Finite Group Databasebeta

← #33112532

Subgroups — #33112532

Order 18688.

944 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556587C211yesmaximal, characteristic
2#22610229C211yesmaximal, characteristic, complemented
3#22610227C211yesmaximal, characteristic, complemented
4#22610226C211yesmaximal, characteristic, complemented
5#22610226C211yesmaximal, characteristic, complemented
6#22610225C211yesmaximal, characteristic, complemented
7#22610225C211yesmaximal, characteristic, complemented
8#22610223C211yesmaximal, characteristic, complemented
9#22610223C211yesmaximal, characteristic, complemented
10#22610222C211yesmaximal, characteristic, complemented
11#22610220C211yesmaximal, characteristic, complemented
12#22610220C211yesmaximal, characteristic, complemented
13#22610073C211yesmaximal, characteristic, complemented
14#22610073C211yesmaximal, characteristic, complemented
15C73×#1869C211yesmaximal, characteristic, complemented
16C22×#11924012C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C22×C8×D73C2211yescharacteristic
19C2×#14556587C411yescharacteristic
20C2×C4×D292C2211yescharacteristic
21C2×C4×C22⋊D73C2211yescharacteristic
22C2×C4×C22⋊D73C2211yescharacteristic
23C2×C4×C22⋊D73C2211yescharacteristic
24C2×C4×C22⋊D73C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34#17988490C411yescharacteristic
35#17988488C411yescharacteristic
36#17988487C411yescharacteristic
37#17988487C411yescharacteristic
38#17988487C411yescharacteristic
39#17988487C411yescharacteristic
40#17988456C411yescharacteristic
41C42×Dic73C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44#17988341C2211yescharacteristic
45#17988341C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C23×C8×C73C2211yescharacteristic
53C2×C4×D4×C73C2211yescharacteristic
54C2×C22⋊C8×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×D292C2×C411yescharacteristic
60C22×C22⋊D73C2×C411yescharacteristic
61C22×C22⋊D73C2×C411yescharacteristic
62C22×C22⋊D73C2×C411yescharacteristic
63C22×C22⋊D73C2×C411yescharacteristic
64C22×C4×D73C2311yescharacteristic
65C22×C4×D73C2311yescharacteristic
66C2×#11924012—41no—
67C2×#11924012—41no—
68C2×#11924012—41no—
69C2×#11924011—41no—
70C2×#11924011—41no—
71C2×#11924011—41no—
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C2×C8×D73—41no—
77C2×C8×D73—41no—
78C2×C8×D73—41no—
79#14556587—24no—
80C4×D292—41no—
81C4×D292—41no—
82C4×C22⋊D73—41no—
83C4×C22⋊D73—41no—
84C4×C22⋊D73—41no—
85C4×C22⋊D73—41no—
86C4×C22⋊D73—41no—
87C4×C22⋊D73—41no—
88C4×C22⋊D73—41no—
89C4×C22⋊D73—41no—
90C2×C4⋊Dic73C2×C411yescharacteristic
91C2×#11924007C2×C411yescharacteristic
92C2×#11924007C2×C411yescharacteristic
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×Dic73C2×C411yescharacteristic
106C2×C4×Dic73C2×C411yescharacteristic
107C2×C4×Dic73C2×C411yescharacteristic
108C2×C4×Dic73C2×C411yescharacteristic
109C2×C4×Dic73C2311yescharacteristic
110C2×C4×Dic73C2311yescharacteristic
111C22⋊#10596831—41no—
112C22⋊#10596831—41no—
113C22⋊#10596831—41no—
114#14556503—41no—
115#14556503—41no—
116#14556503—41no—
117#14556503—41no—
118#14556503—41no—
119#14556503—41no—
120C22×D4×C73C2×C411yescharacteristic
121C23×C4×C73C2311yescharacteristic
122C23×C4×C73C2311yescharacteristic
123C22×C8×C73—41no—
124C22×C8×C73—41no—
125C22×C8×C73—41no—
126C22×C8×C73C2311yescharacteristic
127C22×C8×C73C2311yescharacteristic
128C22×C8×C73C2311yescharacteristic
129C22×C8×C73C2311yescharacteristic
130C4×D4×C73—41no—
131C4×D4×C73—41no—
132C2×C4⋊C4×C73C2×C411yescharacteristic
133C2×C22⋊C4×C73C2×C411yescharacteristic
134C2×C22⋊C4×C73C2×C411yescharacteristic
135C2×C42×C73C2311yescharacteristic
136C22⋊C8×C73—41no—
137C22⋊C8×C73—41no—
138C22⋊C8×C73—41no—
139C23×D73C22×C411yescharacteristic
140C23×D73C22×C411yescharacteristic
141C2×D292—22no—
142C2×D292—22no—
143C2×D292—41no—
144C2×C22⋊D73—22no—
145C2×C22⋊D73—22no—
146C2×C22⋊D73—22no—
147C2×C22⋊D73—22no—
148C2×C22⋊D73—22no—
149C2×C22⋊D73—41no—
150C2×C22⋊D73—41no—
151C2×C22⋊D73—41no—
152C2×C22⋊D73—41no—
153C2×C22⋊D73—41no—
154C2×C22⋊D73—41no—
155C2×C22⋊D73M1614yescomplemented
156C22×Dic73C22×C411yescharacteristic
157C22×Dic73C22×C411yescharacteristic
158C22×Dic73C22×C411yescharacteristic
159C22×Dic73C22×C411yescharacteristic
160C22×Dic73C22×C411yescharacteristic
161C22×Dic73C22×C411yescharacteristic
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—21no—
166C2×C4×D73—21no—
167C2×C4×D73—21no—
168C2×C4×D73—21no—
169C2×C4×D73—21no—
170C2×C4×D73—21no—
171C2×C4×D73—21no—
172C2×C4×D73—21no—
173C2×C4×D73—21no—
174#11924012—44no—
175#11924011—44no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—21no—
180C2×#10596831—21no—
181C2×#10596831—21no—
182C2×#10596831—21no—
183C2×#10596831—21no—
184C2×#10596831—21no—
185C2×#10596831—21no—
186C2×#10596831—21no—
187C2×#10596831—21no—
188C8×D73—44no—
189C4⋊Dic73—41no—
190#11924007—41no—
191#11924007—41no—
192#11924007—41no—
193#11924007—41no—
194C22⋊Dic73—41no—
195C22⋊Dic73—41no—
196C22⋊Dic73—41no—
197C22⋊Dic73—41no—
198#11924005—41no—
199#11924005—41no—
200#11924005—41no—
201#11924005—41no—
202#11924005—41no—
203#11924005—41no—
204C4×Dic73—22no—
205C4×Dic73—21no—
206C4×Dic73—21no—
207C4×Dic73—21no—
208C4×Dic73—21no—
209C4×Dic73—22no—
210C4×Dic73—22no—
211C4×Dic73—41no—
212C24×C73C22×C411yescharacteristic
213C24×C73C22×C411yescharacteristic
214C2×D4×C73—22no—
215C2×D4×C73—22no—
216C2×D4×C73—41no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73C22×C411yescharacteristic
230C22×C4×C73C22×C411yescharacteristic
231C22×C4×C73C22×C411yescharacteristic
232C22×C4×C73C22×C411yescharacteristic
233C22×C4×C73C2411yescharacteristic
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—44no—
247C4⋊C4×C73—41no—
248C22⋊C4×C73—41no—
249C22⋊C4×C73—41no—
250C42×C73—21no—
251C42×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73C2×M1612yes—
266C23×C73C23×C411yescharacteristic
267C22×D73—21no—
268C22×D73—21no—
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×D73C2×M1612yes—
281D4×C73—44no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73#13112yes—
302C2×C4×C73H(5,𝔽2)11yescharacteristic
303C2×C4×C73H(5,𝔽2)11yescharacteristic
304C2×C4×C73H(5,𝔽2)11yescharacteristic
305C2×C4×C73H(5,𝔽2)11yescharacteristic
306C2×C4×C73H(5,𝔽2)11yescharacteristic
307C2×C4×C73H(5,𝔽2)11yescharacteristic
308C22⋊D73—44no—
309C22⋊D73—44no—
310C22⋊D73—44no—
311C22⋊D73—44no—
312C2×Dic73—21no—
313C2×Dic73—21no—
314C2×Dic73—21no—
315C2×Dic73—21no—
316C2×Dic73—21no—
317C2×Dic73—21no—
318C2×Dic73—21no—
319C2×Dic73—21no—
320C2×Dic73—21no—
321C2×Dic73—21no—
322C2×Dic73—21no—
323C2×Dic73—21no—
324C2×Dic73—21no—
325C2×Dic73—21no—
326C2×Dic73—21no—
327C2×Dic73—21no—
328C2×Dic73C2×M1612yes—
329C2×Dic73#13112yes—
330D292—44no—
331C4×D73—41no—
332C4×D73—41no—
333C4×D73—41no—
334C4×D73—41no—
335C4×D73—41no—
336C4×D73—41no—
337C4×D73—41no—
338C4×D73—41no—
339C8×C73—41no—
340C8×C73—41no—
341C8×C73—41no—
342C8×C73—41no—
343#10596831—41no—
344#10596831—41no—
345#10596831—41no—
346#10596831—41no—
347C22×C73—22no—
348C22×C73—22no—
349C22×C73—22no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73—41no—
355C22×C73—41no—
356C22×C73—41no—
357C22×C73—41no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73#51811yescharacteristic
362C22×C73#51811yescharacteristic
363C22×C73#51811yescharacteristic
364C22×C73C22×M1611yescharacteristic
365C22×C73C2×#13111yescharacteristic
366C22×C73C2×#13111yescharacteristic
367C22×C73#56811yescharacteristic
368C2×D73—22no—
369C2×D73—22no—
370C2×D73—22no—
371C2×D73—41no—
372C2×D73—41no—
373C2×D73—41no—
374C2×D73—41no—
375C2×D73—41no—
376C2×D73—41no—
377C2×D73—41no—
378C2×D73—41no—
379C2×D73—41no—
380C2×D73—41no—
381C2×D73—41no—
382C4×C73—22no—
383C4×C73—41no—
384C4×C73—41no—
385C4×C73—41no—
386C4×C73#56011yescharacteristic
387C4×C73#56011yescharacteristic
388C4×C73#56011yescharacteristic
389C4×C73#56011yescharacteristic
390Dic73—22no—
391Dic73—22no—
392Dic73—41no—
393Dic73—41no—
394Dic73—41no—
395Dic73—41no—
396#23356—731nomaximal, Sylow
397C2×C73—42no—
398C2×C73—81no—
399C2×C73#238011yescharacteristic
400C2×C73#297311yescharacteristic
401C2×C73#297411yescharacteristic
402C2×C73#297411yescharacteristic
403C2×C73#297911yescharacteristic
404C2×C73#298111yescharacteristic
405C2×C73#298111yescharacteristic
406D73—42no—
407D73—81no—
408C4×#127—731no—
409#1870—731no—
410#1870—731no—
411#1870—731no—
412#1870—731no—
413#1870—731no—
414#1870—731no—
415#1869—731no—
416#1869—731no—
417#1869—731no—
418#1869—731no—
419#1869—731no—
420#1869D7311yescharacteristic, complemented
421#1839—731no—
422#1839—731no—
423C73#2335611yescharacteristic, complemented, Sylow
424C22×M16—731no—
425C22×M16—731no—
426C23×C8—731no—
427C23×C8C2×D7311yescharacteristic
428C2×#127—731no—
429C2×C4×D4—731no—
430C2×C4×D4—731no—
431C2×C4×D4—731no—
432C2×C4×D4—731no—
433C2×C4×D4—731no—
434C2×C4×D4C2×D7311yescharacteristic
435C2×C22⋊C8—731no—
436C2×C22⋊C8—731no—
437C2×C22⋊C8—731no—
438C2×C22⋊C8—731no—
439C2×C22⋊C8—731no—
440C2×C22⋊C8—731no—
441C2×C22⋊C8—731no—
442C2×C22⋊C8—731no—
443C2×C22⋊C8—731no—
444C2×C22⋊C8C2×D7311yescharacteristic
445C2×C22⋊C8C2×D7311yescharacteristic
446C2×C22⋊C8C2×D7311yescharacteristic
447#390—731no—
448#390—731no—
449#390—731no—
450#390—731no—
451#390—731no—
452#390—731no—
453#384—731no—
454C43—731no—
455#336—731no—
456#336—731no—
457#336—731no—
458#336—731no—
459#336—731no—
460#336—731no—
461#336—731no—
462#336—731no—
463#336—731no—
464#336—731no—
465#336C2×D7311yescharacteristic
466#336C2×D7311yescharacteristic
467C22×D4—731no—
468C22×D4—731no—
469C22×D4—731no—
470C22×D4—731no—
471C22×D4—731no—
472C22×D4C4×D7311yescharacteristic
473C23×C4—731no—
474C23×C4—731no—
475C23×C4C22×D7311yescharacteristic
476C23×C4C22×D7311yescharacteristic
477C2×M16—2921no—
478C2×M16—2921no—
479C2×M16—2921no—
480C2×M16—2921no—
481C2×M16—2921no—
482C2×M16—2921no—
483C22×C8—41no—
484C22×C8—41no—
485C22×C8—41no—
486C22×C8—2921no—
487C22×C8—2921no—
488C22×C8—2921no—
489C22×C8—731no—
490C22×C8—731no—
491C22×C8—731no—
492C22×C8—731no—
493C22×C8C22×D7311yescharacteristic
494C22×C8C22×D7311yescharacteristic
495C22×C8C22×D7311yescharacteristic
496C22×C8C22×D7311yescharacteristic
497#127—1464no—
498C4×D4—41no—
499C4×D4—41no—
500C4×D4—2921no—
501C4×D4—2921no—
502C4×D4—2921no—
503C4×D4—2921no—
504C4×D4—2921no—
505C4×D4—2921no—
506C4×D4—2921no—
507C4×D4—2921no—
508C4×D4—2921no—
509C4×D4—2921no—
510C2×C4⋊C4—731no—
511C2×C4⋊C4—731no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4—731no—
514C2×C4⋊C4—731no—
515C2×C4⋊C4C4×D7311yescharacteristic
516C2×C22⋊C4—731no—
517C2×C22⋊C4—731no—
518C2×C22⋊C4—731no—
519C2×C22⋊C4—731no—
520C2×C22⋊C4—731no—
521C2×C22⋊C4—731no—
522C2×C22⋊C4—731no—
523C2×C22⋊C4—731no—
524C2×C22⋊C4—731no—
525C2×C22⋊C4—731no—
526C2×C22⋊C4C4×D7311yescharacteristic
527C2×C22⋊C4C4×D7311yescharacteristic
528C2×C42—731no—
529C2×C42—731no—
530C2×C42—731no—
531C2×C42—731no—
532C2×C42—731no—
533C2×C42—731no—
534C2×C42C22×D7311yescharacteristic
535C22⋊C8—41no—
536C22⋊C8—41no—
537C22⋊C8—41no—
538C22⋊C8—2921no—
539C22⋊C8—2921no—
540C22⋊C8—2921no—
541C22⋊C8—2921no—
542C22⋊C8—2921no—
543C22⋊C8—2921no—
544C22⋊C8—2921no—
545C22⋊C8—2921no—
546C22⋊C8—2921no—
547C24—731no—
548C24—731no—
549C24C2×C4×D7311yescharacteristic
550C24C2×C4×D7311yescharacteristic
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—41no—
554C2×D4—2921no—
555C2×D4—2921no—
556C2×D4—2921no—
557C2×D4—2921no—
558C2×D4—2921no—
559C2×D4—2921no—
560C2×D4—2921no—
561C2×D4—734no—
562C2×D4—1462no—
563C2×D4—1462no—
564C2×D4—1462no—
565C2×D4—1462no—
566C2×D4—1462no—
567C2×D4—1462no—
568C2×D4—1462no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—731no—
582C22×C4—731no—
583C22×C4—731no—
584C22×C4—731no—
585C22×C4—731no—
586C22×C4—731no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1461no—
596C22×C4—1461no—
597C22×C4—1461no—
598C22×C4—1461no—
599C22×C4C2×C4×D7311yescharacteristic
600C22×C4C2×C4×D7311yescharacteristic
601C22×C4C2×C4×D7311yescharacteristic
602C22×C4C2×C4×D7311yescharacteristic
603C22×C4C23×D7311yescharacteristic
604M16—2924no—
605M16—2924no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—44no—
619C2×C8—2924no—
620C2×C8—1461no—
621C2×C8—1461no—
622C2×C8—1461no—
623C2×C8—1461no—
624C2×C8—1461no—
625C2×C8—1461no—
626C2×C8—1461no—
627C2×C8—1461no—
628C2×C8—1461no—
629C2×C8—1461no—
630C2×C8—1461no—
631C2×C8—1461no—
632C4⋊C4—41no—
633C4⋊C4—2921no—
634C4⋊C4—2921no—
635C4⋊C4—2921no—
636C4⋊C4—2921no—
637C4⋊C4—2921no—
638C22⋊C4—41no—
639C22⋊C4—41no—
640C22⋊C4—2921no—
641C22⋊C4—2921no—
642C22⋊C4—2921no—
643C22⋊C4—2921no—
644C22⋊C4—2921no—
645C22⋊C4—2921no—
646C22⋊C4—2921no—
647C22⋊C4—2921no—
648C22⋊C4—2921no—
649C22⋊C4—2921no—
650C42—21no—
651C42—21no—
652C42—2921no—
653C42—1462no—
654C42—1462no—
655C42—1462no—
656C42—1461no—
657C42—1461no—
658C42—1461no—
659C42—1461no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—732no—
674C23—1461no—
675C23—1461no—
676C23—1461no—
677C23—1461no—
678C23—1461no—
679C23—1461no—
680C23—1461no—
681C23—1461no—
682C23—1461no—
683C23—1461no—
684C23—1461no—
685C23—1461no—
686C23—1461no—
687C23M16×D7312yes—
688C23C22×C4×D7311yescharacteristic
689D4—44no—
690D4—2924no—
691D4—2924no—
692D4—2924no—
693D4—2924no—
694D4—2924no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—2921no—
715C2×C4—2921no—
716C2×C4—2921no—
717C2×C4—2921no—
718C2×C4—2921no—
719C2×C4—2921no—
720C2×C4—2921no—
721C2×C4—2921no—
722C2×C4—732no—
723C2×C4—732no—
724C2×C4—1461no—
725C2×C4—1461no—
726C2×C4—1461no—
727C2×C4—1461no—
728C2×C4—1461no—
729C2×C4—1461no—
730C2×C4—1461no—
731C2×C4—1461no—
732C2×C4—1461no—
733C2×C4—1461no—
734C2×C4—1461no—
735C2×C4—1461no—
736C2×C4—1461no—
737C2×C4—1461no—
738C2×C4—1461no—
739C2×C4—1461no—
740C2×C4#1455659712yes—
741C2×C4#1455663611yescharacteristic
742C2×C4#1455663611yescharacteristic
743C2×C4#1455663611yescharacteristic
744C2×C4#1455663611yescharacteristic
745C2×C4#1455663711yescharacteristic
746C2×C4#1455663711yescharacteristic
747C8—41no—
748C8—41no—
749C8—41no—
750C8—41no—
751C8—2921no—
752C8—2921no—
753C8—2921no—
754C8—2921no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—2921no—
770C22—2921no—
771C22—2921no—
772C22—2921no—
773C22—2921no—
774C22—2921no—
775C22—2921no—
776C22—2921no—
777C22—2921no—
778C22—2921no—
779C22—2921no—
780C22—1462no—
781C22—1462no—
782C22—1462no—
783C22#1798905911yescharacteristic
784C22#1798905911yescharacteristic
785C22#1798906011yescharacteristic
786C22C2×M16×D7311yescharacteristic
787C22#131×D7311yescharacteristic
788C22C2×#1455659711yescharacteristic
789C22#1798935211yescharacteristic
790C4—22no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—2921no—
795C4—2921no—
796C4—2921no—
797C4—2921no—
798C4—1462no—
799C4—1462no—
800C4#1798932511yescharacteristic
801C4#1798932511yescharacteristic
802C4#1798932611yescharacteristic
803C4#1798932711yescharacteristic
804C2—42no—
805C2—81no—
806C2—2922no—
807C2—5841no—
808C2#2261310611yescharacteristic
809C2#2261895611yescharacteristic
810C2#2261896111yescharacteristic
811C2#2261896211yescharacteristic
812C2#2261899411yescharacteristic
813C2#2261900411yescharacteristic
814C2#2261900511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1869C2
prime radicalC2×#14556587C4
cosocleC22×C4×C73C24
hypercenter#1869D73
hypocenterC73#23356
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. #22610229C2semidirect
3. #22610227C2semidirect
4. #22610226C2semidirect
5. #22610226C2semidirect
6. #22610225C2semidirect
7. #22610225C2semidirect
8. #22610223C2semidirect
9. #22610223C2semidirect
10. #22610222C2semidirect
11. #22610220C2semidirect
12. #22610220C2semidirect
13. #22610073C2semidirect
14. #22610073C2semidirect
15. C73×#1869C2semidirect
155. C2×C22⋊D73M16semidirect
420. #1869D73semidirect
423. C73#23356semidirect

Maximal subgroups

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

subgroupindex
C4×#145565872
#226102292
#226102272
#226102262
#226102252
#226102232
#226102222
#226102202
#226100732
C73×#18692
#2335673