Finite Group Databasebeta

← #33097103

Subgroups — #33097103

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×#17988662C211yesmaximal, characteristic, complemented
2C2×#17988552C211yesmaximal, characteristic, complemented
3#22613146C211yesmaximal, 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#22610220C211yesmaximal, characteristic, complemented
12#22610107C211yesmaximal, characteristic, complemented
13#22609842C211yesmaximal, characteristic, complemented
14#22609716C211yesmaximal, characteristic, complemented
15C73×#1955C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17C22×#11924012C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19C22×C8×D73C2211yescharacteristic
20C2×C4×C22⋊D73C2211yescharacteristic
21C2×C4×C22⋊D73C2211yescharacteristic
22#17988662—24no—
23C2×#14556520C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25#17988552—24no—
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556503C2211yescharacteristic
35C2×C8×Dic73C2211yescharacteristic
36C2×C8×Dic73C2211yescharacteristic
37#17988507C411yescharacteristic
38#17988504C411yescharacteristic
39#17988502C411yescharacteristic
40#17988502C411yescharacteristic
41#17988499C411yescharacteristic
42#17988496C411yescharacteristic
43#17988495C411yescharacteristic
44#17988495C411yescharacteristic
45C4×#11924005C2211yescharacteristic
46C4×#11924005C2211yescharacteristic
47C4×C22⋊Dic73C2211yescharacteristic
48#17988342C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C2×C4×D4×C73C2211yescharacteristic
55C2×C4⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57C2×C22⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60C2×#97×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
75C2×#11924012—22no—
76C2×#11924012—41no—
77C2×#11924012—41no—
78C2×#11924011—41no—
79C2×#11924011—41no—
80C2×#11924011D414yescomplemented
81C22×#10596831C2311yescharacteristic
82C22×#10596831C2311yescharacteristic
83C22×#10596831C2311yescharacteristic
84C22×#10596831C2311yescharacteristic
85C2×C8×D73—22no—
86C2×C8×D73—41no—
87C2×C8×D73—41no—
88C4×C22⋊D73—22no—
89C4×C22⋊D73—22no—
90C4×C22⋊D73—41no—
91C4×C22⋊D73—41no—
92C2×#11924007C2×C411yescharacteristic
93C2×#11924007C2×C411yescharacteristic
94C2×C22⋊Dic73C2×C411yescharacteristic
95C2×C22⋊Dic73C2×C411yescharacteristic
96C2×C22⋊Dic73C2×C411yescharacteristic
97C2×C22⋊Dic73C2×C411yescharacteristic
98C2×#11924005C2×C411yescharacteristic
99C2×#11924005C2×C411yescharacteristic
100C2×#11924005C2×C411yescharacteristic
101C2×#11924005C2×C411yescharacteristic
102C2×#11924005C2×C411yescharacteristic
103C2×#11924005C2×C411yescharacteristic
104C2×C4×Dic73C2311yescharacteristic
105C2×C4×Dic73C2311yescharacteristic
106#14556520—22no—
107#14556520—41no—
108C22⋊#10596831—22no—
109C22⋊#10596831—41no—
110C22⋊#10596831—41no—
111#14556503—22no—
112#14556503—22no—
113#14556503—22no—
114#14556503—22no—
115#14556503—41no—
116#14556503—41no—
117C8×Dic73—22no—
118C8×Dic73—41no—
119#14556498C2×C411yescharacteristic
120#14556498C2×C411yescharacteristic
121#14556498C2×C411yescharacteristic
122#14556498C2×C411yescharacteristic
123#14556498C2×C411yescharacteristic
124#14556498C2×C411yescharacteristic
125C22×D4×C73C2×C411yescharacteristic
126C23×C4×C73C2311yescharacteristic
127C23×C4×C73C2311yescharacteristic
128C22×C8×C73C2311yescharacteristic
129C22×C8×C73C2311yescharacteristic
130C22×C8×C73C2311yescharacteristic
131C22×C8×C73C2311yescharacteristic
132C4×D4×C73—41no—
133C4×D4×C73—41no—
134C2×C4⋊C4×C73C2×C411yescharacteristic
135C2×C22⋊C4×C73C2×C411yescharacteristic
136C2×C22⋊C4×C73C2×C411yescharacteristic
137C2×C42×C73C2311yescharacteristic
138C4⋊C8×C73—41no—
139C22⋊C8×C73—22no—
140C22⋊C8×C73—22no—
141C22⋊C8×C73—41no—
142C22⋊C8×C73—41no—
143#97×C73—41no—
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—22no—
160C2×C22⋊D73—22no—
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×D73C2×D412yes—
185C2×C4×D73#4112yes—
186#11924012—44no—
187#11924011—44no—
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—21no—
199C2×#10596831C2×D412yes—
200C8×D73—44no—
201#11924007—22no—
202#11924007—41no—
203C22⋊Dic73—22no—
204C22⋊Dic73—22no—
205C22⋊Dic73—22no—
206C22⋊Dic73—41no—
207#11924005—22no—
208#11924005—22no—
209#11924005—22no—
210#11924005—41no—
211#11924005—41no—
212#11924005—41no—
213C4×Dic73—21no—
214C4×Dic73—21no—
215C4×Dic73—21no—
216C4×Dic73—21no—
217C24×C73C22×C411yescharacteristic
218C24×C73C22×C411yescharacteristic
219C2×D4×C73—41no—
220C2×D4×C73—41no—
221C2×D4×C73—41no—
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×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×C73C2411yescharacteristic
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×C73—21no—
250C2×C8×C73C2×D412yes—
251C4⋊C4×C73—41no—
252C22⋊C4×C73—41no—
253C22⋊C4×C73—41no—
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×C73—21no—
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×D73C4×D412yes—
285D4×C73—44no—
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—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
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×Dic73C4×D412yes—
332C2×Dic73#13112yes—
333C2×Dic73#13112yes—
334D292—44no—
335C4×D73—22no—
336C4×D73—22no—
337C4×D73—22no—
338C4×D73—22no—
339C4×D73—41no—
340C4×D73—41no—
341C4×D73—41no—
342C4×D73—41no—
343Dic146—44no—
344C8×C73—22no—
345C8×C73—41no—
346C8×C73—41no—
347C8×C73—41no—
348#10596831—22no—
349#10596831—41no—
350#10596831—41no—
351#10596831—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—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—22no—
374C2×D73—22no—
375C2×D73—22no—
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—41no—
388C4×C73—41no—
389C4×C73—41no—
390C4×C73—41no—
391C4×C73#53411yescharacteristic
392C4×C73#53511yescharacteristic
393C4×C73#53811yescharacteristic
394C4×C73#53811yescharacteristic
395Dic73—22no—
396Dic73—22no—
397Dic73—22no—
398Dic73—41no—
399Dic73—41no—
400Dic73—41no—
401#22039—731nomaximal, Sylow
402C2×C73—81no—
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—42no—
412D73—81no—
413C2×#436—731no—
414C2×#408—731no—
415#2388—731no—
416#1955D7311yescharacteristic, complemented
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×M16—731no—
431C22×M16—731no—
432C23×C8—731no—
433C2×C4×D4—731no—
434C2×C4×D4—731no—
435C2×C4×D4C2×D7311yescharacteristic
436#436—1464no—
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⋊C8C2×D7311yescharacteristic
451C2×C22⋊C8C2×D7311yescharacteristic
452C2×C22⋊C8C2×D7311yescharacteristic
453C2×C22⋊C8C2×D7311yescharacteristic
454C2×#97C2×D7311yescharacteristic
455C2×C4×C8—731no—
456C2×C4×C8—731no—
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—2921no—
492C2×M16—2921no—
493C2×M16—2921no—
494C2×M16—2921no—
495C2×M16—734no—
496C2×M16—1462no—
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—41no—
509C4×D4—41no—
510C4×D4—2921no—
511C4×D4—2921no—
512C4×D4—1462no—
513C4×D4—1462no—
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—41no—
533C4⋊C8—2921no—
534C4⋊C8—1462no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—41no—
538C22⋊C8—41no—
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—41no—
549C4×C8—2921no—
550C4×C8—1462no—
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—41no—
569C2×D4—41no—
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—1462no—
581C2×D4—1462no—
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—21no—
597C22×C4—21no—
598C22×C4—731no—
599C22×C4—731no—
600C22×C4—731no—
601C22×C4—732no—
602C22×C4—732no—
603C22×C4—731no—
604C22×C4—731no—
605C22×C4—731no—
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×C4—1461no—
615C22×C4—1461no—
616C22×C4C2×C4×D7311yescharacteristic
617C22×C4C2×C4×D7311yescharacteristic
618C22×C4C2×C4×D7311yescharacteristic
619C22×C4C2×C4×D7311yescharacteristic
620C22×C4C23×D7311yescharacteristic
621M16—2924no—
622M16—2924no—
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—21no—
634C2×C8—2924no—
635C2×C8—732no—
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×C8—1461no—
647C2×C8D4×D7312yes—
648C4⋊C4—41no—
649C4⋊C4—2921no—
650C4⋊C4—1462no—
651C22⋊C4—41no—
652C22⋊C4—41no—
653C22⋊C4—2921no—
654C22⋊C4—2921no—
655C22⋊C4—2921no—
656C22⋊C4—2921no—
657C22⋊C4—1462no—
658C22⋊C4—1462no—
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—21no—
683C23—732no—
684C23—1461no—
685C23—1461no—
686C23—1461no—
687C23—1461no—
688C23—1461no—
689C23—1461no—
690C23—1461no—
691C23—1461no—
692C23—1461no—
693C23—1461no—
694C23—1461no—
695C23—1461no—
696C23—1461no—
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—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—2921no—
726C2×C4—2921no—
727C2×C4—2921no—
728C2×C4—2921no—
729C2×C4—732no—
730C2×C4—732no—
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—1462no—
748C2×C4—1462no—
749C2×C4—1462no—
750C2×C4—1462no—
751C2×C4C2×D4×D7311yescharacteristic
752C2×C4#41×D7311yescharacteristic
753C2×C4#1455663611yescharacteristic
754C2×C4#1455663611yescharacteristic
755C2×C4#1455663611yescharacteristic
756C2×C4#1455663711yescharacteristic
757C8—22no—
758C8—41no—
759C8—41no—
760C8—41no—
761C8—2921no—
762C8—2921no—
763C8—2921no—
764C8—1462no—
765C22—41no—
766C22—41no—
767C22—41no—
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—1462no—
791C22—1462no—
792C22—1462no—
793C22C4×D4×D7311yescharacteristic
794C22#1798905911yescharacteristic
795C22#1798906011yescharacteristic
796C22#131×D7311yescharacteristic
797C22#131×D7311yescharacteristic
798C22#1798935311yescharacteristic
799C22#1798935311yescharacteristic
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—2921no—
805C4—2921no—
806C4—2921no—
807C4—1462no—
808C4—1462no—
809C4—1462no—
810C4#1798914511yescharacteristic
811C4#1798915011yescharacteristic
812C4#1798916911yescharacteristic
813C4#1798917111yescharacteristic
814C2—81no—
815C2—81no—
816C2—2922no—
817C2—5841no—
818C2#2261259011yescharacteristic
819C2#2261865411yescharacteristic
820C2#2261867211yescharacteristic
821C2#2261897811yescharacteristic
822C2#2261899111yescharacteristic
823C2#2261899511yescharacteristic
824C2#2261900311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1955C2
prime radical#22613146C2
cosocleC22×C4×C73C24
hypercenter#1955D73
hypocenterC73#22039
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×#17988552C2semidirect
4. #22610723C2semidirect
5. #22610544C2semidirect
6. #22610540C2semidirect
7. #22610540C2semidirect
8. #22610536C2semidirect
9. #22610229C2semidirect
10. #22610226C2semidirect
11. #22610220C2semidirect
12. #22610107C2semidirect
13. #22609842C2semidirect
14. #22609716C2semidirect
15. C73×#1955C2semidirect
80. C2×#11924011D4semidirect
416. #1955D73semidirect
428. C73#22039semidirect

Maximal subgroups

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

subgroupindex
C2×#179886622
C2×#179885522
#226131462
#226107232
#226105442
#226105402
#226105362
#226102292
#226102262
#226102202
#226101072
#226098422
#226097162
C73×#19552
#2203973