Finite Group Databasebeta

← #33097089

Subgroups — #33097089

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×#17988663C211yesmaximal, characteristic, complemented
2C2×#17988550C211yesmaximal, characteristic, complemented
3C4×#14556561C211yesmaximal, characteristic
4#22610729C211yesmaximal, characteristic, complemented
5#22610725C211yesmaximal, characteristic, complemented
6#22610544C211yesmaximal, characteristic, complemented
7#22610538C211yesmaximal, characteristic, complemented
8#22610538C211yesmaximal, characteristic, complemented
9#22610537C211yesmaximal, characteristic, complemented
10#22610227C211yesmaximal, characteristic, complemented
11#22610227C211yesmaximal, characteristic, complemented
12#22610226C211yesmaximal, characteristic, complemented
13#22610116C211yesmaximal, characteristic, complemented
14#22609840C211yesmaximal, characteristic, complemented
15C73×#1753C211yesmaximal, characteristic, complemented
16C23×C4×D73C2211yescharacteristic
17C22×#11924012C2211yescharacteristic
18C22×#11924011C2211yescharacteristic, complemented
19C2×#14556561C411yescharacteristic
20C2×C4×D292C2211yescharacteristic
21C2×C4×D292C2211yescharacteristic
22C2×C4×C22⋊D73C2211yescharacteristic
23#17988663—24no—
24C2×C4⋊#10596831C2211yescharacteristic, complemented
25C2×C4⋊#10596831C2211yescharacteristic, complemented
26C2×#14556520C2211yescharacteristic, complemented
27#17988550—24no—
28C2×C22⋊#10596831C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556503C2211yescharacteristic
35C2×#14556503C2211yescharacteristic
36C2×#14556503C2211yescharacteristic
37C2×#14556503C2211yescharacteristic, complemented
38C2×#14556503C2211yescharacteristic, complemented
39C2×#14556503C2211yescharacteristic, complemented
40C2×C8×Dic73C2211yescharacteristic, complemented
41#17988465C411yescharacteristic
42#17988465C411yescharacteristic
43#17988464C411yescharacteristic
44#17988462C411yescharacteristic
45#17988461C411yescharacteristic
46#17988461C411yescharacteristic
47#17988442C411yescharacteristic
48C4×#11924005C2211yescharacteristic
49C4×#11924005C2211yescharacteristic
50#17988342C2211yescharacteristic, complemented
51#17988342C2211yescharacteristic, complemented
52#17988341C2211yescharacteristic, complemented
53#17988341C2211yescharacteristic, complemented
54C22×M16×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×#97×C73C2211yescharacteristic, complemented
57C2×C4×C8×C73C2211yescharacteristic, complemented
58C4×C22⋊C4×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic, complemented
60#336×C73C2211yescharacteristic, complemented
61C24×D73C2×C411yescharacteristic
62C22×D292C2×C411yescharacteristic
63C22×D292C2×C411yescharacteristic
64C22×C22⋊D73C2×C411yescharacteristic
65C23×Dic73C2×C411yescharacteristic
66C22×C4×D73—22no—
67C22×C4×D73—22no—
68C22×C4×D73—41no—
69C22×C4×D73—41no—
70C22×C4×D73—41no—
71C22×C4×D73—41no—
72C22×C4×D73C2×C411yescharacteristic
73C22×C4×D73C2×C411yescharacteristic
74C22×C4×D73C2311yescharacteristic
75C22×C4×D73C2311yescharacteristic
76C22×C4×D73C2311yescharacteristic
77C2×#11924012—22no—
78C2×#11924012—41no—
79C2×#11924012—41no—
80C2×#11924011—22no—
81C2×#11924011—41no—
82C2×#11924011—41no—
83C22×#10596831C2311yescharacteristic
84C22×#10596831C2311yescharacteristic
85C22×#10596831C2311yescharacteristic
86C22×#10596831C2311yescharacteristic
87#14556561—24no—
88C4×D292—41no—
89C4×D292—41no—
90C4×D292—41no—
91C4×D292—41no—
92C4×C22⋊D73—22no—
93C4×C22⋊D73—22no—
94C2×C4⋊Dic73C2×C411yescharacteristic
95C2×C4⋊Dic73C2×C411yescharacteristic
96C2×#11924007C2×C411yescharacteristic
97C2×C22⋊Dic73C2×C411yescharacteristic
98C2×#11924005C2×C411yescharacteristic
99C2×#11924005C2×C411yescharacteristic
100C2×#11924005C2×C411yescharacteristic
101C2×#11924005C2×C411yescharacteristic
102C2×#11924005C2×C411yescharacteristic
103C2×#11924005C2×C411yescharacteristic
104C2×#11924005C2×C411yescharacteristic
105C2×#11924005C2×C411yescharacteristic
106C2×#11924005C2×C411yescharacteristic
107C2×C4×Dic73C2311yescharacteristic
108C4⋊#10596831—41no—
109C4⋊#10596831—41no—
110#14556520—22no—
111C22⋊#10596831—22no—
112#14556503—22no—
113#14556503—22no—
114#14556503—22no—
115#14556503—22no—
116#14556503—22no—
117#14556503—41no—
118#14556503—41no—
119#14556503—41no—
120#14556503—41no—
121#14556503—41no—
122#14556503—41no—
123C8×Dic73—22no—
124#14556498C2×C411yescharacteristic
125#14556498C2×C411yescharacteristic
126#14556498C2×C411yescharacteristic
127#14556498C2×C411yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C2×M16×C73—41no—
130C2×M16×C73—41no—
131C2×M16×C73D414yescomplemented
132C22×C8×C73C2311yescharacteristic
133C22×C8×C73C2311yescharacteristic
134C22×C8×C73C2311yescharacteristic
135C22×C8×C73C2311yescharacteristic
136C2×C22⋊C4×C73C2×C411yescharacteristic
137C2×C22⋊C4×C73C2×C411yescharacteristic
138C2×C42×C73C2311yescharacteristic
139C2×C42×C73C2311yescharacteristic
140C22⋊C8×C73—22no—
141#97×C73—41no—
142C4×C8×C73—41no—
143#95×C73C2×C411yescharacteristic
144#95×C73C2×C411yescharacteristic
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
154C23×D73C22×C411yescharacteristic
155C2×D292—22no—
156C2×D292—22no—
157C2×D292—22no—
158C2×D292—41no—
159C2×D292—41no—
160C2×D292—41no—
161C2×C22⋊D73—22no—
162C2×C22⋊D73—22no—
163C2×C22⋊D73—41no—
164C22×Dic73—22no—
165C22×Dic73—41no—
166C22×Dic73—41no—
167C22×Dic73C22×C411yescharacteristic
168C22×Dic73C22×C411yescharacteristic
169C22×Dic73C22×C411yescharacteristic
170C22×Dic73C22×C411yescharacteristic
171C22×Dic73C22×C411yescharacteristic
172C2×C4×D73—22no—
173C2×C4×D73—22no—
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—21no—
184C2×C4×D73—21no—
185C2×C4×D73—21no—
186C2×C4×D73—21no—
187C2×C4×D73—21no—
188C2×C4×D73—21no—
189C2×C4×D73—21no—
190C2×C4×D73—21no—
191C2×C4×D73—21no—
192C2×C4×D73—41no—
193C2×C4×D73—41no—
194C2×C4×D73—41no—
195C2×C4×D73—41no—
196C2×C4×D73—44no—
197C2×C4×D73—44no—
198C2×C4×D73—44no—
199C2×C4×D73—44no—
200#11924012—44no—
201#11924011—44no—
202C2×#10596831—21no—
203C2×#10596831—21no—
204C2×#10596831—21no—
205C2×#10596831—21no—
206C2×#10596831—21no—
207C2×#10596831—21no—
208C2×#10596831—21no—
209C2×#10596831—21no—
210C2×#10596831—21no—
211C2×#10596831—21no—
212C2×#10596831—21no—
213C2×#10596831—21no—
214C4⋊Dic73—41no—
215C4⋊Dic73—41no—
216#11924007—22no—
217C22⋊Dic73—22no—
218#11924005—22no—
219#11924005—22no—
220#11924005—22no—
221#11924005—41no—
222#11924005—41no—
223#11924005—41no—
224#11924005—41no—
225#11924005—41no—
226#11924005M1614yescomplemented
227C4×Dic73—21no—
228C4×Dic73—21no—
229C24×C73C22×C411yescharacteristic
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73C22×C411yescharacteristic
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—
243C2×C8×C73—21no—
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×C73C2×D412yes—
254C2×C8×C73C2×D412yes—
255C22⋊C4×C73—22no—
256C22⋊C4×C73—41no—
257C42×C73—21no—
258C42×C73—21no—
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×C73C4×D412yes—
268C23×C73C23×C411yescharacteristic
269C22×D73—21no—
270C22×D73—21no—
271C22×D73—21no—
272C22×D73—21no—
273C22×D73—21no—
274C22×D73—21no—
275C22×D73—21no—
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—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—21no—
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—21no—
313C2×C4×C73—21no—
314C2×C4×C73C4×D412yes—
315C2×C4×C73C2×M1612yes—
316C2×C4×C73C22×D411yescharacteristic
317C2×C4×C73C2×#4111yescharacteristic
318C2×C4×C73H(5,𝔽2)11yescharacteristic
319C2×C4×C73H(5,𝔽2)11yescharacteristic
320C2×C4×C73H(5,𝔽2)11yescharacteristic
321C2×C4×C73H(5,𝔽2)11yescharacteristic
322C22⋊D73—44no—
323C2×Dic73—21no—
324C2×Dic73—21no—
325C2×Dic73—21no—
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—44no—
338C2×Dic73C2×M1612yes—
339D292—44no—
340D292—44no—
341C4×D73—44no—
342C4×D73—44no—
343C4×D73—41no—
344C4×D73—41no—
345C4×D73—41no—
346C4×D73—41no—
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×C73C2×C4×D411yescharacteristic
371C22×C73#51811yescharacteristic
372C22×C73#51811yescharacteristic
373C22×C73C22×M1611yescharacteristic
374C22×C73C2×#13111yescharacteristic
375C22×C73#56811yescharacteristic
376C22×C73#56811yescharacteristic
377C2×D73—22no—
378C2×D73—22no—
379C2×D73—22no—
380C2×D73—22no—
381C2×D73—22no—
382C2×D73—22no—
383C2×D73—416no—
384C2×D73—41no—
385C2×D73—41no—
386C2×D73—41no—
387C2×D73—41no—
388C2×D73—41no—
389C2×D73—41no—
390C2×D73—41no—
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—41no—
404C4×C73#53411yescharacteristic
405C4×C73#53511yescharacteristic
406C4×C73#53811yescharacteristic
407C4×C73#53811yescharacteristic
408Dic73—22no—
409Dic73—41no—
410Dic73—41no—
411Dic73—41no—
412Dic73—41no—
413#22038—731nomaximal, Sylow
414C2×C73—42no—
415C2×C73#232111yescharacteristic
416C2×C73#293311yescharacteristic
417C2×C73D4×M1611yescharacteristic
418C2×C73#297411yescharacteristic
419C2×C73#297511yescharacteristic
420C2×C73#297611yescharacteristic
421C2×C73#297811yescharacteristic
422D73—42no—
423D73—42no—
424D73—81no—
425C2×#436—731no—
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#1753D7311yescharacteristic, complemented
440C73#2203811yescharacteristic, complemented, Sylow
441C24×C4—731no—
442C22×M16—731no—
443C22×M16—731no—
444C22×M16C2×D7311yescharacteristic
445C2×#120—731no—
446C2×C4×D4—731no—
447C2×C4×D4—731no—
448C2×C4×D4—731no—
449#436—1464no—
450C2×C4⋊C8—731no—
451C2×C4⋊C8—731no—
452C2×C4⋊C8—731no—
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⋊C8—731no—
466C2×C22⋊C8C2×D7311yescharacteristic
467C2×#97C2×D7311yescharacteristic, complemented
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⋊C4C2×D7311yescharacteristic
480#336—731no—
481#336—731no—
482#336—731no—
483#336—731no—
484#336C2×D7311yescharacteristic, complemented
485#336C2×D7311yescharacteristic, complemented
486C25—731no—
487C22×D4—731no—
488C22×D4—731no—
489C22×D4—731no—
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—731no—
500C23×C4—1462no—
501C23×C4—1462no—
502C23×C4C22×D7311yescharacteristic
503C2×M16—41no—
504C2×M16—41no—
505C2×M16—2921no—
506C2×M16—2921no—
507C2×M16—2921no—
508C2×M16—2921no—
509C2×M16—1462no—
510C2×M16—1462no—
511C2×M16D29214yescomplemented
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—2921no—
522C4×D4—2921no—
523C4×D4—2921no—
524C4×D4—2921no—
525C4×D4—1462no—
526C4×D4—1462no—
527C2×C4⋊C4—731no—
528C2×C4⋊C4—731no—
529C2×C4⋊C4—731no—
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×C42C22×D7311yescharacteristic
544C2×C42C22×D7311yescharacteristic
545C4⋊C8—2921no—
546C4⋊C8—2921no—
547C4⋊C8—1462no—
548C22⋊C8—22no—
549C22⋊C8—2921no—
550C22⋊C8—2921no—
551C22⋊C8—2921no—
552C22⋊C8—2921no—
553C22⋊C8—2921no—
554C22⋊C8—2921no—
555C22⋊C8—1462no—
556C22⋊C8—1462no—
557C22⋊C8—1462no—
558C22⋊C8—1462no—
559C22⋊C8—1462no—
560C22⋊C8—1462no—
561#97—41no—
562C4×C8—41no—
563C4×C8—1462no—
564#95—731no—
565#95—731no—
566#95—731no—
567#95—731no—
568#95C4×D7311yescharacteristic
569#95C4×D7311yescharacteristic
570C24—2921no—
571C24—2921no—
572C24—2921no—
573C24—2921no—
574C24—731no—
575C24—731no—
576C24—731no—
577C24—1462no—
578C24—1462no—
579C24—1462no—
580C24C2×C4×D7311yescharacteristic
581C2×D4—2921no—
582C2×D4—2921no—
583C2×D4—2921no—
584C2×D4—2921no—
585C2×D4—1462no—
586C2×D4—1462no—
587C2×D4—1462no—
588C2×D4—1462no—
589C2×D4—1462no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—2924no—
595C22×C4—2924no—
596C22×C4—2924no—
597C22×C4—2924no—
598C22×C4—2921no—
599C22×C4—2921no—
600C22×C4—2921no—
601C22×C4—2921no—
602C22×C4—2921no—
603C22×C4—2921no—
604C22×C4—731no—
605C22×C4—731no—
606C22×C4—731no—
607C22×C4—731no—
608C22×C4—731no—
609C22×C4—1462no—
610C22×C4—1462no—
611C22×C4—1462no—
612C22×C4—1461no—
613C22×C4—1461no—
614C22×C4—1461no—
615C22×C4—1461no—
616C22×C4—1461no—
617C22×C4—1461no—
618C22×C4—1461no—
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×C4C2×C4×D7311yescharacteristic
631C22×C4C2×C4×D7311yescharacteristic
632C22×C4C2×C4×D7311yescharacteristic
633C22×C4C2×C4×D7311yescharacteristic
634C22×C4C2×C4×D7311yescharacteristic
635C22×C4C2×D29212yes—
636C22×C4#1192402812yes—
637C22×C4C23×D7311yescharacteristic
638M16—44no—
639M16—2924no—
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×D29212yes—
664C2×C8C2×D29212yes—
665C4⋊C4—2921no—
666C4⋊C4—2921no—
667C4⋊C4—1462no—
668C22⋊C4—22no—
669C22⋊C4—41no—
670C22⋊C4—2921no—
671C22⋊C4—2921no—
672C22⋊C4—2921no—
673C22⋊C4—2921no—
674C22⋊C4—2921no—
675C22⋊C4—734no—
676C22⋊C4—1462no—
677C22⋊C4—1462no—
678C22⋊C4—1462no—
679C22⋊C4—1462no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—1461no—
685C42—1461no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—2924no—
693C23—2924no—
694C23—2924no—
695C23—2924no—
696C23—2924no—
697C23—2924no—
698C23—2924no—
699C23—732no—
700C23—732no—
701C23—1461no—
702C23—1461no—
703C23—1461no—
704C23—1461no—
705C23—1461no—
706C23—1461no—
707C23—1461no—
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×D29212yes—
721C23C22×C4×D7311yescharacteristic
722D4—2924no—
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—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—2924no—
743C2×C4—2924no—
744C2×C4—2924no—
745C2×C4—2921no—
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—2921no—
755C2×C4—2921no—
756C2×C4—2921no—
757C2×C4—732no—
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×D29212yes—
773C2×C4M16×D7312yes—
774C2×C4C22×D29211yescharacteristic
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—29216no—
796C22—2921no—
797C22—2921no—
798C22—2921no—
799C22—2921no—
800C22—2921no—
801C22—2921no—
802C22—2921no—
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×D29211yescharacteristic
818C22#1798905911yescharacteristic
819C22#1798905911yescharacteristic
820C22C2×M16×D7311yescharacteristic
821C22#131×D7311yescharacteristic
822C22#1798935211yescharacteristic
823C22#1798935311yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—2921no—
830C4—2921no—
831C4—2921no—
832C4—2921no—
833C4—1462no—
834C4#1798914911yescharacteristic
835C4#1798915611yescharacteristic
836C4#1798917011yescharacteristic
837C4#1798917011yescharacteristic
838C2—42no—
839C2—2922no—
840C2—2922no—
841C2—5841no—
842C2#2261259111yescharacteristic
843C2#2261865911yescharacteristic
844C2M16×D29211yescharacteristic
845C2#2261896111yescharacteristic
846C2#2261896911yescharacteristic
847C2#2261897511yescharacteristic
848C2#2261899011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1753C2
prime radicalC2×#14556561C4
cosocleC22×C4×C73C24
hypercenter#1753D73
hypocenterC73#22038
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#17988663C2semidirect
2. C2×#17988550C2semidirect
4. #22610729C2semidirect
5. #22610725C2semidirect
6. #22610544C2semidirect
7. #22610538C2semidirect
8. #22610538C2semidirect
9. #22610537C2semidirect
10. #22610227C2semidirect
11. #22610227C2semidirect
12. #22610226C2semidirect
13. #22610116C2semidirect
14. #22609840C2semidirect
15. C73×#1753C2semidirect
18. C22×#11924011C22semidirect
24. C2×C4⋊#10596831C22semidirect
25. C2×C4⋊#10596831C22semidirect
26. C2×#14556520C22semidirect
37. C2×#14556503C22semidirect
38. C2×#14556503C22semidirect
39. C2×#14556503C22semidirect
40. C2×C8×Dic73C22semidirect
50. #17988342C22semidirect
51. #17988342C22semidirect
52. #17988341C22semidirect
53. #17988341C22semidirect
56. C2×#97×C73C22semidirect
57. C2×C4×C8×C73C22semidirect
59. #336×C73C22semidirect
60. #336×C73C22semidirect
131. C2×M16×C73D4semidirect
226. #11924005M16semidirect
439. #1753D73semidirect
440. C73#22038semidirect
467. C2×#97C2×D73semidirect
469. C2×C4×C8C2×D73semidirect
484. #336C2×D73semidirect
485. #336C2×D73semidirect
511. C2×M16D292semidirect

Maximal subgroups

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

subgroupindex
C2×#179886632
C2×#179885502
C4×#145565612
#226107292
#226107252
#226105442
#226105382
#226105372
#226102272
#226102262
#226101162
#226098402
C73×#17532
#2203873