Finite Group Databasebeta

← #33097096

Subgroups — #33097096

Order 18688.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988555C211yesmaximal, characteristic, complemented
2#22613146C211yesmaximal, 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#22610228C211yesmaximal, characteristic, complemented
10#22610228C211yesmaximal, characteristic, complemented
11#22610224C211yesmaximal, characteristic, complemented
12#22610108C211yesmaximal, characteristic, complemented
13#22609842C211yesmaximal, characteristic, complemented
14#22609712C211yesmaximal, characteristic, complemented
15C2×#436×C73C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C2×C4×C22⋊D73C2211yescharacteristic
19C2×C4×C22⋊D73C2211yescharacteristic
20C2×#14556520C2211yescharacteristic
21C2×#14556520C2211yescharacteristic
22#17988555—24no—
23C2×C22⋊#10596831C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556501C2211yescharacteristic
35C2×C8×Dic73C2211yescharacteristic
36#17988507C411yescharacteristic
37#17988504C411yescharacteristic
38#17988502C411yescharacteristic
39#17988502C411yescharacteristic
40#17988499C411yescharacteristic
41#17988496C411yescharacteristic
42#17988495C411yescharacteristic
43#17988495C411yescharacteristic
44C4×#11924005C2211yescharacteristic
45C4×#11924005C2211yescharacteristic
46C4×C22⋊Dic73C2211yescharacteristic
47#17988342C2211yescharacteristic
48#17988342C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53C22×M16×C73C2211yescharacteristic
54C22×M16×C73C2211yescharacteristic
55C2×C4×D4×C73C2211yescharacteristic
56#436×C73—24no—
57C2×C4⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60C2×C4×C8×C73C2211yescharacteristic
61C2×#11924028—22no—
62C2×#11924028—22no—
63C2×#11924028—41no—
64C2×#11924028—41no—
65C2×#11924028—41no—
66C2×#11924028—41no—
67C22×Dic146C2×C411yescharacteristic
68C22×D292C2×C411yescharacteristic
69C22×C22⋊D73C2×C411yescharacteristic
70C22×C22⋊D73C2×C411yescharacteristic
71C22×C22⋊D73C2×C411yescharacteristic
72C22×C22⋊D73C2×C411yescharacteristic
73C22×C4×D73C2311yescharacteristic
74C22×C4×D73C2311yescharacteristic
75C22×#10596831—22no—
76C22×#10596831—41no—
77C22×#10596831—41no—
78C22×#10596831C2311yescharacteristic
79C22×#10596831C2311yescharacteristic
80C22×#10596831C2311yescharacteristic
81C22×#10596831C2311yescharacteristic
82C4×C22⋊D73—41no—
83C4×C22⋊D73—41no—
84C4×C22⋊D73—41no—
85C4×C22⋊D73—41no—
86C2×#11924007C2×C411yescharacteristic
87C2×#11924007C2×C411yescharacteristic
88C2×C22⋊Dic73C2×C411yescharacteristic
89C2×C22⋊Dic73C2×C411yescharacteristic
90C2×C22⋊Dic73C2×C411yescharacteristic
91C2×C22⋊Dic73C2×C411yescharacteristic
92C2×#11924005C2×C411yescharacteristic
93C2×#11924005C2×C411yescharacteristic
94C2×#11924005C2×C411yescharacteristic
95C2×#11924005C2×C411yescharacteristic
96C2×#11924005C2×C411yescharacteristic
97C2×#11924005C2×C411yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99C2×C4×Dic73C2311yescharacteristic
100#14556520—41no—
101#14556520—41no—
102C22⋊#10596831—22no—
103C22⋊#10596831—41no—
104C22⋊#10596831—41no—
105#14556503—22no—
106#14556503—22no—
107#14556503—22no—
108#14556503—22no—
109#14556503—41no—
110#14556503—41no—
111#14556503—41no—
112#14556503—41no—
113#14556501—41no—
114C8×Dic73—41no—
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120#14556498C2×C411yescharacteristic
121C22×D4×C73C2×C411yescharacteristic
122C23×C4×C73C2311yescharacteristic
123C23×C4×C73C2311yescharacteristic
124C2×M16×C73—22no—
125C2×M16×C73—41no—
126C2×M16×C73—41no—
127C2×M16×C73—41no—
128C2×M16×C73—41no—
129C2×M16×C73D414yescomplemented
130C22×C8×C73C2311yescharacteristic
131C22×C8×C73C2311yescharacteristic
132C22×C8×C73C2311yescharacteristic
133C22×C8×C73C2311yescharacteristic
134C4×D4×C73—22no—
135C4×D4×C73—22no—
136C2×C4⋊C4×C73C2×C411yescharacteristic
137C2×C22⋊C4×C73C2×C411yescharacteristic
138C2×C22⋊C4×C73C2×C411yescharacteristic
139C2×C42×C73C2311yescharacteristic
140C4⋊C8×C73—22no—
141C22⋊C8×C73—22no—
142C22⋊C8×C73—22no—
143C4×C8×C73—22no—
144C23×D73C22×C411yescharacteristic
145C23×D73C22×C411yescharacteristic
146#11924028—44no—
147#11924028—44no—
148#11924028—44no—
149#11924028—44no—
150C2×Dic146—22no—
151C2×Dic146—41no—
152C2×Dic146—41no—
153C2×D292—22no—
154C2×D292—41no—
155C2×D292—41no—
156C2×C22⋊D73—22no—
157C2×C22⋊D73—22no—
158C2×C22⋊D73—22no—
159C2×C22⋊D73—41no—
160C2×C22⋊D73—41no—
161C2×C22⋊D73—41no—
162C2×C22⋊D73—41no—
163C2×C22⋊D73—41no—
164C2×C22⋊D73—41no—
165C2×C22⋊D73—41no—
166C2×C22⋊D73—41no—
167C2×C22⋊D73—41no—
168C22×Dic73C22×C411yescharacteristic
169C22×Dic73C22×C411yescharacteristic
170C22×Dic73C22×C411yescharacteristic
171C22×Dic73C22×C411yescharacteristic
172C22×Dic73C22×C411yescharacteristic
173C22×Dic73C22×C411yescharacteristic
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×#10596831—21no—
187C2×#10596831—21no—
188C2×#10596831—21no—
189C2×#10596831—21no—
190C2×#10596831—21no—
191C2×#10596831—21no—
192C2×#10596831—21no—
193C2×#10596831—21no—
194C2×#10596831—21no—
195C2×#10596831—21no—
196C2×#10596831—21no—
197C2×#10596831—21no—
198C2×#10596831—44no—
199#11924007—41no—
200#11924007—41no—
201C22⋊Dic73—22no—
202C22⋊Dic73—41no—
203C22⋊Dic73—41no—
204C22⋊Dic73—41no—
205#11924005—22no—
206#11924005—22no—
207#11924005—22no—
208#11924005—41no—
209#11924005—41no—
210#11924005—41no—
211C4×Dic73—21no—
212C4×Dic73—21no—
213C4×Dic73—21no—
214C4×Dic73—21no—
215C24×C73C22×C411yescharacteristic
216C24×C73C22×C411yescharacteristic
217C2×D4×C73—22no—
218C2×D4×C73—22no—
219C2×D4×C73—41no—
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×C73—21no—
230C22×C4×C73C22×C411yescharacteristic
231C22×C4×C73C22×C411yescharacteristic
232C22×C4×C73C22×C411yescharacteristic
233C22×C4×C73C22×C411yescharacteristic
234C22×C4×C73C2×D412yes—
235C22×C4×C73#4112yes—
236C22×C4×C73C2411yescharacteristic
237M16×C73—44no—
238M16×C73—44no—
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—21no—
247C2×C8×C73—21no—
248C2×C8×C73—21no—
249C2×C8×C73C2×D412yes—
250C2×C8×C73C2×D412yes—
251C4⋊C4×C73—22no—
252C22⋊C4×C73—22no—
253C22⋊C4×C73—22no—
254C42×C73—21no—
255C42×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×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73C4×D412yes—
270C23×C73C23×C411yescharacteristic
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—
285D4×C73—44no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73C4×D412yes—
305C2×C4×C73#13112yes—
306C2×C4×C73C22×D411yescharacteristic
307C2×C4×C73C2×#4111yescharacteristic
308C2×C4×C73H(5,𝔽2)11yescharacteristic
309C2×C4×C73H(5,𝔽2)11yescharacteristic
310C2×C4×C73H(5,𝔽2)11yescharacteristic
311C2×C4×C73H(5,𝔽2)11yescharacteristic
312C22⋊D73—44no—
313C22⋊D73—44no—
314C22⋊D73—44no—
315C22⋊D73—44no—
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×Dic73—21no—
329C2×Dic73—21no—
330C2×Dic73—21no—
331C2×Dic73—21no—
332C2×Dic73—21no—
333C2×Dic73#13112yes—
334D292—44no—
335C4×D73—41no—
336C4×D73—41no—
337C4×D73—41no—
338C4×D73—41no—
339C4×D73—41no—
340C4×D73—41no—
341C4×D73—41no—
342C4×D73—41no—
343Dic146—44no—
344C8×C73—22no—
345C8×C73—22no—
346C8×C73—41no—
347C8×C73—41no—
348#10596831—41no—
349#10596831—41no—
350#10596831—41no—
351#10596831—41no—
352C22×C73—22no—
353C22×C73—22no—
354C22×C73—22no—
355C22×C73—41no—
356C22×C73—41no—
357C22×C73—41no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73—41no—
363C22×C73—41no—
364C22×C73—41no—
365C22×C73—41no—
366C22×C73C2×C4×D411yescharacteristic
367C22×C73#51811yescharacteristic
368C22×C73#51811yescharacteristic
369C22×C73C2×#13111yescharacteristic
370C22×C73C2×#13111yescharacteristic
371C22×C73#56811yescharacteristic
372C22×C73#56811yescharacteristic
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—
382C2×D73—41no—
383C2×D73—41no—
384C2×D73—41no—
385C2×D73—41no—
386C2×D73—41no—
387C4×C73—22no—
388C4×C73—22no—
389C4×C73—41no—
390C4×C73—41no—
391C4×C73#53411yescharacteristic
392C4×C73#53511yescharacteristic
393C4×C73#53811yescharacteristic
394C4×C73#53811yescharacteristic
395Dic73—22no—
396Dic73—41no—
397Dic73—41no—
398Dic73—41no—
399Dic73—41no—
400Dic73—41no—
401#22039—731nomaximal, Sylow
402C2×C73—42no—
403C2×C73—81no—
404C2×C73#232111yescharacteristic
405C2×C73#293311yescharacteristic
406C2×C73#293511yescharacteristic
407C2×C73#297611yescharacteristic
408C2×C73#297811yescharacteristic
409C2×C73#297911yescharacteristic
410C2×C73#298111yescharacteristic
411D73—81no—
412D73—81no—
413C2×#436D7311yescharacteristic, complemented
414C2×#408—731no—
415#2388—731no—
416#1955—731no—
417#1954—731no—
418#1924—731no—
419#1923—731no—
420#1923—731no—
421#1923—731no—
422#1870—731no—
423#1870—731no—
424#1869—731no—
425#1850—731no—
426#1780—731no—
427#1753—731no—
428C73#2203911yescharacteristic, complemented, Sylow
429C22×#41—731no—
430C22×M16C2×D7311yescharacteristic
431C22×M16C2×D7311yescharacteristic
432C23×C8—731no—
433C2×C4×D4—731no—
434C2×C4×D4—731no—
435C2×C4×D4C2×D7311yescharacteristic
436#436—24no—
437C2×C4⋊C8—731no—
438C2×C4⋊C8—731no—
439C2×C4⋊C8C2×D7311yescharacteristic
440#408—1464no—
441C2×C22⋊C8—731no—
442C2×C22⋊C8—731no—
443C2×C22⋊C8—731no—
444C2×C22⋊C8—731no—
445C2×C22⋊C8—731no—
446C2×C22⋊C8—731no—
447C2×C22⋊C8—731no—
448C2×C22⋊C8—731no—
449C2×C22⋊C8—731no—
450C2×C22⋊C8—731no—
451C2×C22⋊C8—731no—
452C2×C22⋊C8C2×D7311yescharacteristic
453C2×C22⋊C8C2×D7311yescharacteristic
454C2×#97—731no—
455C2×C4×C8—731no—
456C2×C4×C8C2×D7311yescharacteristic
457#395—731no—
458#394—731no—
459#394—731no—
460#394—731no—
461#393—731no—
462#392—731no—
463#392—731no—
464#392—731no—
465C4×C22⋊C4—731no—
466C4×C22⋊C4—731no—
467C4×C22⋊C4—731no—
468#336—731no—
469#336—731no—
470#336—731no—
471#336—731no—
472#336—731no—
473#336—731no—
474C2×#41—2921no—
475C2×#41—2921no—
476C2×#41—2921no—
477C2×#41—2921no—
478C2×#41—1462no—
479C2×#41—1462no—
480C22×Q8—731no—
481C22×D4—731no—
482C22×D4—731no—
483C22×D4—731no—
484C22×D4—731no—
485C22×D4—731no—
486C22×D4C4×D7311yescharacteristic
487C23×C4—731no—
488C23×C4—731no—
489C23×C4C22×D7311yescharacteristic
490C23×C4C22×D7311yescharacteristic
491C2×M16—22no—
492C2×M16—41no—
493C2×M16—41no—
494C2×M16—41no—
495C2×M16—41no—
496C2×M16C22⋊D7314yescomplemented
497C22×C8—2921no—
498C22×C8—2921no—
499C22×C8—731no—
500C22×C8—731no—
501C22×C8—731no—
502C22×C8—731no—
503C22×C8—1462no—
504C22×C8C22×D7311yescharacteristic
505C22×C8C22×D7311yescharacteristic
506C22×C8C22×D7311yescharacteristic
507C22×C8C22×D7311yescharacteristic
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—2921no—
511C4×D4—2921no—
512C4×D4—2921no—
513C4×D4—2921no—
514C2×C4⋊C4—731no—
515C2×C4⋊C4—731no—
516C2×C4⋊C4C4×D7311yescharacteristic
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⋊C4—731no—
527C2×C22⋊C4C4×D7311yescharacteristic
528C2×C22⋊C4C4×D7311yescharacteristic
529C2×C42—731no—
530C2×C42—731no—
531C2×C42C22×D7311yescharacteristic
532C4⋊C8—22no—
533C4⋊C8—2921no—
534C4⋊C8—2921no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—2921no—
538C22⋊C8—2921no—
539C22⋊C8—2921no—
540C22⋊C8—2921no—
541C22⋊C8—2921no—
542C22⋊C8—2921no—
543C22⋊C8—1462no—
544C22⋊C8—1462no—
545C22⋊C8—1462no—
546C22⋊C8—1462no—
547C22⋊C8—1462no—
548#97—2921no—
549C4×C8—22no—
550C4×C8—2921no—
551#95—731no—
552#95—731no—
553#95—731no—
554#95—731no—
555#95—731no—
556#95—731no—
557C24—731no—
558C24—731no—
559C24C2×C4×D7311yescharacteristic
560C24C2×C4×D7311yescharacteristic
561#41—2924no—
562#41—2924no—
563#41—2924no—
564#41—2924no—
565C2×Q8—2921no—
566C2×Q8—2921no—
567C2×Q8—1462no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—41no—
571C2×D4—2921no—
572C2×D4—2921no—
573C2×D4—2921no—
574C2×D4—2921no—
575C2×D4—2921no—
576C2×D4—2921no—
577C2×D4—2921no—
578C2×D4—2921no—
579C2×D4—2921no—
580C2×D4—2921no—
581C2×D4—2921no—
582C2×D4—1462no—
583C2×D4—1462no—
584C2×D4—1462no—
585C2×D4—1462no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—731no—
597C22×C4—731no—
598C22×C4—731no—
599C22×C4—731no—
600C22×C4—731no—
601C22×C4—731no—
602C22×C4—1461no—
603C22×C4—1461no—
604C22×C4—1461no—
605C22×C4—1461no—
606C22×C4—1461no—
607C22×C4—1461no—
608C22×C4—1461no—
609C22×C4—1461no—
610C22×C4—1461no—
611C22×C4—1461no—
612C22×C4—1461no—
613C22×C4—1461no—
614C22×C4C2×C4×D7311yescharacteristic
615C22×C4C2×C4×D7311yescharacteristic
616C22×C4C2×C4×D7311yescharacteristic
617C22×C4C2×C4×D7311yescharacteristic
618C22×C4C2×C22⋊D7312yes—
619C22×C4#1192402812yes—
620C22×C4C23×D7311yescharacteristic
621M16—44no—
622M16—44no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—2924no—
634C2×C8—1461no—
635C2×C8—1461no—
636C2×C8—1461no—
637C2×C8—1461no—
638C2×C8—1461no—
639C2×C8—1461no—
640C2×C8—1461no—
641C2×C8—1461no—
642C2×C8—1461no—
643C2×C8—1461no—
644C2×C8—1461no—
645C2×C8—1461no—
646C2×C8C2×C22⋊D7312yes—
647C2×C8C2×C22⋊D7312yes—
648C4⋊C4—22no—
649C4⋊C4—2921no—
650C4⋊C4—2921no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—2921no—
654C22⋊C4—2921no—
655C22⋊C4—2921no—
656C22⋊C4—2921no—
657C22⋊C4—2921no—
658C22⋊C4—2921no—
659C22⋊C4—1462no—
660C22⋊C4—1462no—
661C22⋊C4—1462no—
662C22⋊C4—1462no—
663C42—21no—
664C42—21no—
665C42—1461no—
666C42—1461no—
667C42—1461no—
668C42—1461no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—1461no—
683C23—1461no—
684C23—1461no—
685C23—1461no—
686C23—1461no—
687C23—1461no—
688C23—1461no—
689C23—1461no—
690C23—1461no—
691C23—1461no—
692C23—1461no—
693C23—1461no—
694C23—1461no—
695C23—1461no—
696C23C4×C22⋊D7312yes—
697C23C22×C4×D7311yescharacteristic
698Q8—2924no—
699D4—44no—
700D4—2924no—
701D4—2924no—
702D4—2924no—
703D4—2924no—
704D4—2924no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—2921no—
724C2×C4—2921no—
725C2×C4—2921no—
726C2×C4—2921no—
727C2×C4—2921no—
728C2×C4—2921no—
729C2×C4—2921no—
730C2×C4—2921no—
731C2×C4—732no—
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—1461no—
741C2×C4—1461no—
742C2×C4—1461no—
743C2×C4—1461no—
744C2×C4—1461no—
745C2×C4—1461no—
746C2×C4—1461no—
747C2×C4—1461no—
748C2×C4—1461no—
749C2×C4C4×C22⋊D7312yes—
750C2×C4#1455659912yes—
751C2×C4C22×C22⋊D7311yescharacteristic
752C2×C4C2×#1192402811yescharacteristic
753C2×C4#1455663611yescharacteristic
754C2×C4#1455663611yescharacteristic
755C2×C4#1455663711yescharacteristic
756C2×C4#1455663711yescharacteristic
757C8—22no—
758C8—22no—
759C8—41no—
760C8—41no—
761C8—2921no—
762C8—2921no—
763C8—2921no—
764C8—2921no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—2921no—
780C22—2921no—
781C22—2921no—
782C22—2921no—
783C22—2921no—
784C22—2921no—
785C22—2921no—
786C22—2921no—
787C22—2921no—
788C22—2921no—
789C22—2921no—
790C22—2921no—
791C22—2921no—
792C22—2921no—
793C22C2×C4×C22⋊D7311yescharacteristic
794C22#1798905911yescharacteristic
795C22#1798905911yescharacteristic
796C22#131×D7311yescharacteristic
797C22C2×#1455659911yescharacteristic
798C22#1798935211yescharacteristic
799C22#1798935311yescharacteristic
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—2921no—
805C4—2921no—
806C4—2921no—
807C4—2921no—
808C4—2921no—
809C4—1462no—
810C4#1798914611yescharacteristic
811C4#1798915111yescharacteristic
812C4#1798917011yescharacteristic
813C4#1798917011yescharacteristic
814C2—42no—
815C2—81no—
816C2—5841no—
817C2—5841no—
818C2#2261258511yescharacteristic
819C2#2261865611yescharacteristic
820C2#2261867311yescharacteristic
821C2#2261897511yescharacteristic
822C2#2261898811yescharacteristic
823C2#2261899611yescharacteristic
824C2#2261900811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC2×#436×C73C2
prime radical#22613146C2
cosocleC22×C4×C73C24
hypercenterC2×#436D73
hypocenterC73#22039
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×#17988555C2semidirect
3. #22610727C2semidirect
4. #22610723C2semidirect
5. #22610543C2semidirect
6. #22610537C2semidirect
7. #22610537C2semidirect
8. #22610536C2semidirect
9. #22610228C2semidirect
10. #22610228C2semidirect
11. #22610224C2semidirect
12. #22610108C2semidirect
13. #22609842C2semidirect
14. #22609712C2semidirect
15. C2×#436×C73C2semidirect
129. C2×M16×C73D4semidirect
413. C2×#436D73semidirect
428. C73#22039semidirect
496. C2×M16C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179885552
#226131462
#226107272
#226107232
#226105432
#226105372
#226105362
#226102282
#226102242
#226101082
#226098422
#226097122
C2×#436×C732
#2203973