Finite Group Databasebeta

← #33097098

Subgroups — #33097098

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×#17988554C211yesmaximal, characteristic, complemented
3#22613144C211yesmaximal, characteristic
4#22610727C211yesmaximal, characteristic, complemented
5#22610723C211yesmaximal, characteristic, complemented
6#22610541C211yesmaximal, characteristic, complemented
7#22610540C211yesmaximal, characteristic, complemented
8#22610540C211yesmaximal, characteristic, complemented
9#22610534C211yesmaximal, characteristic, complemented
10#22610225C211yesmaximal, characteristic, complemented
11#22610225C211yesmaximal, characteristic, complemented
12#22610221C211yesmaximal, characteristic, complemented
13#22610108C211yesmaximal, characteristic, complemented
14#22609717C211yesmaximal, characteristic, complemented
15C73×#1780C211yesmaximal, characteristic, complemented
16C22×#11924012C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C23×#10596831C2211yescharacteristic
19C2×C4×C22⋊D73C2211yescharacteristic
20C2×C4×C22⋊D73C2211yescharacteristic
21C2×C4×C22⋊D73C2211yescharacteristic
22#17988662—24no—
23C2×#14556520C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×#14556520C2211yescharacteristic
26#17988554—24no—
27C2×C22⋊#10596831C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29C2×C22⋊#10596831C2211yescharacteristic
30C2×C22⋊#10596831C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556501C2211yescharacteristic
35C2×C8×Dic73C2211yescharacteristic
36C2×C8×Dic73C2211yescharacteristic
37#17988506C411yescharacteristic
38#17988501C411yescharacteristic
39#17988501C411yescharacteristic
40#17988501C411yescharacteristic
41#17988498C411yescharacteristic
42#17988495C411yescharacteristic
43#17988495C411yescharacteristic
44#17988495C411yescharacteristic
45C4×C22⋊Dic73C2211yescharacteristic
46C4×C22⋊Dic73C2211yescharacteristic
47C4×C22⋊Dic73C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C22×#41×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57C2×C22⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60C2×C22⋊C8×C73C2211yescharacteristic
61C22×C22⋊D73C2×C411yescharacteristic
62C22×C22⋊D73C2×C411yescharacteristic
63C22×C22⋊D73C2×C411yescharacteristic
64C22×C4×D73C2311yescharacteristic
65C2×#11924012—41no—
66C2×#11924012—41no—
67C2×#11924012D414yescomplemented
68C2×#11924011—22no—
69C2×#11924011—41no—
70C2×#11924011—41no—
71C22×#10596831—22no—
72C22×#10596831—41no—
73C22×#10596831—41no—
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78C4×C22⋊D73—22no—
79C4×C22⋊D73—22no—
80C4×C22⋊D73—41no—
81C4×C22⋊D73—41no—
82C4×C22⋊D73—41no—
83C4×C22⋊D73—41no—
84C2×#11924007C2×C411yescharacteristic
85C2×#11924007C2×C411yescharacteristic
86C2×#11924007C2×C411yescharacteristic
87C2×C22⋊Dic73C2×C411yescharacteristic
88C2×C22⋊Dic73C2×C411yescharacteristic
89C2×C22⋊Dic73C2×C411yescharacteristic
90C2×C22⋊Dic73C2×C411yescharacteristic
91C2×C22⋊Dic73C2×C411yescharacteristic
92C2×C22⋊Dic73C2×C411yescharacteristic
93C2×C22⋊Dic73C2×C411yescharacteristic
94C2×C22⋊Dic73C2×C411yescharacteristic
95C2×C22⋊Dic73C2×C411yescharacteristic
96C2×#11924005C2×C411yescharacteristic
97C2×#11924005C2×C411yescharacteristic
98C2×#11924005C2×C411yescharacteristic
99C2×C4×Dic73C2311yescharacteristic
100C2×C4×Dic73C2311yescharacteristic
101C2×C4×Dic73C2311yescharacteristic
102#14556520—22no—
103#14556520—41no—
104#14556520—41no—
105C22⋊#10596831—22no—
106C22⋊#10596831—22no—
107C22⋊#10596831—22no—
108C22⋊#10596831—22no—
109#14556503—22no—
110#14556503—41no—
111#14556503—41no—
112#14556501—41no—
113C8×Dic73—22no—
114C8×Dic73—41no—
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120#14556498C2×C411yescharacteristic
121C2×#41×C73—22no—
122C2×#41×C73—22no—
123C2×#41×C73—41no—
124C2×#41×C73—41no—
125C2×#41×C73—41no—
126C2×#41×C73—41no—
127C22×Q8×C73C2×C411yescharacteristic
128C22×D4×C73C2×C411yescharacteristic
129C22×D4×C73C2×C411yescharacteristic
130C22×D4×C73C2×C411yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C22×C8×C73C2311yescharacteristic
135C22×C8×C73C2311yescharacteristic
136C22×C8×C73C2311yescharacteristic
137C22×C8×C73C2311yescharacteristic
138C22⋊C8×C73—22no—
139C22⋊C8×C73—22no—
140C22⋊C8×C73—41no—
141C22⋊C8×C73—41no—
142C22⋊C8×C73—41no—
143C22⋊C8×C73—41no—
144C23×D73C22×C411yescharacteristic
145C2×C22⋊D73—22no—
146C2×C22⋊D73—22no—
147C2×C22⋊D73—22no—
148C2×C22⋊D73—41no—
149C2×C22⋊D73—41no—
150C2×C22⋊D73—41no—
151C2×C22⋊D73—41no—
152C2×C22⋊D73—41no—
153C2×C22⋊D73—41no—
154C22×Dic73C22×C411yescharacteristic
155C22×Dic73C22×C411yescharacteristic
156C22×Dic73C22×C411yescharacteristic
157C22×Dic73C22×C411yescharacteristic
158C22×Dic73C22×C411yescharacteristic
159C22×Dic73C22×C411yescharacteristic
160C22×Dic73C22×C411yescharacteristic
161C2×C4×D73—21no—
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—21no—
166C2×C4×D73—21no—
167#11924012—44no—
168#11924011—44no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—44no—
180C2×#10596831C2×D412yes—
181C2×#10596831C2×D412yes—
182#11924007—22no—
183#11924007—41no—
184#11924007—41no—
185C22⋊Dic73—22no—
186C22⋊Dic73—22no—
187C22⋊Dic73—22no—
188C22⋊Dic73—22no—
189C22⋊Dic73—22no—
190C22⋊Dic73—41no—
191C22⋊Dic73—41no—
192C22⋊Dic73—41no—
193C22⋊Dic73—41no—
194#11924005—22no—
195#11924005—41no—
196#11924005—41no—
197C4×Dic73—21no—
198C4×Dic73—21no—
199C4×Dic73—21no—
200C4×Dic73—21no—
201C4×Dic73—21no—
202C4×Dic73—21no—
203C24×C73C22×C411yescharacteristic
204C24×C73C22×C411yescharacteristic
205C24×C73C22×C411yescharacteristic
206#41×C73—44no—
207#41×C73—44no—
208#41×C73—44no—
209#41×C73—44no—
210C2×Q8×C73—22no—
211C2×Q8×C73—41no—
212C2×Q8×C73—41no—
213C2×D4×C73—22no—
214C2×D4×C73—22no—
215C2×D4×C73—22no—
216C2×D4×C73—41no—
217C2×D4×C73—41no—
218C2×D4×C73—41no—
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×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73C22×C411yescharacteristic
239C22×C4×C73C22×C411yescharacteristic
240C22×C4×C73C22×C411yescharacteristic
241C22×C4×C73C2×D412yes—
242C22×C4×C73#4112yes—
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×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×C73—21no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—21no—
274C23×C73—21no—
275C23×C73—21no—
276C23×C73C4×D412yes—
277C23×C73C23×C411yescharacteristic
278C22×D73—21no—
279C22×D73—21no—
280C22×D73—21no—
281C22×D73—21no—
282C22×D73—21no—
283C22×D73—21no—
284C22×D73—21no—
285Q8×C73—44no—
286D4×C73—44no—
287D4×C73—44no—
288D4×C73—44no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73C4×D412yes—
310C2×C4×C73C22×D411yescharacteristic
311C2×C4×C73C2×#4111yescharacteristic
312C2×C4×C73H(5,𝔽2)11yescharacteristic
313C2×C4×C73H(5,𝔽2)11yescharacteristic
314C2×C4×C73H(5,𝔽2)11yescharacteristic
315C2×C4×C73H(5,𝔽2)11yescharacteristic
316C22⋊D73—44no—
317C22⋊D73—44no—
318C22⋊D73—44no—
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—21no—
334C2×Dic73—21no—
335C2×Dic73—21no—
336C2×Dic73—21no—
337C2×Dic73—21no—
338C2×Dic73#13112yes—
339C2×Dic73#13112yes—
340C4×D73—41no—
341C4×D73—41no—
342C4×D73—41no—
343C4×D73—41no—
344C8×C73—41no—
345C8×C73—41no—
346C8×C73—41no—
347C8×C73—41no—
348#10596831—22no—
349#10596831—22no—
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×C73—41no—
367C22×C73—41no—
368C22×C73—41no—
369C22×C73—41no—
370C22×C73—41no—
371C22×C73—41no—
372C22×C73—41no—
373C22×C73C2×C4×D411yescharacteristic
374C22×C73#51811yescharacteristic
375C22×C73#51811yescharacteristic
376C22×C73C2×#13111yescharacteristic
377C22×C73C2×#13111yescharacteristic
378C22×C73#56811yescharacteristic
379C22×C73#56811yescharacteristic
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—41no—
389C4×C73—41no—
390C4×C73#53411yescharacteristic
391C4×C73#53511yescharacteristic
392C4×C73#53811yescharacteristic
393C4×C73#53811yescharacteristic
394Dic73—22no—
395Dic73—22no—
396Dic73—41no—
397Dic73—41no—
398Dic73—41no—
399Dic73—41no—
400Dic73—41no—
401#22039—731nomaximal, Sylow
402C2×C73—42no—
403C2×C73—81no—
404C2×C73—81no—
405C2×C73#232111yescharacteristic
406C2×C73#293311yescharacteristic
407C2×C73#293511yescharacteristic
408C2×C73#297611yescharacteristic
409C2×C73#297811yescharacteristic
410C2×C73#297911yescharacteristic
411C2×C73#298111yescharacteristic
412D73—81no—
413C2×#436—731no—
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#1780D7311yescharacteristic, complemented
427#1753—731no—
428C73#2203911yescharacteristic, complemented, Sylow
429C22×#41C2×D7311yescharacteristic
430C22×M16—731no—
431C22×M16—731no—
432C23×C8—731no—
433C2×C4×D4—731no—
434C2×C4×D4—731no—
435C2×C4×D4—731no—
436#436—1464no—
437C2×C4⋊C8—731no—
438C2×C4⋊C8—731no—
439C2×C4⋊C8—731no—
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⋊C8C2×D7311yescharacteristic
449C2×C22⋊C8C2×D7311yescharacteristic
450C2×C22⋊C8C2×D7311yescharacteristic
451C2×C22⋊C8C2×D7311yescharacteristic
452C2×C22⋊C8C2×D7311yescharacteristic
453C2×C22⋊C8C2×D7311yescharacteristic
454C2×#97—731no—
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—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41—41no—
480C22×Q8C4×D7311yescharacteristic
481C22×D4—731no—
482C22×D4—731no—
483C22×D4—731no—
484C22×D4C4×D7311yescharacteristic
485C22×D4C4×D7311yescharacteristic
486C22×D4C4×D7311yescharacteristic
487C23×C4—731no—
488C23×C4C22×D7311yescharacteristic
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—2921no—
509C4×D4—2921no—
510C4×D4—2921no—
511C4×D4—2921no—
512C4×D4—1462no—
513C4×D4—1462no—
514C2×C4⋊C4—731no—
515C2×C4⋊C4—731no—
516C2×C4⋊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⋊C4—731no—
527C2×C22⋊C4—731no—
528C2×C22⋊C4—731no—
529C2×C42—731no—
530C2×C42—731no—
531C2×C42—731no—
532C4⋊C8—2921no—
533C4⋊C8—2921no—
534C4⋊C8—1462no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—41no—
538C22⋊C8—41no—
539C22⋊C8—41no—
540C22⋊C8—41no—
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—2921no—
550C4×C8—1462no—
551#95—731no—
552#95—731no—
553#95—731no—
554#95—731no—
555#95—731no—
556#95—731no—
557C24—731no—
558C24C2×C4×D7311yescharacteristic
559C24C2×C4×D7311yescharacteristic
560C24C2×C4×D7311yescharacteristic
561#41—44no—
562#41—44no—
563#41—44no—
564#41—44no—
565C2×Q8—22no—
566C2×Q8—41no—
567C2×Q8—41no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—2921no—
578C2×D4—2921no—
579C2×D4—2921no—
580C2×D4—2921no—
581C2×D4—2921no—
582C2×D4—2921no—
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—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—731no—
603C22×C4—731no—
604C22×C4—731no—
605C22×C4—731no—
606C22×C4—731no—
607C22×C4—731no—
608C22×C4—731no—
609C22×C4—1461no—
610C22×C4—1461no—
611C22×C4—1461no—
612C22×C4—1461no—
613C22×C4—1461no—
614C22×C4—1461no—
615C22×C4C2×C4×D7311yescharacteristic
616C22×C4C2×C4×D7311yescharacteristic
617C22×C4C2×C4×D7311yescharacteristic
618C22×C4D4×D7312yes—
619C22×C4#1192402712yes—
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—21no—
635C2×C8—2924no—
636C2×C8—732no—
637C2×C8—732no—
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×C8—1461no—
648C4⋊C4—2921no—
649C4⋊C4—2921no—
650C4⋊C4—1462no—
651C22⋊C4—2921no—
652C22⋊C4—2921no—
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—1461no—
664C42—1461no—
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—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—1461no—
690C23—1461no—
691C23—1461no—
692C23—1461no—
693C23—1461no—
694C23—1461no—
695C23—1461no—
696C23#1455655112yes—
697C23C22×C4×D7311yescharacteristic
698Q8—44no—
699D4—44no—
700D4—44no—
701D4—44no—
702D4—2924no—
703D4—2924no—
704D4—2924no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
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—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—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×C4—1461no—
750C2×C4#1455655112yes—
751C2×C4C2×D4×D7311yescharacteristic
752C2×C4C2×#1192402711yescharacteristic
753C2×C4#1455663611yescharacteristic
754C2×C4#1455663611yescharacteristic
755C2×C4#1455663611yescharacteristic
756C2×C4#1455663611yescharacteristic
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C8—2921no—
762C8—2921no—
763C8—1462no—
764C8—1462no—
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—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—2921no—
787C22—2921no—
788C22—2921no—
789C22—2921no—
790C22—2921no—
791C22—2921no—
792C22—2921no—
793C22C2×#1455655111yescharacteristic
794C22#1798906011yescharacteristic
795C22#1798906011yescharacteristic
796C22#131×D7311yescharacteristic
797C22#131×D7311yescharacteristic
798C22#1798935211yescharacteristic
799C22#1798935211yescharacteristic
800C4—22no—
801C4—41no—
802C4—41no—
803C4—2921no—
804C4—2921no—
805C4—2921no—
806C4—2921no—
807C4—2921no—
808C4—1462no—
809C4—1462no—
810C4#1798914711yescharacteristic
811C4#1798915211yescharacteristic
812C4#1798917211yescharacteristic
813C4#1798917211yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—5841no—
818C2#2261258611yescharacteristic
819C2#2261866111yescharacteristic
820C2#2261867111yescharacteristic
821C2#2261897411yescharacteristic
822C2#2261898911yescharacteristic
823C2#2261899511yescharacteristic
824C2#2261900411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1780C2
prime radical#22613144C2
cosocleC22×C4×C73C24
hypercenter#1780D73
hypocenterC73#22039
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1780

Complements

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

NH ≅ G/Ntype
1. C2×#17988662C2semidirect
2. C2×#17988554C2semidirect
4. #22610727C2semidirect
5. #22610723C2semidirect
6. #22610541C2semidirect
7. #22610540C2semidirect
8. #22610540C2semidirect
9. #22610534C2semidirect
10. #22610225C2semidirect
11. #22610225C2semidirect
12. #22610221C2semidirect
13. #22610108C2semidirect
14. #22609717C2semidirect
15. C73×#1780C2semidirect
67. C2×#11924012D4semidirect
426. #1780D73semidirect
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×#179885542
#226131442
#226107272
#226107232
#226105412
#226105402
#226105342
#226102252
#226102212
#226101082
#226097172
C73×#17802
#2203973