Finite Group Databasebeta

← #33097081

Subgroups — #33097081

Order 18688.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988550C211yesmaximal, characteristic, complemented
2C4×#14556559C211yesmaximal, characteristic
3#22610727C211yesmaximal, characteristic, complemented
4#22610723C211yesmaximal, characteristic, complemented
5#22610543C211yesmaximal, characteristic, complemented
6#22610537C211yesmaximal, characteristic, complemented
7#22610537C211yesmaximal, characteristic, complemented
8#22610536C211yesmaximal, characteristic, complemented
9#22610229C211yesmaximal, characteristic, complemented
10#22610228C211yesmaximal, characteristic, complemented
11#22610228C211yesmaximal, characteristic, complemented
12#22610113C211yesmaximal, characteristic, complemented
13#22609840C211yesmaximal, characteristic, complemented
14#22609712C211yesmaximal, characteristic, complemented
15C2×#436×C73C211yesmaximal, characteristic, complemented
16C23×C4×D73C2211yescharacteristic
17C22×#11924012C2211yescharacteristic
18C2×#14556559C411yescharacteristic
19C2×C4×C22⋊D73C2211yescharacteristic
20C2×C4×C22⋊D73C2211yescharacteristic
21C2×#14556520C2211yescharacteristic, complemented
22C2×#14556520C2211yescharacteristic, complemented
23#17988550—24no—
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic, complemented
26C2×C22⋊#10596831C2211yescharacteristic, complemented
27C2×#14556503C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556503C2211yescharacteristic
35C2×#14556501C2211yescharacteristic, complemented
36C2×C8×Dic73C2211yescharacteristic, complemented
37#17988467C411yescharacteristic
38#17988463C411yescharacteristic
39#17988463C411yescharacteristic
40#17988459C411yescharacteristic
41#17988458C411yescharacteristic
42#17988458C411yescharacteristic
43#17988442C411yescharacteristic
44C4×#11924005C2211yescharacteristic
45C4×#11924005C2211yescharacteristic
46C4×C22⋊Dic73C2211yescharacteristic
47#17988342C2211yescharacteristic, complemented
48#17988342C2211yescharacteristic, complemented
49#17988341C2211yescharacteristic, complemented
50#17988341C2211yescharacteristic, complemented
51#17988341C2211yescharacteristic, complemented
52#17988341C2211yescharacteristic, complemented
53C22×M16×C73C2211yescharacteristic
54C22×M16×C73C2211yescharacteristic, complemented
55C2×C4×D4×C73C2211yescharacteristic
56#436×C73—24no—
57C2×C4⋊C8×C73C2211yescharacteristic, complemented
58C2×C22⋊C8×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic, complemented
60C2×C4×C8×C73C2211yescharacteristic, complemented
61C24×D73C2×C411yescharacteristic
62C22×C22⋊D73C2×C411yescharacteristic
63C22×C22⋊D73C2×C411yescharacteristic
64C23×Dic73C2×C411yescharacteristic
65C22×C4×D73—22no—
66C22×C4×D73—22no—
67C22×C4×D73—41no—
68C22×C4×D73—41no—
69C22×C4×D73—41no—
70C22×C4×D73—41no—
71C22×C4×D73C2×C411yescharacteristic
72C22×C4×D73C2×C411yescharacteristic
73C22×C4×D73C2311yescharacteristic
74C22×C4×D73C2311yescharacteristic
75C2×#11924012—22no—
76C2×#11924012—41no—
77C2×#11924012—41no—
78C22×#10596831C2311yescharacteristic
79C22×#10596831C2311yescharacteristic
80C22×#10596831C2311yescharacteristic
81C22×#10596831C2311yescharacteristic
82#14556559—24no—
83C4×C22⋊D73—41no—
84C4×C22⋊D73—41no—
85C4×C22⋊D73—41no—
86C4×C22⋊D73—41no—
87C2×#11924007C2×C411yescharacteristic
88C2×#11924007C2×C411yescharacteristic
89C2×C22⋊Dic73C2×C411yescharacteristic
90C2×C22⋊Dic73C2×C411yescharacteristic
91C2×C22⋊Dic73C2×C411yescharacteristic
92C2×C22⋊Dic73C2×C411yescharacteristic
93C2×#11924005C2×C411yescharacteristic
94C2×#11924005C2×C411yescharacteristic
95C2×#11924005C2×C411yescharacteristic
96C2×#11924005C2×C411yescharacteristic
97C2×#11924005C2×C411yescharacteristic
98C2×#11924005C2×C411yescharacteristic
99C2×C4×Dic73C2311yescharacteristic
100C2×C4×Dic73C2311yescharacteristic
101#14556520—41no—
102#14556520—41no—
103C22⋊#10596831—22no—
104C22⋊#10596831—41no—
105C22⋊#10596831—41no—
106#14556503—22no—
107#14556503—22no—
108#14556503—22no—
109#14556503—22no—
110#14556503—41no—
111#14556503—41no—
112#14556503—41no—
113#14556503—41no—
114#14556501—41no—
115C8×Dic73—41no—
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120#14556498C2×C411yescharacteristic
121#14556498C2×C411yescharacteristic
122C22×D4×C73C2×C411yescharacteristic
123C23×C4×C73C2311yescharacteristic
124C23×C4×C73C2311yescharacteristic
125C2×M16×C73—22no—
126C2×M16×C73—41no—
127C2×M16×C73—41no—
128C2×M16×C73—41no—
129C2×M16×C73—41no—
130C2×M16×C73D414yescomplemented
131C22×C8×C73C2311yescharacteristic
132C22×C8×C73C2311yescharacteristic
133C22×C8×C73C2311yescharacteristic
134C22×C8×C73C2311yescharacteristic
135C4×D4×C73—22no—
136C4×D4×C73—22no—
137C2×C4⋊C4×C73C2×C411yescharacteristic
138C2×C22⋊C4×C73C2×C411yescharacteristic
139C2×C22⋊C4×C73C2×C411yescharacteristic
140C2×C42×C73C2311yescharacteristic
141C4⋊C8×C73—22no—
142C22⋊C8×C73—22no—
143C22⋊C8×C73—22no—
144C4×C8×C73—22no—
145C23×D73—22no—
146C23×D73—22no—
147C23×D73—22no—
148C23×D73—41no—
149C23×D73—41no—
150C23×D73—41no—
151C23×D73—41no—
152C23×D73C22×C411yescharacteristic
153C23×D73C22×C411yescharacteristic
154C2×C22⋊D73—22no—
155C2×C22⋊D73—22no—
156C2×C22⋊D73—22no—
157C2×C22⋊D73—41no—
158C2×C22⋊D73—41no—
159C2×C22⋊D73—41no—
160C22×Dic73—22no—
161C22×Dic73—41no—
162C22×Dic73—41no—
163C22×Dic73C22×C411yescharacteristic
164C22×Dic73C22×C411yescharacteristic
165C22×Dic73C22×C411yescharacteristic
166C22×Dic73C22×C411yescharacteristic
167C22×Dic73C22×C411yescharacteristic
168C22×Dic73C22×C411yescharacteristic
169C2×C4×D73—22no—
170C2×C4×D73—22no—
171C2×C4×D73—21no—
172C2×C4×D73—21no—
173C2×C4×D73—21no—
174C2×C4×D73—21no—
175C2×C4×D73—21no—
176C2×C4×D73—21no—
177C2×C4×D73—21no—
178C2×C4×D73—21no—
179C2×C4×D73—21no—
180C2×C4×D73—21no—
181C2×C4×D73—21no—
182C2×C4×D73—21no—
183C2×C4×D73—41no—
184C2×C4×D73—41no—
185C2×C4×D73—41no—
186C2×C4×D73—41no—
187C2×C4×D73—44no—
188C2×C4×D73—44no—
189C2×C4×D73—44no—
190C2×C4×D73—44no—
191#11924012—44no—
192C2×#10596831—21no—
193C2×#10596831—21no—
194C2×#10596831—21no—
195C2×#10596831—21no—
196C2×#10596831—21no—
197C2×#10596831—21no—
198C2×#10596831—21no—
199C2×#10596831—21no—
200C2×#10596831—21no—
201C2×#10596831—21no—
202C2×#10596831—21no—
203C2×#10596831—21no—
204#11924007—41no—
205#11924007—41no—
206C22⋊Dic73—22no—
207C22⋊Dic73—41no—
208C22⋊Dic73—41no—
209C22⋊Dic73—41no—
210#11924005—22no—
211#11924005—22no—
212#11924005—41no—
213#11924005—41no—
214#11924005—41no—
215#11924005M1614yescomplemented
216C4×Dic73—21no—
217C4×Dic73—21no—
218C4×Dic73—21no—
219C4×Dic73—21no—
220C24×C73C22×C411yescharacteristic
221C24×C73C22×C411yescharacteristic
222C2×D4×C73—22no—
223C2×D4×C73—22no—
224C2×D4×C73—41no—
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×C73C22×C411yescharacteristic
236C22×C4×C73C22×C411yescharacteristic
237C22×C4×C73C22×C411yescharacteristic
238C22×C4×C73C22×C411yescharacteristic
239C22×C4×C73C2×D412yes—
240C22×C4×C73#4112yes—
241C22×C4×C73C2411yescharacteristic
242M16×C73—44no—
243M16×C73—44no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C2×C8×C73—21no—
249C2×C8×C73—21no—
250C2×C8×C73—21no—
251C2×C8×C73—21no—
252C2×C8×C73—21no—
253C2×C8×C73—21no—
254C2×C8×C73C2×D412yes—
255C2×C8×C73C2×D412yes—
256C4⋊C4×C73—22no—
257C22⋊C4×C73—22no—
258C22⋊C4×C73—22no—
259C42×C73—21no—
260C42×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—21no—
274C23×C73C4×D412yes—
275C23×C73C23×C411yescharacteristic
276C22×D73—21no—
277C22×D73—21no—
278C22×D73—21no—
279C22×D73—21no—
280C22×D73—21no—
281C22×D73—21no—
282C22×D73—21no—
283C22×D73—21no—
284C22×D73—21no—
285C22×D73—21no—
286C22×D73—21no—
287C22×D73—21no—
288C22×D73—44no—
289C22×D73—44no—
290C22×D73—44no—
291C22×D73—44no—
292C22×D73—44no—
293C22×D73—44no—
294C22×D73—44no—
295C22×D73C2×M1612yes—
296C22×D73#13112yes—
297D4×C73—44no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73C4×D412yes—
317C2×C4×C73C2×M1612yes—
318C2×C4×C73C22×D411yescharacteristic
319C2×C4×C73C2×#4111yescharacteristic
320C2×C4×C73H(5,𝔽2)11yescharacteristic
321C2×C4×C73H(5,𝔽2)11yescharacteristic
322C2×C4×C73H(5,𝔽2)11yescharacteristic
323C2×C4×C73H(5,𝔽2)11yescharacteristic
324C22⋊D73—44no—
325C22⋊D73—44no—
326C2×Dic73—21no—
327C2×Dic73—21no—
328C2×Dic73—21no—
329C2×Dic73—21no—
330C2×Dic73—21no—
331C2×Dic73—21no—
332C2×Dic73—21no—
333C2×Dic73—21no—
334C2×Dic73—21no—
335C2×Dic73—21no—
336C2×Dic73—21no—
337C2×Dic73—21no—
338C2×Dic73—21no—
339C2×Dic73—21no—
340C2×Dic73—21no—
341C2×Dic73—21no—
342C2×Dic73—21no—
343C2×Dic73—44no—
344C2×Dic73C2×M1612yes—
345C4×D73—44no—
346C4×D73—44no—
347C4×D73—41no—
348C4×D73—41no—
349C4×D73—41no—
350C4×D73—41no—
351C4×D73—41no—
352C4×D73—41no—
353C4×D73—41no—
354C4×D73—41no—
355C8×C73—22no—
356C8×C73—22no—
357C8×C73—41no—
358C8×C73—41no—
359#10596831—41no—
360#10596831—41no—
361#10596831—41no—
362#10596831—41no—
363C22×C73—22no—
364C22×C73—22no—
365C22×C73—22no—
366C22×C73—41no—
367C22×C73—41no—
368C22×C73—41no—
369C22×C73—41no—
370C22×C73—41no—
371C22×C73—41no—
372C22×C73—41no—
373C22×C73—41no—
374C22×C73—41no—
375C22×C73—41no—
376C22×C73—41no—
377C22×C73C2×C4×D411yescharacteristic
378C22×C73#51811yescharacteristic
379C22×C73#51811yescharacteristic
380C22×C73C22×M1611yescharacteristic
381C22×C73C2×#13111yescharacteristic
382C22×C73#56811yescharacteristic
383C22×C73#56811yescharacteristic
384C2×D73—22no—
385C2×D73—22no—
386C2×D73—22no—
387C2×D73—22no—
388C2×D73—22no—
389C2×D73—22no—
390C2×D73—416no—
391C2×D73—41no—
392C2×D73—41no—
393C2×D73—41no—
394C2×D73—41no—
395C2×D73—41no—
396C2×D73—41no—
397C2×D73—41no—
398C2×D73—41no—
399C4×C73—22no—
400C4×C73—22no—
401C4×C73—41no—
402C4×C73—41no—
403C4×C73#53411yescharacteristic
404C4×C73#53511yescharacteristic
405C4×C73#53811yescharacteristic
406C4×C73#53811yescharacteristic
407Dic73—22no—
408Dic73—41no—
409Dic73—41no—
410Dic73—41no—
411Dic73—41no—
412Dic73—41no—
413#22038—731nomaximal, Sylow
414C2×C73—42no—
415C2×C73—81no—
416C2×C73#232111yescharacteristic
417C2×C73#293311yescharacteristic
418C2×C73D4×M1611yescharacteristic
419C2×C73#297411yescharacteristic
420C2×C73#297511yescharacteristic
421C2×C73#297611yescharacteristic
422C2×C73#297811yescharacteristic
423D73—42no—
424D73—42no—
425C2×#436D7311yescharacteristic, complemented
426C2×#407—731no—
427C4×#120—731no—
428#1955—731no—
429#1954—731no—
430#1924—731no—
431#1923—731no—
432#1923—731no—
433#1923—731no—
434#1870—731no—
435#1870—731no—
436#1870—731no—
437#1851—731no—
438#1779—731no—
439#1753—731no—
440C73#2203811yescharacteristic, complemented, Sylow
441C24×C4—731no—
442C22×M16—731no—
443C22×M16C2×D7311yescharacteristic
444C22×M16C2×D7311yescharacteristic, complemented
445C2×#120—731no—
446C2×C4×D4—731no—
447C2×C4×D4—731no—
448C2×C4×D4C2×D7311yescharacteristic
449#436—24no—
450C2×C4⋊C8—731no—
451C2×C4⋊C8—731no—
452C2×C4⋊C8C2×D7311yescharacteristic, complemented
453#407—1464no—
454C2×C22⋊C8—731no—
455C2×C22⋊C8—731no—
456C2×C22⋊C8—731no—
457C2×C22⋊C8—731no—
458C2×C22⋊C8—731no—
459C2×C22⋊C8—731no—
460C2×C22⋊C8—731no—
461C2×C22⋊C8—731no—
462C2×C22⋊C8—731no—
463C2×C22⋊C8—731no—
464C2×C22⋊C8—731no—
465C2×C22⋊C8C2×D7311yescharacteristic
466C2×C22⋊C8C2×D7311yescharacteristic, complemented
467C2×#97—731no—
468C2×C4×C8—731no—
469C2×C4×C8C2×D7311yescharacteristic, complemented
470#386—731no—
471#386—731no—
472#386—731no—
473#385—731no—
474#385—731no—
475#385—731no—
476#379—731no—
477C4×C22⋊C4—731no—
478C4×C22⋊C4—731no—
479C4×C22⋊C4—731no—
480#336—731no—
481#336—731no—
482#336—731no—
483#336—731no—
484#336—731no—
485#336—731no—
486C25—731no—
487C22×D4—731no—
488C22×D4—731no—
489C22×D4C4×D7311yescharacteristic
490C23×C4—2921no—
491C23×C4—2921no—
492C23×C4—2921no—
493C23×C4—2921no—
494C23×C4—731no—
495C23×C4—731no—
496C23×C4—731no—
497C23×C4—731no—
498C23×C4—731no—
499C23×C4—1462no—
500C23×C4—1462no—
501C23×C4C22×D7311yescharacteristic
502C23×C4C22×D7311yescharacteristic
503C2×M16—22no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—41no—
507C2×M16—41no—
508C2×M16—2921no—
509C2×M16—2921no—
510C2×M16—1462no—
511C2×M16C22⋊D7314yescomplemented
512C22×C8—731no—
513C22×C8—731no—
514C22×C8—731no—
515C22×C8—731no—
516C22×C8C22×D7311yescharacteristic
517C22×C8C22×D7311yescharacteristic
518C22×C8C22×D7311yescharacteristic
519C22×C8C22×D7311yescharacteristic
520#120—1464no—
521C4×D4—22no—
522C4×D4—22no—
523C4×D4—2921no—
524C4×D4—2921no—
525C4×D4—2921no—
526C4×D4—2921no—
527C2×C4⋊C4—731no—
528C2×C4⋊C4—731no—
529C2×C4⋊C4C4×D7311yescharacteristic
530C2×C22⋊C4—731no—
531C2×C22⋊C4—731no—
532C2×C22⋊C4—731no—
533C2×C22⋊C4—731no—
534C2×C22⋊C4—731no—
535C2×C22⋊C4—731no—
536C2×C22⋊C4—731no—
537C2×C22⋊C4—731no—
538C2×C22⋊C4—731no—
539C2×C22⋊C4—731no—
540C2×C22⋊C4C4×D7311yescharacteristic
541C2×C22⋊C4C4×D7311yescharacteristic
542C2×C42—731no—
543C2×C42—731no—
544C2×C42C22×D7311yescharacteristic
545C4⋊C8—22no—
546C4⋊C8—2921no—
547C4⋊C8—2921no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—2921no—
551C22⋊C8—2921no—
552C22⋊C8—2921no—
553C22⋊C8—2921no—
554C22⋊C8—2921no—
555C22⋊C8—2921no—
556C22⋊C8—1462no—
557C22⋊C8—1462no—
558C22⋊C8—1462no—
559C22⋊C8—1462no—
560C22⋊C8—1462no—
561#97—2921no—
562C4×C8—22no—
563C4×C8—2921no—
564#95—731no—
565#95—731no—
566#95—731no—
567#95—731no—
568#95—731no—
569#95—731no—
570C24—2921no—
571C24—2921no—
572C24—2921no—
573C24—2921no—
574C24—731no—
575C24—731no—
576C24—1462no—
577C24—1462no—
578C24—1462no—
579C24C2×C4×D7311yescharacteristic
580C24C2×C4×D7311yescharacteristic
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—41no—
584C2×D4—2921no—
585C2×D4—2921no—
586C2×D4—2921no—
587C2×D4—1462no—
588C2×D4—1462no—
589C2×D4—1462no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—2924no—
601C22×C4—2924no—
602C22×C4—2924no—
603C22×C4—2924no—
604C22×C4—2921no—
605C22×C4—2921no—
606C22×C4—2921no—
607C22×C4—2921no—
608C22×C4—2921no—
609C22×C4—2921no—
610C22×C4—731no—
611C22×C4—731no—
612C22×C4—731no—
613C22×C4—731no—
614C22×C4—731no—
615C22×C4—731no—
616C22×C4—1462no—
617C22×C4—1462no—
618C22×C4—1462no—
619C22×C4—1461no—
620C22×C4—1461no—
621C22×C4—1461no—
622C22×C4—1461no—
623C22×C4—1461no—
624C22×C4—1461no—
625C22×C4—1461no—
626C22×C4—1461no—
627C22×C4—1461no—
628C22×C4—1461no—
629C22×C4—1461no—
630C22×C4—1461no—
631C22×C4C2×C4×D7311yescharacteristic
632C22×C4C2×C4×D7311yescharacteristic
633C22×C4C2×C4×D7311yescharacteristic
634C22×C4C2×C4×D7311yescharacteristic
635C22×C4C2×C22⋊D7312yes—
636C22×C4#1192402812yes—
637C22×C4C23×D7311yescharacteristic
638M16—44no—
639M16—44no—
640M16—2924no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—1461no—
652C2×C8—1461no—
653C2×C8—1461no—
654C2×C8—1461no—
655C2×C8—1461no—
656C2×C8—1461no—
657C2×C8—1461no—
658C2×C8—1461no—
659C2×C8—1461no—
660C2×C8—1461no—
661C2×C8—1461no—
662C2×C8—1461no—
663C2×C8C2×C22⋊D7312yes—
664C2×C8C2×C22⋊D7312yes—
665C4⋊C4—22no—
666C4⋊C4—2921no—
667C4⋊C4—2921no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—2921no—
671C22⋊C4—2921no—
672C22⋊C4—2921no—
673C22⋊C4—2921no—
674C22⋊C4—2921no—
675C22⋊C4—2921no—
676C22⋊C4—734no—
677C22⋊C4—1462no—
678C22⋊C4—1462no—
679C22⋊C4—1462no—
680C42—21no—
681C42—21no—
682C42—1461no—
683C42—1461no—
684C42—1461no—
685C42—1461no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—2924no—
700C23—2924no—
701C23—2924no—
702C23—2924no—
703C23—2924no—
704C23—2924no—
705C23—2924no—
706C23—732no—
707C23—732no—
708C23—1461no—
709C23—1461no—
710C23—1461no—
711C23—1461no—
712C23—1461no—
713C23—1461no—
714C23—1461no—
715C23—1461no—
716C23—1461no—
717C23—1461no—
718C23—1461no—
719C23—1461no—
720C23C4×C22⋊D7312yes—
721C23C22×C4×D7311yescharacteristic
722D4—44no—
723D4—2924no—
724D4—2924no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—2924no—
744C2×C4—2924no—
745C2×C4—2924no—
746C2×C4—2921no—
747C2×C4—2921no—
748C2×C4—2921no—
749C2×C4—2921no—
750C2×C4—2921no—
751C2×C4—2921no—
752C2×C4—2921no—
753C2×C4—2921no—
754C2×C4—732no—
755C2×C4—1461no—
756C2×C4—1461no—
757C2×C4—1461no—
758C2×C4—1461no—
759C2×C4—1461no—
760C2×C4—1461no—
761C2×C4—1461no—
762C2×C4—1461no—
763C2×C4—1461no—
764C2×C4—1461no—
765C2×C4—1461no—
766C2×C4—1461no—
767C2×C4—1461no—
768C2×C4—1461no—
769C2×C4—1461no—
770C2×C4—1461no—
771C2×C4—1461no—
772C2×C4C4×C22⋊D7312yes—
773C2×C4M16×D7312yes—
774C2×C4C22×C22⋊D7311yescharacteristic
775C2×C4C2×#1192402811yescharacteristic
776C2×C4#1455663611yescharacteristic
777C2×C4#1455663611yescharacteristic
778C2×C4#1455663711yescharacteristic
779C2×C4#1455663711yescharacteristic
780C8—22no—
781C8—22no—
782C8—41no—
783C8—41no—
784C8—2921no—
785C8—2921no—
786C8—2921no—
787C8—2921no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—29216no—
803C22—2921no—
804C22—2921no—
805C22—2921no—
806C22—2921no—
807C22—2921no—
808C22—2921no—
809C22—2921no—
810C22—2921no—
811C22—1462no—
812C22—1462no—
813C22—1462no—
814C22—1462no—
815C22—1462no—
816C22—1462no—
817C22C2×C4×C22⋊D7311yescharacteristic
818C22#1798905911yescharacteristic
819C22#1798905911yescharacteristic
820C22C2×M16×D7311yescharacteristic
821C22#131×D7311yescharacteristic
822C22#1798935211yescharacteristic
823C22#1798935311yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—2921no—
829C4—2921no—
830C4—2921no—
831C4—2921no—
832C4—2921no—
833C4—1462no—
834C4#1798914611yescharacteristic
835C4#1798915111yescharacteristic
836C4#1798917011yescharacteristic
837C4#1798917011yescharacteristic
838C2—42no—
839C2—81no—
840C2—2922no—
841C2—2922no—
842C2#2261258511yescharacteristic
843C2#2261865311yescharacteristic
844C2M16×C22⋊D7311yescharacteristic
845C2#2261896311yescharacteristic
846C2#2261896911yescharacteristic
847C2#2261897511yescharacteristic
848C2#2261898811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC2×#436×C73C2
prime radicalC2×#14556559C4
cosocleC22×C4×C73C24
hypercenterC2×#436D73
hypocenterC73#22038
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#17988550C2semidirect
3. #22610727C2semidirect
4. #22610723C2semidirect
5. #22610543C2semidirect
6. #22610537C2semidirect
7. #22610537C2semidirect
8. #22610536C2semidirect
9. #22610229C2semidirect
10. #22610228C2semidirect
11. #22610228C2semidirect
12. #22610113C2semidirect
13. #22609840C2semidirect
14. #22609712C2semidirect
15. C2×#436×C73C2semidirect
21. C2×#14556520C22semidirect
22. C2×#14556520C22semidirect
25. C2×C22⋊#10596831C22semidirect
26. C2×C22⋊#10596831C22semidirect
35. C2×#14556501C22semidirect
36. C2×C8×Dic73C22semidirect
47. #17988342C22semidirect
48. #17988342C22semidirect
49. #17988341C22semidirect
50. #17988341C22semidirect
51. #17988341C22semidirect
52. #17988341C22semidirect
54. C22×M16×C73C22semidirect
57. C2×C4⋊C8×C73C22semidirect
59. C2×C22⋊C8×C73C22semidirect
60. C2×C4×C8×C73C22semidirect
130. C2×M16×C73D4semidirect
215. #11924005M16semidirect
425. C2×#436D73semidirect
440. C73#22038semidirect
444. C22×M16C2×D73semidirect
452. C2×C4⋊C8C2×D73semidirect
466. C2×C22⋊C8C2×D73semidirect
469. C2×C4×C8C2×D73semidirect
511. C2×M16C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179885502
C4×#145565592
#226107272
#226107232
#226105432
#226105372
#226105362
#226102292
#226102282
#226101132
#226098402
#226097122
C2×#436×C732
#2203873