Finite Group Databasebeta

← #33097088

Subgroups — #33097088

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×#17988662C211yesmaximal, characteristic, complemented
2C2×#17988549C211yesmaximal, characteristic, complemented
3C4×#14556559C211yesmaximal, characteristic
4#22610723C211yesmaximal, characteristic, complemented
5#22610544C211yesmaximal, characteristic, complemented
6#22610540C211yesmaximal, characteristic, complemented
7#22610540C211yesmaximal, characteristic, complemented
8#22610536C211yesmaximal, characteristic, complemented
9#22610229C211yesmaximal, characteristic, complemented
10#22610226C211yesmaximal, characteristic, complemented
11#22610225C211yesmaximal, characteristic, complemented
12#22610112C211yesmaximal, characteristic, complemented
13#22609840C211yesmaximal, characteristic, complemented
14#22609716C211yesmaximal, characteristic, complemented
15C73×#1955C211yesmaximal, characteristic, complemented
16C23×C4×D73C2211yescharacteristic
17C22×#11924012C2211yescharacteristic, complemented
18C22×#11924011C2211yescharacteristic
19C22×#11924011C2211yescharacteristic
20C2×#14556559C411yescharacteristic
21C2×C4×C22⋊D73C2211yescharacteristic
22C2×C4×C22⋊D73C2211yescharacteristic
23#17988662—24no—
24C2×#14556520C2211yescharacteristic, complemented
25C2×#14556520C2211yescharacteristic, complemented
26#17988549—24no—
27C2×C22⋊#10596831C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29C2×C22⋊#10596831C2211yescharacteristic, complemented
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556503C2211yescharacteristic
35C2×#14556503C2211yescharacteristic
36C2×C8×Dic73C2211yescharacteristic, complemented
37C2×C8×Dic73C2211yescharacteristic, complemented
38#17988467C411yescharacteristic
39#17988463C411yescharacteristic
40#17988463C411yescharacteristic
41#17988459C411yescharacteristic
42#17988458C411yescharacteristic
43#17988458C411yescharacteristic
44#17988442C411yescharacteristic
45C4×#11924005C2211yescharacteristic
46C4×#11924005C2211yescharacteristic
47C4×C22⋊Dic73C2211yescharacteristic
48#17988342C2211yescharacteristic, complemented
49#17988342C2211yescharacteristic, complemented
50#17988341C2211yescharacteristic, complemented
51#17988341C2211yescharacteristic, complemented
52#17988341C2211yescharacteristic, complemented
53#17988341C2211yescharacteristic, complemented
54C2×C4×D4×C73C2211yescharacteristic
55C2×C4⋊C8×C73C2211yescharacteristic, complemented
56C2×C22⋊C8×C73C2211yescharacteristic
57C2×C22⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic, complemented
59C2×C22⋊C8×C73C2211yescharacteristic, complemented
60C2×#97×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—
78C2×#11924011—22no—
79C2×#11924011—41no—
80C2×#11924011—41no—
81C2×#11924011—41no—
82C2×#11924011—41no—
83C2×#11924011D414yescomplemented
84C22×#10596831C2311yescharacteristic
85C22×#10596831C2311yescharacteristic
86C22×#10596831C2311yescharacteristic
87C22×#10596831C2311yescharacteristic
88#14556559—24no—
89C4×C22⋊D73—22no—
90C4×C22⋊D73—22no—
91C4×C22⋊D73—41no—
92C4×C22⋊D73—41no—
93C2×#11924007C2×C411yescharacteristic
94C2×#11924007C2×C411yescharacteristic
95C2×C22⋊Dic73C2×C411yescharacteristic
96C2×C22⋊Dic73C2×C411yescharacteristic
97C2×C22⋊Dic73C2×C411yescharacteristic
98C2×C22⋊Dic73C2×C411yescharacteristic
99C2×#11924005C2×C411yescharacteristic
100C2×#11924005C2×C411yescharacteristic
101C2×#11924005C2×C411yescharacteristic
102C2×#11924005C2×C411yescharacteristic
103C2×#11924005C2×C411yescharacteristic
104C2×#11924005C2×C411yescharacteristic
105C2×C4×Dic73C2311yescharacteristic
106C2×C4×Dic73C2311yescharacteristic
107#14556520—22no—
108#14556520—41no—
109C22⋊#10596831—22no—
110C22⋊#10596831—41no—
111C22⋊#10596831—41no—
112#14556503—22no—
113#14556503—22no—
114#14556503—22no—
115#14556503—22no—
116#14556503—41no—
117#14556503—41no—
118C8×Dic73—22no—
119C8×Dic73—41no—
120#14556498C2×C411yescharacteristic
121#14556498C2×C411yescharacteristic
122#14556498C2×C411yescharacteristic
123#14556498C2×C411yescharacteristic
124#14556498C2×C411yescharacteristic
125#14556498C2×C411yescharacteristic
126C22×D4×C73C2×C411yescharacteristic
127C23×C4×C73C2311yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C22×C8×C73C2311yescharacteristic
130C22×C8×C73C2311yescharacteristic
131C22×C8×C73C2311yescharacteristic
132C22×C8×C73C2311yescharacteristic
133C4×D4×C73—41no—
134C4×D4×C73—41no—
135C2×C4⋊C4×C73C2×C411yescharacteristic
136C2×C22⋊C4×C73C2×C411yescharacteristic
137C2×C22⋊C4×C73C2×C411yescharacteristic
138C2×C42×C73C2311yescharacteristic
139C4⋊C8×C73—41no—
140C22⋊C8×C73—22no—
141C22⋊C8×C73—22no—
142C22⋊C8×C73—41no—
143C22⋊C8×C73—41no—
144#97×C73—41no—
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—22no—
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—21no—
170C2×C4×D73—21no—
171C2×C4×D73—21no—
172C2×C4×D73—21no—
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—22no—
181C2×C4×D73—44no—
182C2×C4×D73—44no—
183C2×C4×D73—44no—
184C2×C4×D73—44no—
185C2×C4×D73—41no—
186C2×C4×D73—41no—
187C2×C4×D73—41no—
188C2×C4×D73—41no—
189C2×C4×D73C2×D412yes—
190C2×C4×D73#4112yes—
191#11924012—44no—
192#11924011—44no—
193#11924011—44no—
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—
204C2×#10596831—21no—
205C2×#10596831C2×D412yes—
206#11924007—22no—
207#11924007—41no—
208C22⋊Dic73—22no—
209C22⋊Dic73—41no—
210C22⋊Dic73—41no—
211C22⋊Dic73M1614yescomplemented
212#11924005—22no—
213#11924005—22no—
214#11924005—22no—
215#11924005—22no—
216#11924005—41no—
217#11924005—41no—
218C4×Dic73—21no—
219C4×Dic73—21no—
220C4×Dic73—21no—
221C4×Dic73—21no—
222C24×C73C22×C411yescharacteristic
223C24×C73C22×C411yescharacteristic
224C2×D4×C73—22no—
225C2×D4×C73—41no—
226C2×D4×C73—41no—
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×C73C22×C411yescharacteristic
240C22×C4×C73C22×C411yescharacteristic
241C22×C4×C73C22×C411yescharacteristic
242C22×C4×C73C22×C411yescharacteristic
243C22×C4×C73C2411yescharacteristic
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×C73—21no—
255C2×C8×C73C2×D412yes—
256C4⋊C4×C73—41no—
257C22⋊C4×C73—41no—
258C22⋊C4×C73—41no—
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×C73C2×M1612yes—
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×D73C4×D412yes—
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—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—41no—
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—44no—
342C2×Dic73C4×D412yes—
343C2×Dic73C2×M1612yes—
344C2×Dic73C2×M1612yes—
345C4×D73—22no—
346C4×D73—22no—
347C4×D73—22no—
348C4×D73—22no—
349C4×D73—44no—
350C4×D73—44no—
351C4×D73—41no—
352C4×D73—41no—
353C4×D73—41no—
354C4×D73—41no—
355C8×C73—22no—
356C8×C73—41no—
357C8×C73—41no—
358C8×C73—41no—
359#10596831—22no—
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—41no—
400C4×C73—41no—
401C4×C73—41no—
402C4×C73—41no—
403C4×C73#53411yescharacteristic
404C4×C73#53511yescharacteristic
405C4×C73#53811yescharacteristic
406C4×C73#53811yescharacteristic
407Dic73—22no—
408Dic73—22no—
409Dic73—22no—
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×#436—731no—
426C2×#407—731no—
427C4×#120—731no—
428#1955D7311yescharacteristic, complemented
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×M16—731no—
444C22×M16—731no—
445C2×#120—731no—
446C2×C4×D4—731no—
447C2×C4×D4—731no—
448C2×C4×D4C2×D7311yescharacteristic
449#436—1464no—
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⋊C8C2×D7311yescharacteristic
464C2×C22⋊C8C2×D7311yescharacteristic
465C2×C22⋊C8C2×D7311yescharacteristic, complemented
466C2×C22⋊C8C2×D7311yescharacteristic, complemented
467C2×#97C2×D7311yescharacteristic, complemented
468C2×C4×C8—731no—
469C2×C4×C8—731no—
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—2921no—
504C2×M16—2921no—
505C2×M16—2921no—
506C2×M16—2921no—
507C2×M16—2921no—
508C2×M16—2921no—
509C2×M16—734no—
510C2×M16—1462no—
511C2×M16—1462no—
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—41no—
522C4×D4—41no—
523C4×D4—2921no—
524C4×D4—2921no—
525C4×D4—1462no—
526C4×D4—1462no—
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—41no—
546C4⋊C8—2921no—
547C4⋊C8—1462no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—41no—
551C22⋊C8—41no—
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—41no—
562C4×C8—2921no—
563C4×C8—1462no—
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—41no—
583C2×D4—41no—
584C2×D4—2921no—
585C2×D4—2921no—
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—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—2921no—
603C22×C4—2921no—
604C22×C4—2921no—
605C22×C4—2921no—
606C22×C4—2924no—
607C22×C4—2924no—
608C22×C4—2924no—
609C22×C4—2924no—
610C22×C4—2921no—
611C22×C4—2921no—
612C22×C4—731no—
613C22×C4—731no—
614C22×C4—731no—
615C22×C4—732no—
616C22×C4—732no—
617C22×C4—731no—
618C22×C4—731no—
619C22×C4—731no—
620C22×C4—1462no—
621C22×C4—1462no—
622C22×C4—1462no—
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×C4—1461no—
632C22×C4—1461no—
633C22×C4C2×C4×D7311yescharacteristic
634C22×C4C2×C4×D7311yescharacteristic
635C22×C4C2×C4×D7311yescharacteristic
636C22×C4C2×C4×D7311yescharacteristic
637C22×C4C23×D7311yescharacteristic
638M16—2924no—
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—21no—
652C2×C8—732no—
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×C8—1461no—
664C2×C8D4×D7312yes—
665C4⋊C4—41no—
666C4⋊C4—2921no—
667C4⋊C4—1462no—
668C22⋊C4—41no—
669C22⋊C4—41no—
670C22⋊C4—2921no—
671C22⋊C4—2921no—
672C22⋊C4—2921no—
673C22⋊C4—2921no—
674C22⋊C4—734no—
675C22⋊C4—1462no—
676C22⋊C4—1462no—
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—
720C23M16×D7312yes—
721C23C22×C4×D7311yescharacteristic
722D4—44no—
723D4—2924no—
724D4—2924no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—2924no—
746C2×C4—2924no—
747C2×C4—2924no—
748C2×C4—2921no—
749C2×C4—2921no—
750C2×C4—2921no—
751C2×C4—2921no—
752C2×C4—732no—
753C2×C4—732no—
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—1462no—
771C2×C4—1462no—
772C2×C4—1462no—
773C2×C4—1462no—
774C2×C4C2×D4×D7311yescharacteristic
775C2×C4#41×D7311yescharacteristic
776C2×C4#1455663611yescharacteristic
777C2×C4#1455663611yescharacteristic
778C2×C4#1455663611yescharacteristic
779C2×C4#1455663711yescharacteristic
780C8—22no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—2921no—
785C8—2921no—
786C8—2921no—
787C8—1462no—
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—
817C22C4×D4×D7311yescharacteristic
818C22#1798905911yescharacteristic
819C22#1798906011yescharacteristic
820C22C2×M16×D7311yescharacteristic
821C22#131×D7311yescharacteristic
822C22#1798935211yescharacteristic
823C22#1798935311yescharacteristic
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—2921no—
829C4—2921no—
830C4—2921no—
831C4—1462no—
832C4—1462no—
833C4—1462no—
834C4#1798914511yescharacteristic
835C4#1798915011yescharacteristic
836C4#1798916911yescharacteristic
837C4#1798917111yescharacteristic
838C2—42no—
839C2—81no—
840C2—2922no—
841C2—2922no—
842C2#2261259011yescharacteristic
843C2#2261865411yescharacteristic
844C2#2261866411yescharacteristic
845C2#2261896111yescharacteristic
846C2#2261897011yescharacteristic
847C2#2261897411yescharacteristic
848C2#2261899011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1955C2
prime radicalC2×#14556559C4
cosocleC22×C4×C73C24
hypercenter#1955D73
hypocenterC73#22038
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. C2×#17988662C2semidirect
2. C2×#17988549C2semidirect
4. #22610723C2semidirect
5. #22610544C2semidirect
6. #22610540C2semidirect
7. #22610540C2semidirect
8. #22610536C2semidirect
9. #22610229C2semidirect
10. #22610226C2semidirect
11. #22610225C2semidirect
12. #22610112C2semidirect
13. #22609840C2semidirect
14. #22609716C2semidirect
15. C73×#1955C2semidirect
17. C22×#11924012C22semidirect
24. C2×#14556520C22semidirect
25. C2×#14556520C22semidirect
29. C2×C22⋊#10596831C22semidirect
36. C2×C8×Dic73C22semidirect
37. C2×C8×Dic73C22semidirect
48. #17988342C22semidirect
49. #17988342C22semidirect
50. #17988341C22semidirect
51. #17988341C22semidirect
52. #17988341C22semidirect
53. #17988341C22semidirect
55. C2×C4⋊C8×C73C22semidirect
58. C2×C22⋊C8×C73C22semidirect
59. C2×C22⋊C8×C73C22semidirect
60. C2×#97×C73C22semidirect
83. C2×#11924011D4semidirect
211. C22⋊Dic73M16semidirect
428. #1955D73semidirect
440. C73#22038semidirect
452. C2×C4⋊C8C2×D73semidirect
465. C2×C22⋊C8C2×D73semidirect
466. C2×C22⋊C8C2×D73semidirect
467. C2×#97C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886622
C2×#179885492
C4×#145565592
#226107232
#226105442
#226105402
#226105362
#226102292
#226102262
#226102252
#226101122
#226098402
#226097162
C73×#19552
#2203873