11924005—42no—
197#11924005—42no—
198#11924005—42no—
199#11924005—42no—
200#11924005—42no—
201C4×Dic73—42no—
202C4×Dic73—42no—
203C4×Dic73—42no—
204C24×C73C2×D411yescharacteristic
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73C22×C412yes—
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×Q812yes—
216C22×C4×C73C2411yescharacteristic
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73C22×C412yes—
222C2×C8×C73C22×C412yes—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73—21no—
227C4⋊C4×C73—21no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C22⋊C4×C73—42no—
232C22⋊C4×C73—42no—
233C42×C73—42no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73C2×C4⋊C412yes—
241C23×C73C22×D411yescharacteristic
242C22×D73—21no—
243C22×D73—21no—
244C22×D73—21no—
245C22×D73—21no—
246C22×D73—21no—
247C22×D73—21no—
248C22×D73—21no—
249C22×D73—21no—
250C22×D73—21no—
251C22×D73—21no—
252C22×D73—21no—
253C22×D73—21no—
254C22×D73—44no—
255C22×D73—44no—
256C22×D73—44no—
257C22×D73—44no—
258C22×D73—44no—
259C22×D73—44no—
260C22×D73—44no—
261C22×D73C2×C4⋊C412yes—
262C22×D73C2×C4⋊C412yes—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73C2×C4⋊C412yes—
282C2×C4×C73C23×C411yescharacteristic
283C2×C4×C73C22×Q811yescharacteristic
284C2×C4×C73H(5,𝔽2)11yescharacteristic
285C2×C4×C73H(5,𝔽2)11yescharacteristic
286C2×C4×C73H(5,𝔽2)11yescharacteristic
287C2×C4×C73H(5,𝔽2)11yescharacteristic
288C2×Dic73—21no—
289C2×Dic73—21no—
290C2×Dic73—21no—
291C2×Dic73—21no—
292C2×Dic73—44no—
293C2×Dic73—41no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297C2×Dic73—41no—
298C2×Dic73—41no—
299C2×Dic73—41no—
300C2×Dic73—41no—
301C2×Dic73—41no—
302C2×Dic73—41no—
303C2×Dic73—41no—
304C2×Dic73—41no—
305C2×Dic73C2×C4⋊C412yes—
306C2×Dic73C2×C4⋊C412yes—
307C4×D73—22no—
308C4×D73—22no—
309C4×D73—22no—
310C4×D73—22no—
311C4×D73—22no—
312C4×D73—22no—
313C4×D73—22no—
314C4×D73—22no—
315C4×D73—44no—
316C4×D73—44no—
317C8×C73—22no—
318C8×C73—22no—
319#10596831—22no—
320#10596831—22no—
321C22×C73—22no—
322C22×C73—22no—
323C22×C73—22no—
324C22×C73—41no—
325C22×C73—41no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73C22×C4⋊C411yescharacteristic
329C22×C73#53411yescharacteristic
330C22×C73#53411yescharacteristic
331C22×C73#57511yescharacteristic
332C22×C73#57511yescharacteristic
333C22×C73#57511yescharacteristic
334C22×C73#57511yescharacteristic
335C2×D73—22no—
336C2×D73—22no—
337C2×D73—22no—
338C2×D73—22no—
339C2×D73—22no—
340C2×D73—22no—
341C2×D73—416no—
342C2×D73—41no—
343C2×D73—41no—
344C2×D73—41no—
345C2×D73—41no—
346C2×D73—41no—
347C2×D73—41no—
348C2×D73—41no—
349C2×D73—41no—
350C4×C73—22no—
351C4×C73—81no—
352C4×C73—81no—
353C4×C73—81no—
354C4×C73—81no—
355C4×C73#51811yescharacteristic
356C4×C73#51811yescharacteristic
357C4×C73#54311yescharacteristic
358C4×C73#54311yescharacteristic
359Dic73—22no—
360Dic73—22no—
361Dic73—81no—
362Dic73—81no—
363Dic73—81no—
364Dic73—81no—
365#21943—731nomaximal, Sylow
366C2×C73—42no—
367C2×C73#231511yescharacteristic
368C2×C73#291111yescharacteristic
369C2×C73#291111yescharacteristic
370C2×C73#319711yescharacteristic
371C2×C73#319711yescharacteristic
372C2×C73#319711yescharacteristic
373C2×C73#319711yescharacteristic
374D73—42no—
375D73—42no—
376C2×#407—731no—
377#2280—731no—
378#2280—731no—
379#1854—731no—
380#1854—731no—
381#1854—731no—
382#1854—731no—
383#1854—731no—
384#1854—731no—
385#1854—731no—
386#1854D7311yescharacteristic, complemented
387#1809—731no—
388#1809—731no—
389#1809—731no—
390#1809—731no—
391C73#2194311yescharacteristic, complemented, Sylow
392C24×C4—731no—
393C22×M16—731no—
394C22×M16—731no—
395C2×#117—731no—
396C2×#117—731no—
397C2×#117—731no—
398C2×#117C2×D7311yescharacteristic
399C2×#107—731no—
400C2×#107—731no—
401C2×#107—731no—
402C2×#107C2×D7311yescharacteristic, complemented
403C2×#106—731no—
404C2×#106—731no—
405C2×#106—731no—
406C2×#106C2×D7311yescharacteristic, complemented
407#407—738no—
408C2×C22⋊C8—731no—
409C2×C22⋊C8—731no—
410C2×C22⋊C8—731no—
411C2×C22⋊C8C2×D7311yescharacteristic
412#381—1461no—
413#381—1461no—
414#380—731no—
415#380—731no—
416#380—731no—
417#380—731no—
418#380—731no—
419#380—731no—
420#380—731no—
421#380C2×D7311yescharacteristic
422#379—1461no—
423#379—1461no—
424C4×C22⋊C4—1461no—
425C4×C22⋊C4—1461no—
426C4×C22⋊C4—1461no—
427C4×C22⋊C4—1461no—
428#340—731no—
429#340—731no—
430#340—731no—
431#340—731no—
432#340—731no—
433#340—731no—
434#340C2×D7311yescharacteristic, complemented
435#340C2×D7311yescharacteristic, complemented
436C25—731no—
437C23×C4—2921no—
438C23×C4—2921no—
439C23×C4—2921no—
440C23×C4—2921no—
441C23×C4—731no—
442C23×C4—734no—
443C23×C4—731no—
444C23×C4—731no—
445C23×C4—734no—
446C23×C4—731no—
447C23×C4—731no—
448C23×C4C22×D7311yescharacteristic
449C2×M16—2921no—
450C2×M16—2921no—
451C2×M16—2921no—
452C2×M16—2921no—
453C2×M16—734no—
454C2×M16—734no—
455C22×C8—731no—
456C22×C8—731no—
457C22×C8C22×D7311yescharacteristic
458C22×C8C22×D7311yescharacteristic
459#117—41no—
460#117—41no—
461#117—2921no—
462#117—2921no—
463#117—2921no—
464#117—2921no—
465#117—2921no—
466#117—2921no—
467C2×C4⋊C4—731no—
468C2×C4⋊C4—731no—
469C2×C4⋊C4—731no—
470C2×C4⋊C4—731no—
471C2×C4⋊C4C22×D7311yescharacteristic
472C2×C4⋊C4C22×D7311yescharacteristic
473C2×C4⋊C4C22×D7311yescharacteristic
474C2×C4⋊C4C22×D7311yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—1461no—
478C2×C22⋊C4—1461no—
479C2×C22⋊C4—1461no—
480C2×C22⋊C4—1461no—
481C2×C22⋊C4—1461no—
482C2×C22⋊C4—1461no—
483C2×C22⋊C4—1461no—
484C2×C22⋊C4—1461no—
485C2×C22⋊C4—1461no—
486C2×C22⋊C4—1461no—
487C2×C42—21no—
488C2×C42—1461no—
489C2×C42—1461no—
490C2×C42—1461no—
491#107—41no—
492#107—2921no—
493#107—2921no—
494#107—2921no—
495#106—41no—
496#106—2921no—
497#106—2921no—
498#106—2921no—
499C22⋊C8—734no—
500C22⋊C8—734no—
501C22⋊C8—734no—
502C22⋊C8C4×D7314yes—
503#95—21no—
504#95—1461no—
505#95—1461no—
506#95—1461no—
507#95—1461no—
508#95—1461no—
509#95—1461no—
510#95—1461no—
511C24—2921no—
512C24—2921no—
513C24—2921no—
514C24—2921no—
515C24—2921no—
516C24—2921no—
517C24—734no—
518C24—731no—
519C24—731no—
520C24D4×D7311yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—2921no—
530C22×C4—2921no—
531C22×C4—2921no—
532C22×C4—2921no—
533C22×C4—2924no—
534C22×C4—2924no—
535C22×C4—2924no—
536C22×C4—2924no—
537C22×C4—2921no—
538C22×C4—2921no—
539C22×C4—734no—
540C22×C4—734no—
541C22×C4—734no—
542C22×C4—731no—
543C22×C4—731no—
544C22×C4—732no—
545C22×C4—732no—
546C22×C4—732no—
547C22×C4—732no—
548C22×C4—1461no—
549C22×C4—1461no—
550C22×C4—1461no—
551C22×C4—1461no—
552C22×C4—1461no—
553C22×C4—1461no—
554C22×C4—1461no—
555C22×C4—1461no—
556C22×C4—1461no—
557C22×C4—1461no—
558C22×C4—1461no—
559C22×C4—1461no—
560C22×C4C2×C4×D7312yes—
561C22×C4D4×D7311yescharacteristic
562C22×C4Q8×D7312yes—
563C22×C4C23×D7311yescharacteristic
564M16—2924no—
565M16—2924no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—732no—
571C2×C8—732no—
572C2×C8—1461no—
573C2×C8—1461no—
574C2×C8—1461no—
575C2×C8—1461no—
576C2×C8C2×C4×D7312yes—
577C2×C8C2×C4×D7312yes—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—1461no—
587C4⋊C4—1461no—
588C4⋊C4—1461no—
589C4⋊C4—1461no—
590C4⋊C4—1461no—
591C4⋊C4—1461no—
592C4⋊C4—1461no—
593C4⋊C4—1461no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—2922no—
597C22⋊C4—2922no—
598C22⋊C4—2922no—
599C22⋊C4—2922no—
600C22⋊C4—2922no—
601C22⋊C4—2922no—
602C22⋊C4—2922no—
603C22⋊C4—2922no—
604C22⋊C4—2922no—
605C22⋊C4—2922no—
606C42—42no—
607C42—2922no—
608C42—2922no—
609C42—2922no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—2924no—
617C23—2924no—
618C23—2924no—
619C23—2924no—
620C23—2924no—
621C23—2924no—
622C23—2924no—
623C23—732no—
624C23—732no—
625C23—1461no—
626C23—1461no—
627C23—1461no—
628C23—1461no—
629C23—1461no—
630C23—1461no—
631C23—1461no—
632C23—1461no—
633C23—1461no—
634C23—1461no—
635C23—1461no—
636C23—1461no—
637C23C4⋊C4×D7312yes—
638C23C2×D4×D7311yescharacteristic
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—2924no—
658C2×C4—2924no—
659C2×C4—2921no—
660C2×C4—2921no—
661C2×C4—2921no—
662C2×C4—2921no—
663C2×C4—2921no—
664C2×C4—2921no—
665C2×C4—2921no—
666C2×C4—2921no—
667C2×C4—2921no—
668C2×C4—2921no—
669C2×C4—2921no—
670C2×C4—2921no—
671C2×C4—2924no—
672C2×C4—732no—
673C2×C4—732no—
674C2×C4—1461no—
675C2×C4—1461no—
676C2×C4—1461no—
677C2×C4—1461no—
678C2×C4—1462no—
679C2×C4—1462no—
680C2×C4—1462no—
681C2×C4—1462no—
682C2×C4—1462no—
683C2×C4—1462no—
684C2×C4—1462no—
685C2×C4—1462no—
686C2×C4C4⋊C4×D7312yes—
687C2×C4C22×C4×D7311yescharacteristic
688C2×C4C2×Q8×D7311yescharacteristic
689C2×C4#1455663611yescharacteristic
690C2×C4#1455663611yescharacteristic
691C2×C4#1455663711yescharacteristic
692C2×C4#1455663711yescharacteristic
693C8—22no—
694C8—22no—
695C8—1462no—
696C8—1462no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—29216no—
705C22—2921no—
706C22—2921no—
707C22—2921no—
708C22—2921no—
709C22—2921no—
710C22—2921no—
711C22—2921no—
712C22—2921no—
713C22—1462no—
714C22—1462no—
715C22—1462no—
716C22—1462no—
717C22—1462no—
718C22—1462no—
719C22C2×C4⋊C4×D7311yescharacteristic
720C22#1798914711yescharacteristic
721C22#1798914811yescharacteristic
722C22#1798938311yescharacteristic
723C22#1798938411yescharacteristic
724C22#1798938411yescharacteristic
725C22#1798938611yescharacteristic
726C4—22no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4—5841no—
732C4—5841no—
733C4—5841no—
734C4—5841no—
735C4—1462no—
736C4—1462no—
737C4#1798905911yescharacteristic
738C4#1798905911yescharacteristic
739C4#1798921211yescharacteristic
740C4#1798921211yescharacteristic
741C2—42no—
742C2—2922no—
743C2—2922no—
744C2#2261254211yescharacteristic
745C2#2261851811yescharacteristic
746C2#2261851911yescharacteristic
747C2#2262077011yescharacteristic
748C2#2262077111yescharacteristic
749C2#2262077211yescharacteristic
750C2#2262077511yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1854C2
socleC23×C73C22×D4
prime radicalC24×D73D4
cosocleC22×C4×C73C24
hypercenter#1854D73
hypocenterC73#21943
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #22610133C2semidirect
5. #22610132C2semidirect
6. #22610131C2semidirect
7. #22610130C2semidirect
8. #22610129C2semidirect
9. #22610128C2semidirect
10. #22610127C2semidirect
11. #22609965C2semidirect
12. #22609963C2semidirect
13. #22609963C2semidirect
14. #22609961C2semidirect
15. C73×#1854C2semidirect
22. C2×#14556525C22semidirect
23. C2×#14556524C22semidirect
24. C2×#14556524C22semidirect
25. C2×#14556523C22semidirect
26. C2×#14556522C22semidirect
27. C2×#14556522C22semidirect
28. #17988549C4semidirect
47. #17988350C22semidirect
48. #17988350C22semidirect
49. #17988349C22semidirect
50. #17988349C22semidirect
51. #17988349C22semidirect
52. #17988349C22semidirect
54. C2×#107×C73C22semidirect
55. C2×#106×C73C22semidirect
58. #340×C73C22semidirect
59. #340×C73C22semidirect
386. #1854D73semidirect
391. C73#21943semidirect
402. C2×#107C2×D73semidirect
406. C2×#106C2×D73semidirect
434. #340C2×D73semidirect
435. #340C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179885492
#226123132
#226123102
#226101332
#226101322
#226101312
#226101302
#226101292
#226101282
#226101272
#226099652
#226099632
#226099612
C73×#18542
#2194373