Finite Group Databasebeta

← #33095786

Subgroups — #33095786

Order 18688.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989098C211yesmaximal, characteristic
2C2×#17988447C211yesmaximal, characteristic, complemented
3#22610916C212yesmaximal, complemented
4#22610767C212yesmaximal, complemented
5#22610382C214yesmaximal, complemented
6#22609916C214yesmaximal, complemented
7C73×#2280C211yesmaximal, characteristic, complemented
8C22×#11924028C411yescharacteristic, complemented
9#17989098—21no—
10#17989098—21no—
11#17989098—21no—
12#17989098—21no—
13#17989098—21no—
14#17989098—21no—
15#17989098—21no—
16#17989098—21no—
17C2×#14556574C412yescomplemented
18C2×#14556570C411yescharacteristic, complemented
19C2×#14556570C2211yescharacteristic
20C2×#14556565C411yescharacteristic, complemented
21C2×#14556565C2211yescharacteristic
22C2×#14556560C2212yes—
23C2×C4×C22⋊D73C412yescomplemented
24C2×C4×C22⋊D73C2212yes—
25C2×#14556550C411yescharacteristic, complemented
26C22×C4⋊Dic73—21no—
27C22×C22⋊Dic73C2212yes—
28C2×#14556505C2218yes—
29#17988447—21no—
30#17988447—21no—
31#17988447C2212yes—
32#17988447C2212yes—
33C2×#14556498—21no—
34#17988353C2218yes—
35C24×C4×C73C2211yescharacteristic
36C2×#117×C73—21no—
37#381×C73—21no—
38#380×C73—21no—
39#380×C73C2212yes—
40#379×C73C2212yes—
41C4×C22⋊C4×C73—21no—
42C4×C22⋊C4×C73C2212yes—
43C2×#11924028—21no—
44C2×#11924028—21no—
45C2×#11924028—21no—
46C2×#11924028—21no—
47C2×#11924028—44no—
48C22×Dic146C2×C411yescharacteristic, complemented
49C22×D292C2×C411yescharacteristic, complemented
50C22×C22⋊D73C2×C412yes—
51C22×C22⋊D73C2×C412yes—
52C22×C22⋊D73C2312yes—
53C23×Dic73—22no—
54C22×C4×D73C2×C412yescomplemented
55#14556574—22no—
56#14556574—22no—
57#14556574—22no—
58#14556574—22no—
59#14556570—21no—
60#14556570—21no—
61#14556570—21no—
62#14556570—21no—
63#14556570—21no—
64#14556570—21no—
65#14556570—21no—
66#14556570—21no—
67#14556565—21no—
68#14556565—21no—
69#14556565—21no—
70#14556565—21no—
71#14556565—21no—
72#14556565—21no—
73#14556565—21no—
74#14556565—21no—
75#14556560—22no—
76#14556560—22no—
77#14556560—22no—
78#14556560—22no—
79C4×C22⋊D73—22no—
80C4×C22⋊D73—22no—
81C4×C22⋊D73—22no—
82C4×C22⋊D73—22no—
83C4×C22⋊D73—22no—
84C4×C22⋊D73—22no—
85C4×C22⋊D73—22no—
86C4×C22⋊D73—22no—
87#14556550—21no—
88#14556550—21no—
89#14556550—21no—
90#14556550—21no—
91C2×C4⋊Dic73—22no—
92C2×C4⋊Dic73—22no—
93C2×C4⋊Dic73—44no—
94C2×C4⋊Dic73C2×C411yescharacteristic, complemented
95C2×C4⋊Dic73C2×C411yescharacteristic, complemented
96C2×#11924007C2×C412yescomplemented
97C2×#11924007C2×C412yescomplemented
98C2×C22⋊Dic73—22no—
99C2×C22⋊Dic73—44no—
100C2×C22⋊Dic73C2×C412yes—
101C2×C22⋊Dic73C2×C412yes—
102C2×C22⋊Dic73C2314yes—
103C2×C22⋊Dic73C2312yes—
104C2×#11924005C2×C412yescomplemented
105C2×#11924005C2×C412yescomplemented
106C2×C4×Dic73C2×C412yescomplemented
107#14556505—48no—
108#14556498—22no—
109#14556498—22no—
110C25×C73C2311yescharacteristic
111C23×C4×C73—44no—
112C23×C4×C73C2×C411yescharacteristic
113C23×C4×C73C2×C411yescharacteristic
114C23×C4×C73C2×C411yescharacteristic
115C23×C4×C73C2×C411yescharacteristic
116C23×C4×C73D411yescharacteristic
117C23×C4×C73D411yescharacteristic
118C23×C4×C73D411yescharacteristic
119C23×C4×C73D411yescharacteristic
120C23×C4×C73D411yescharacteristic
121C23×C4×C73D411yescharacteristic
122C23×C4×C73D411yescharacteristic
123C23×C4×C73D411yescharacteristic
124C23×C4×C73C2311yescharacteristic
125C23×C4×C73C2311yescharacteristic
126#117×C73—44no—
127C2×C4⋊C4×C73—22no—
128C2×C22⋊C4×C73—22no—
129C2×C22⋊C4×C73—22no—
130C2×C22⋊C4×C73C2314yes—
131C2×C42×C73—22no—
132#95×C73—22no—
133#95×C73—22no—
134C23×D73C22×C412yes—
135#11924028—44no—
136#11924028—44no—
137#11924028—44no—
138#11924028—44no—
139C2×Dic146—21no—
140C2×Dic146—21no—
141C2×Dic146—42no—
142C2×D292—21no—
143C2×D292—21no—
144C2×D292—42no—
145C2×C22⋊D73—22no—
146C2×C22⋊D73—22no—
147C2×C22⋊D73—22no—
148C2×C22⋊D73—22no—
149C2×C22⋊D73—22no—
150C2×C22⋊D73—22no—
151C2×C22⋊D73—24no—
152C2×C22⋊D73—24no—
153C2×C22⋊D73—44no—
154C2×C22⋊D73—44no—
155C22×Dic73—24no—
156C22×Dic73—44no—
157C22×Dic73—44no—
158C22×Dic73—44no—
159C22×Dic73C22×C412yes—
160C22×Dic73C22×C412yes—
161C22×Dic73C22×C412yes—
162C2×C4×D73—22no—
163C2×C4×D73—22no—
164C2×C4×D73—44no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—44no—
170C4⋊Dic73—44no—
171#11924007—22no—
172#11924007—22no—
173#11924007—22no—
174#11924007—22no—
175C22⋊Dic73—22no—
176C22⋊Dic73—22no—
177C22⋊Dic73—22no—
178C22⋊Dic73—22no—
179C22⋊Dic73—22no—
180C22⋊Dic73—22no—
181C22⋊Dic73—28no—
182C22⋊Dic73—44no—
183#11924005—22no—
184#11924005—22no—
185#11924005—22no—
186#11924005—22no—
187C4×Dic73—22no—
188C4×Dic73—22no—
189C24×C73—22no—
190C24×C73—22no—
191C24×C73—42no—
192C24×C73—42no—
193C24×C73C22×C411yescharacteristic
194C24×C73C22×C411yescharacteristic
195C24×C73C2×D411yescharacteristic
196C24×C73C2×D411yescharacteristic
197C24×C73C2×D411yescharacteristic
198C24×C73C2×D411yescharacteristic
199C24×C73C2411yescharacteristic
200C22×C4×C73—24no—
201C22×C4×C73—24no—
202C22×C4×C73—24no—
203C22×C4×C73—24no—
204C22×C4×C73—42no—
205C22×C4×C73—42no—
206C22×C4×C73—42no—
207C22×C4×C73—42no—
208C22×C4×C73—42no—
209C22×C4×C73—42no—
210C22×C4×C73—42no—
211C22×C4×C73—42no—
212C22×C4×C73—42no—
213C22×C4×C73—42no—
214C22×C4×C73—42no—
215C22×C4×C73C22⋊C411yescharacteristic
216C22×C4×C73C22⋊C411yescharacteristic
217C22×C4×C73C22⋊C411yescharacteristic
218C22×C4×C73C22⋊C411yescharacteristic
219C22×C4×C73C22⋊C411yescharacteristic
220C22×C4×C73C22⋊C411yescharacteristic
221C22×C4×C73C22⋊C411yescharacteristic
222C22×C4×C73C22⋊C411yescharacteristic
223C22×C4×C73C22⋊C411yescharacteristic
224C22×C4×C73C22⋊C411yescharacteristic
225C22×C4×C73C22⋊C411yescharacteristic
226C22×C4×C73C22⋊C411yescharacteristic
227C22×C4×C73C22⋊C411yescharacteristic
228C22×C4×C73C22⋊C411yescharacteristic
229C22×C4×C73C22⋊C411yescharacteristic
230C22×C4×C73C22⋊C411yescharacteristic
231C22×C4×C73C22×C411yescharacteristic
232C22×C4×C73C22×C411yescharacteristic
233C22×C4×C73C22×C411yescharacteristic
234C22×C4×C73C22×C411yescharacteristic
235C22×C4×C73C2×D411yescharacteristic
236C22×C4×C73C2×D411yescharacteristic
237C22×C4×C73C2×D411yescharacteristic
238C22×C4×C73C2×D411yescharacteristic
239C22×C4×C73C2×D411yescharacteristic
240C22×C4×C73C2×D411yescharacteristic
241C22×C4×C73C2×D411yescharacteristic
242C22×C4×C73C2×D411yescharacteristic
243C4⋊C4×C73—44no—
244C22⋊C4×C73—24no—
245C22⋊C4×C73—24no—
246C22⋊C4×C73—44no—
247C22⋊C4×C73—44no—
248C42×C73—44no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—22no—
252C23×C73—22no—
253C23×C73—22no—
254C23×C73—22no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—22no—
258C23×C73—22no—
259C23×C73—22no—
260C23×C73—22no—
261C23×C73—22no—
262C23×C73—22no—
263C23×C73—41no—
264C23×C73—41no—
265C23×C73—41no—
266C23×C73—41no—
267C23×C73—41no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—48no—
272C23×C73—48no—
273C23×C73C2×C22⋊C411yescharacteristic
274C23×C73C2×C22⋊C411yescharacteristic
275C23×C73C2×C22⋊C411yescharacteristic
276C23×C73C2×C22⋊C411yescharacteristic
277C23×C73C23×C411yescharacteristic
278C23×C73C22×D411yescharacteristic
279C23×C73C22×D411yescharacteristic
280C23×C73H(5,𝔽2)12yes—
281C23×C732−1+412yes—
282C22×D73—22no—
283C22×D73—24no—
284C22×D73—42no—
285C22×D73—42no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
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×C73—41no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73—44no—
314C2×C4×C73—44no—
315C2×C4×C73—44no—
316C2×C4×C73#9914yescomplemented
317C2×C4×C73C2×C22⋊C411yescharacteristic
318C2×C4×C73C2×C22⋊C411yescharacteristic
319C2×C4×C73C2×C22⋊C411yescharacteristic
320C2×C4×C73C2×C22⋊C411yescharacteristic
321C2×C4×C73C2×C22⋊C411yescharacteristic
322C2×C4×C73C2×C22⋊C411yescharacteristic
323C2×C4×C73C2×C22⋊C411yescharacteristic
324C2×C4×C73C2×C22⋊C411yescharacteristic
325C22⋊D73—44no—
326C22⋊D73—44no—
327C22⋊D73—42no—
328C22⋊D73—42no—
329C22⋊D73—44no—
330C22⋊D73—44no—
331C22⋊D73—44no—
332C2×Dic73—22no—
333C2×Dic73—22no—
334C2×Dic73—22no—
335C2×Dic73—24no—
336C2×Dic73—42no—
337C2×Dic73—42no—
338C2×Dic73—44no—
339C2×Dic73—44no—
340C2×Dic73—44no—
341C2×Dic73—88no—
342D292—42no—
343D292—42no—
344C4×D73—44no—
345C4×D73—44no—
346Dic146—42no—
347Dic146—42no—
348C22×C73—24no—
349C22×C73—24no—
350C22×C73—21no—
351C22×C73—21no—
352C22×C73—21no—
353C22×C73—21no—
354C22×C73—21no—
355C22×C73—21no—
356C22×C73—21no—
357C22×C73—21no—
358C22×C73—21no—
359C22×C73—21no—
360C22×C73—21no—
361C22×C73—21no—
362C22×C73—21no—
363C22×C73—21no—
364C22×C73—21no—
365C22×C73—21no—
366C22×C73—42no—
367C22×C73—42no—
368C22×C73—44no—
369C22×C73—44no—
370C22×C73—44no—
371C22×C73—44no—
372C22×C73—42no—
373C22×C73—42no—
374C22×C73C2×#9912yes—
375C22×C73#41012yes—
376C22×C73C22×C22⋊C411yescharacteristic
377C22×C73#52012yes—
378C22×C73#53511yescharacteristic
379C22×C73#53611yescharacteristic
380C22×C73#53712yes—
381C2×D73—42no—
382C2×D73—42no—
383C2×D73—42no—
384C2×D73—84no—
385C4×C73—21no—
386C4×C73—21no—
387C4×C73—21no—
388C4×C73—21no—
389C4×C73—21no—
390C4×C73—21no—
391C4×C73—84no—
392C4×C73C2×#9912yes—
393C4×C73C2×#9912yes—
394Dic73—42no—
395Dic73—42no—
396Dic73—42no—
397Dic73—84no—
398#21874—731nomaximal, Sylow
399C2×C73—21no—
400C2×C73—22no—
401C2×C73—22no—
402C2×C73—21no—
403C2×C73—22no—
404C2×C73—22no—
405C2×C73—41no—
406C2×C73—41no—
407C2×C73#231111yescharacteristic
408C2×C73C22×#9911yescharacteristic
409C2×C73C2×#41011yescharacteristic
410D73—82no—
411C2×#525—731no—
412#2280D7311yescharacteristic, complemented
413C2×#380—731no—
414#1996—732no—
415#1964—732no—
416#1898—734no—
417#1799—734no—
418C73#2187411yescharacteristic, complemented, Sylow
419C22×#41—731no—
420C24×C4C2×D7311yescharacteristic
421#525—1461no—
422#525—1461no—
423#525—1461no—
424#525—1461no—
425#525—1461no—
426#525—1461no—
427#525—1461no—
428#525—1461no—
429C2×#123—732no—
430C2×C22⋊Q8—731no—
431C2×C22⋊Q8—731no—
432C2×#121—731no—
433C2×#121—731no—
434C2×#120—732no—
435C2×C4×D4—732no—
436C2×C4×D4—732no—
437C2×#117—21no—
438C2×#117—731no—
439C22×C4⋊C4—1461no—
440C22×C22⋊C4—732no—
441C2×#99—738no—
442#381—21no—
443#380—21no—
444#380—732no—
445#380—732no—
446#380—1461no—
447#380—1461no—
448#380C2×D7312yes—
449#379C2×D7312yes—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2×D7312yes—
452C2×#95—1461no—
453#342—738no—
454C25C22×D7311yescharacteristic
455C2×#41—2924no—
456C2×#41—1461no—
457C2×#41—1461no—
458C2×#41—1461no—
459C2×#41—1461no—
460C22×Q8—731no—
461C22×D4—732no—
462C22×D4—732no—
463C22×D4—732no—
464C22×D4—731no—
465C23×C4—44no—
466C23×C4—732no—
467C23×C4—1462no—
468C23×C4C4×D7311yescharacteristic
469C23×C4C4×D7311yescharacteristic
470C23×C4C4×D7311yescharacteristic
471C23×C4C4×D7311yescharacteristic
472C23×C4D29211yescharacteristic
473C23×C4D29211yescharacteristic
474C23×C4D29211yescharacteristic
475C23×C4D29211yescharacteristic
476C23×C4C22⋊D7311yescharacteristic
477C23×C4C22⋊D7311yescharacteristic
478C23×C4C22⋊D7311yescharacteristic
479C23×C4C22⋊D7311yescharacteristic
480C23×C4C22×D7311yescharacteristic
481C23×C4C22×D7311yescharacteristic
482#123—1462no—
483#123—1462no—
484#123—1462no—
485#123—1462no—
486C22⋊Q8—1461no—
487C22⋊Q8—1461no—
488C22⋊Q8—1461no—
489C22⋊Q8—1461no—
490C22⋊Q8—1461no—
491C22⋊Q8—1461no—
492C22⋊Q8—1461no—
493C22⋊Q8—1461no—
494#121—1461no—
495#121—1461no—
496#121—1461no—
497#121—1461no—
498#121—1461no—
499#121—1461no—
500#121—1461no—
501#121—1461no—
502#120—1462no—
503#120—1462no—
504#120—1462no—
505#120—1462no—
506C4×D4—1462no—
507C4×D4—1462no—
508C4×D4—1462no—
509C4×D4—1462no—
510C4×D4—1462no—
511C4×D4—1462no—
512C4×D4—1462no—
513C4×D4—1462no—
514#117—44no—
515#117—1461no—
516#117—1461no—
517#117—1461no—
518#117—1461no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—2924no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—731no—
523C2×C4⋊C4—732no—
524C2×C4⋊C4—732no—
525C2×C4⋊C4—1462no—
526C2×C4⋊C4—1462no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—2924no—
530C2×C22⋊C4—732no—
531C2×C22⋊C4—732no—
532C2×C22⋊C4—732no—
533C2×C22⋊C4—732no—
534C2×C22⋊C4—732no—
535C2×C22⋊C4—734no—
536C2×C22⋊C4—1462no—
537C2×C22⋊C4C22×D7314yes—
538C2×C42—22no—
539C2×C42—732no—
540#99—2928no—
541#95—22no—
542#95—22no—
543#95—1462no—
544#95—1462no—
545C24—22no—
546C24—22no—
547C24—42no—
548C24—42no—
549C24—732no—
550C24C2×C4×D7311yescharacteristic
551C24C2×C4×D7311yescharacteristic
552C24C2×C22⋊D7311yescharacteristic
553C24C2×C22⋊D7311yescharacteristic
554C24C2×D29211yescharacteristic
555C24C2×D29211yescharacteristic
556C24C23×D7311yescharacteristic
557#41—2924no—
558#41—2924no—
559#41—2924no—
560#41—2924no—
561C2×Q8—2922no—
562C2×Q8—1461no—
563C2×Q8—1461no—
564C2×D4—2922no—
565C2×D4—2924no—
566C2×D4—2924no—
567C2×D4—1462no—
568C2×D4—1462no—
569C2×D4—1462no—
570C2×D4—1462no—
571C2×D4—1462no—
572C2×D4—1462no—
573C2×D4—1464no—
574C2×D4—1464no—
575C2×D4—1461no—
576C2×D4—1461no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—2924no—
593C22×C4—2924no—
594C22×C4—2924no—
595C22×C4—2924no—
596C22×C4—732no—
597C22×C4—732no—
598C22×C4—732no—
599C22×C4—1464no—
600C22×C4—1462no—
601C22×C4—1462no—
602C22×C4#1192400511yescharacteristic
603C22×C4#1192400511yescharacteristic
604C22×C4#1192400511yescharacteristic
605C22×C4#1192400511yescharacteristic
606C22×C4#1192400511yescharacteristic
607C22×C4#1192400511yescharacteristic
608C22×C4#1192400511yescharacteristic
609C22×C4#1192400511yescharacteristic
610C22×C4#1192400511yescharacteristic
611C22×C4#1192400511yescharacteristic
612C22×C4#1192400511yescharacteristic
613C22×C4#1192400511yescharacteristic
614C22×C4#1192400511yescharacteristic
615C22×C4#1192400511yescharacteristic
616C22×C4#1192400511yescharacteristic
617C22×C4#1192400511yescharacteristic
618C22×C4C2×C4×D7311yescharacteristic
619C22×C4C2×C4×D7311yescharacteristic
620C22×C4C2×C4×D7311yescharacteristic
621C22×C4C2×C4×D7311yescharacteristic
622C22×C4C2×C22⋊D7311yescharacteristic
623C22×C4C2×C22⋊D7311yescharacteristic
624C22×C4C2×C22⋊D7311yescharacteristic
625C22×C4C2×C22⋊D7311yescharacteristic
626C22×C4C2×D29211yescharacteristic
627C22×C4C2×D29211yescharacteristic
628C22×C4C2×D29211yescharacteristic
629C22×C4C2×D29211yescharacteristic
630C4⋊C4—44no—
631C4⋊C4—2924no—
632C4⋊C4—2924no—
633C4⋊C4—1462no—
634C4⋊C4—1462no—
635C4⋊C4—1462no—
636C4⋊C4—1462no—
637C4⋊C4—1461no—
638C4⋊C4—1461no—
639C4⋊C4—1461no—
640C4⋊C4—1461no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—2924no—
646C22⋊C4—1468no—
647C22⋊C4—1462no—
648C22⋊C4—1462no—
649C22⋊C4—1462no—
650C22⋊C4—1462no—
651C22⋊C4—1462no—
652C22⋊C4—1462no—
653C22⋊C4—1462no—
654C22⋊C4—1462no—
655C22⋊C4—1462no—
656C22⋊C4—1462no—
657C42—44no—
658C42—1462no—
659C42—1462no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—48no—
683C23—48no—
684C23—2922no—
685C23—2922no—
686C23—1462no—
687C23—1464no—
688C23C2×#1192400511yescharacteristic
689C23C2×#1192400511yescharacteristic
690C23C2×#1192400511yescharacteristic
691C23C2×#1192400511yescharacteristic
692C23C22×C4×D7311yescharacteristic
693C23C22×C22⋊D7311yescharacteristic
694C23C22×D29211yescharacteristic
695C23#1455663712yes—
696C23#1455663812yes—
697Q8—2922no—
698Q8—2922no—
699D4—2922no—
700D4—2924no—
701D4—2924no—
702D4—2922no—
703D4—2922no—
704D4—2924no—
705D4—2924no—
706D4—2924no—
707D4—2922no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—2924no—
739C2×C4—2924no—
740C2×C4—2922no—
741C2×C4—2922no—
742C2×C4—2924no—
743C2×C4—2924no—
744C2×C4—2924no—
745C2×C4—5848no—
746C2×C4—1462no—
747C2×C4—1462no—
748C2×C4—1462no—
749C2×C4—1464no—
750C2×C4#1455650514yescomplemented
751C2×C4C2×#1192400511yescharacteristic
752C2×C4C2×#1192400511yescharacteristic
753C2×C4C2×#1192400511yescharacteristic
754C2×C4C2×#1192400511yescharacteristic
755C2×C4C2×#1192400511yescharacteristic
756C2×C4C2×#1192400511yescharacteristic
757C2×C4C2×#1192400511yescharacteristic
758C2×C4C2×#1192400511yescharacteristic
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—2922no—
786C22—2922no—
787C22—2922no—
788C22—5844no—
789C22C2×#1455650512yes—
790C22#1798856012yes—
791C22C22×#1192400511yescharacteristic
792C22#1798906712yes—
793C22#1798915611yescharacteristic
794C22#1798916311yescharacteristic
795C22#1798916512yes—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—84no—
803C4—2922no—
804C4—2922no—
805C4—2922no—
806C4—5844no—
807C4C2×#1455650512yes—
808C4C2×#1455650512yes—
809C2—22no—
810C2—21no—
811C2—21no—
812C2—22no—
813C2—22no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—5842no—
818C2#2261251911yescharacteristic
819C2C22×#1455650511yescharacteristic
820C2C2×#1798856011yescharacteristic
subgroupG/H
centerC22C22×#11924005
commutatorC23×C73C23×C4
FrattiniC24C23×D73
FittingC73×#2280C2
socleC22×C73C22×C22⋊C4
prime radicalC2×#17989098C2
cosocleC24×C73C24
hypercenter#2280D73
hypocenterC73#21874
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#17988447C2semidirect
3. #22610916C2semidirect
4. #22610767C2semidirect
5. #22610382C2semidirect
6. #22609916C2semidirect
7. C73×#2280C2semidirect
8. C22×#11924028C4semidirect
17. C2×#14556574C4semidirect
18. C2×#14556570C4semidirect
20. C2×#14556565C4semidirect
23. C2×C4×C22⋊D73C4semidirect
25. C2×#14556550C4semidirect
48. C22×Dic146C2×C4semidirect
49. C22×D292C2×C4semidirect
54. C22×C4×D73C2×C4semidirect
94. C2×C4⋊Dic73C2×C4semidirect
95. C2×C4⋊Dic73C2×C4semidirect
96. C2×#11924007C2×C4semidirect
97. C2×#11924007C2×C4semidirect
104. C2×#11924005C2×C4semidirect
105. C2×#11924005C2×C4semidirect
106. C2×C4×Dic73C2×C4semidirect
316. C2×C4×C73#99semidirect
412. #2280D73semidirect
418. C73#21874semidirect
750. C2×C4#14556505semidirect

Maximal subgroups

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

subgroupindex
C2×#179890982
C2×#179884472
#226109162
#226107672
#226103822
#226099162
C73×#22802
#2187473