Finite Group Databasebeta

← #33106357

Subgroups — #33106357

Order 18688.

1134 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988749C211yesmaximal, characteristic
2C2×#17988687C211yesmaximal, characteristic, complemented
3C2×#17988588C211yesmaximal, characteristic
4#22612934C211yesmaximal, characteristic, complemented
5#22610791C211yesmaximal, characteristic, complemented
6#22610624C211yesmaximal, characteristic, complemented
7#22610569C211yesmaximal, characteristic, complemented
8#22610362C211yesmaximal, characteristic, complemented
9#22610275C211yesmaximal, characteristic, complemented
10#22610265C211yesmaximal, characteristic, complemented
11#22610178C211yesmaximal, characteristic, complemented
12#22610118C211yesmaximal, characteristic, complemented
13C4×#14556512C211yesmaximal, characteristic, complemented
14#22609715C211yesmaximal, characteristic, complemented
15C73×#2339C211yesmaximal, characteristic
16C22×#11924018C2211yescharacteristic
17C22×#11924016C2211yescharacteristic
18C22×#11924012C2211yescharacteristic
19C2×#14556570C2211yescharacteristic
20C2×C4×Dic146C2211yescharacteristic
21C22×C4⋊Dic73C2211yescharacteristic
22#17988749C418yescomplemented
23#17988687—24no—
24C2×#14556524C2211yescharacteristic
25C2×#14556524C2211yescharacteristic
26#17988588—24no—
27C2×#14556515C2211yescharacteristic
28C2×#14556515C2211yescharacteristic
29C2×#14556515C2211yescharacteristic
30C2×#14556514C2211yescharacteristic
31C2×#14556514C2211yescharacteristic
32C2×#14556512C2211yescharacteristic
33C2×#14556512C2211yescharacteristic
34C2×#14556512C2211yescharacteristic
35C2×C22⋊#10596831C2211yescharacteristic
36C2×#14556502C2211yescharacteristic
37C2×C4×#10596831C2211yescharacteristic
38#17988493C2211yescharacteristic
39#17988485C2211yescharacteristic
40#17988484—21no—
41#17988474—21no—
42#17988459—21no—
43C4×C4⋊Dic73C2211yescharacteristic
44C22⋊C4×Dic73—21no—
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988342C2211yescharacteristic
51C22×#41×C73C2211yescharacteristic
52C2×C4×D4×C73C2211yescharacteristic
53C2×C4×D4×C73C2211yescharacteristic
54#391×C73C2211yescharacteristic
55#391×C73C2211yescharacteristic
56#386×C73—21no—
57#386×C73—21no—
58#381×C73—21no—
59#380×C73C2211yescharacteristic
60C4×C22⋊C4×C73C2211yescharacteristic
61C2×#95×C73—21no—
62C22×Dic146C2311yescharacteristic
63C23×Dic73—21no—
64C2×#11924018—41no—
65C2×#11924018—41no—
66C2×#11924018C2×C414yescomplemented
67C2×#11924016—22no—
68C2×#11924016—22no—
69C2×#11924016C2×C414yescomplemented
70C2×#11924012—22no—
71C2×#11924012—22no—
72C2×#11924012—41no—
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77#14556570—22no—
78#14556570C2×C414yescomplemented
79C4×Dic146—22no—
80C4×Dic146—41no—
81C2×C4⋊Dic73—22no—
82C2×C4⋊Dic73—21no—
83C2×C4⋊Dic73—41no—
84C2×C4⋊Dic73C2311yescharacteristic
85C2×C4⋊Dic73C2311yescharacteristic
86C2×C4⋊Dic73C2311yescharacteristic
87C2×#11924007—21no—
88C2×#11924007—21no—
89C2×#11924007—21no—
90C2×C22⋊Dic73—21no—
91C2×C4×Dic73—21no—
92C2×C4×Dic73—21no—
93#14556524—22no—
94#14556524—41no—
95#14556515—22no—
96#14556515—22no—
97#14556515C2×C414yescomplemented
98#14556514—22no—
99#14556514—41no—
100#14556512—22no—
101#14556512C2×C414yescomplemented
102#14556512D414yes—
103C22⋊#10596831C2×C414yescomplemented
104#14556502—22no—
105C4×#10596831—41no—
106#14556498—21no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110C2×#41×C73—22no—
111C2×#41×C73—22no—
112C2×#41×C73—22no—
113C2×#41×C73—41no—
114C2×#41×C73—41no—
115C2×#41×C73C2×C414yes—
116C22×Q8×C73C2311yescharacteristic
117C22×D4×C73—21no—
118C22×D4×C73C2311yescharacteristic
119C23×C4×C73—21no—
120C23×C4×C73—21no—
121C23×C4×C73—21no—
122C23×C4×C73C2311yescharacteristic
123C4×D4×C73—22no—
124C4×D4×C73—22no—
125C4×D4×C73—41no—
126C4×D4×C73—41no—
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C4⋊C4×C73C2311yescharacteristic
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73—21no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73D411yescharacteristic
133C2×C22⋊C4×C73D411yescharacteristic
134C2×C42×C73C2311yescharacteristic
135C2×C42×C73C2311yescharacteristic
136#95×C73—21no—
137#95×C73—21no—
138#95×C73—21no—
139#95×C73—21no—
140#95×C73—21no—
141#95×C73D411yescharacteristic
142#95×C73D411yescharacteristic
143C2×Dic146—21no—
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146—21no—
147C2×Dic146—21no—
148C2×Dic146C22×C412yes—
149C22×Dic73—21no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73—42no—
154C22×Dic73—42no—
155C22×Dic73—81no—
156#11924018—44no—
157#11924016—28no—
158#11924012—44no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831C22×C412yes—
169C2×#10596831C22×C412yes—
170C2×#10596831C2×D412yes—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73—21no—
175C4⋊Dic73—42no—
176C4⋊Dic73C22×C412yes—
177C4⋊Dic73C2×D412yes—
178#11924007—24no—
179#11924007—42no—
180#11924007—81no—
181C22⋊Dic73—24no—
182C4×Dic73—42no—
183C4×Dic73—81no—
184C24×C73—21no—
185C24×C73C2×D411yescharacteristic
186#41×C73—28no—
187#41×C73—44no—
188#41×C73—44no—
189#41×C73—44no—
190C2×Q8×C73—21no—
191C2×Q8×C73—21no—
192C2×Q8×C73—21no—
193C2×Q8×C73—21no—
194C2×Q8×C73—21no—
195C2×Q8×C73C22×C412yes—
196C2×D4×C73—24no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—42no—
201C2×D4×C73—42no—
202C2×D4×C73C22×C412yes—
203C2×D4×C73C2×D412yes—
204C2×D4×C73#4112yes—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—24no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—42no—
214C22×C4×C73—42no—
215C22×C4×C73—42no—
216C22×C4×C73—42no—
217C22×C4×C73—42no—
218C22×C4×C73—42no—
219C22×C4×C73—81no—
220C22×C4×C73—81no—
221C22×C4×C73C22×C412yes—
222C22×C4×C73C2×D411yescharacteristic
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73C2×D411yescharacteristic
225C22×C4×C73C2×D411yescharacteristic
226C22×C4×C73C2×D411yescharacteristic
227C22×C4×C73#4112yes—
228C22×C4×C73C2411yescharacteristic
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C22⋊C4×C73—22no—
234C22⋊C4×C73—41no—
235C22⋊C4×C73—42no—
236C22⋊C4×C73—42no—
237C22⋊C4×C73—81no—
238C42×C73—21no—
239C42×C73—21no—
240C42×C73—21no—
241C42×C73—21no—
242C23×C73—22no—
243C23×C73—22no—
244C23×C73—21no—
245C23×C73—22no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73C4×D412yes—
256C23×C73C22×D411yescharacteristic
257Q8×C73—22no—
258Q8×C73—22no—
259Q8×C73—41no—
260Q8×C73—41no—
261D4×C73—22no—
262D4×C73—22no—
263D4×C73—22no—
264D4×C73—48no—
265D4×C73C4×D414yes—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—48no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—84no—
294C2×C4×C73—84no—
295C2×C4×C73C4×D412yes—
296C2×C4×C73#13712yes—
297C2×C4×C73C23×C411yescharacteristic
298C2×C4×C73C22×D411yescharacteristic
299C2×C4×C73C2×#4111yescharacteristic
300C2×C4×C73C2×#4111yescharacteristic
301C2×C4×C73H(5,𝔽2)11yescharacteristic
302C2×C4×C73H(5,𝔽2)11yescharacteristic
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—41no—
314C2×Dic73—41no—
315C2×Dic73—84no—
316Dic146—22no—
317Dic146—22no—
318Dic146—41no—
319Dic146—41no—
320#10596831—22no—
321#10596831—22no—
322#10596831—22no—
323#10596831—41no—
324C22×C73—22no—
325C22×C73—24no—
326C22×C73—22no—
327C22×C73—22no—
328C22×C73—42no—
329C22×C73—42no—
330C22×C73—41no—
331C22×C73—42no—
332C22×C73—41no—
333C22×C73—42no—
334C22×C73—42no—
335C22×C73—41no—
336C22×C73—41no—
337C22×C73—42no—
338C22×C73C2×C4×D411yescharacteristic
339C22×C73D4211yescharacteristic
340C22×C73#54611yescharacteristic
341C22×C73C2×#13711yescharacteristic
342C22×C73#57511yescharacteristic
343C22×C73#57611yescharacteristic
344C22×C73#57811yescharacteristic
345C4×C73—22no—
346C4×C73—22no—
347C4×C73—42no—
348C4×C73—41no—
349C4×C73—41no—
350C4×C73—41no—
351C4×C73—81no—
352C4×C73—81no—
353C4×C73C2×C4×D411yescharacteristic
354C4×C73#51811yescharacteristic
355C4×C73#54611yescharacteristic
356C4×C73#55111yescharacteristic
357Dic73—42no—
358Dic73—42no—
359Dic73—42no—
360Dic73—81no—
361#22862—731nomaximal, Sylow
362C2×C73—42no—
363C2×C73—44no—
364C2×C73#235811yescharacteristic
365C2×C73C4×#13711yescharacteristic
366C2×C73#295111yescharacteristic
367C2×C73#327311yescharacteristic
368C2×C73#327611yescharacteristic
369C2×C73#331411yescharacteristic
370C2×C73#331511yescharacteristic
371C2×#452—731no—
372C2×#440—731no—
373C2×#417—731no—
374#2360—731no—
375#2339D7311yescharacteristic
376#1969—731no—
377#1935—731no—
378#1928—731no—
379#1894—731no—
380#1878—731no—
381#1877—731no—
382#1862—731no—
383#1852—731no—
384C4×#102—731no—
385#1753—731no—
386C73#2286211yescharacteristic, complemented, Sylow
387C22×#41C2×D7311yescharacteristic
388C22×Q16—731no—
389C22×SD16—731no—
390C22×M16—731no—
391C2×C22⋊Q8—731no—
392C2×C4×Q8—731no—
393C2×C4×D4C2×D7311yescharacteristic
394C2×C4×D4C2×D7311yescharacteristic
395C22×C4⋊C4—731no—
396#452—738no—
397#440—1464no—
398C2×#107—731no—
399C2×#107—731no—
400#417—1464no—
401C2×#103—731no—
402C2×#103—731no—
403C2×#103—731no—
404C2×#103—731no—
405C2×#103—731no—
406C2×#102—731no—
407C2×#102—731no—
408C2×#102—731no—
409C2×C22⋊C8—731no—
410C2×#97—731no—
411C2×C4×C8—731no—
412#391—731no—
413#391C2×D7311yescharacteristic
414#391C2×D7311yescharacteristic
415#389—731no—
416#389—1461no—
417#387—1461no—
418#386—21no—
419#386—21no—
420#385—1461no—
421#381—21no—
422#380C2×D7311yescharacteristic
423C4×C4⋊C4—731no—
424C4×C22⋊C4—1461no—
425C4×C22⋊C4C2×D7311yescharacteristic
426C2×#95—21no—
427#340—731no—
428#340—731no—
429#340—731no—
430#340—731no—
431#336—731no—
432#336—731no—
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—22no—
436C2×#41—41no—
437C2×#41—41no—
438C2×#41C4×D7314yes—
439C22×Q8—731no—
440C22×Q8C22×D7311yescharacteristic
441C22×D4—21no—
442C22×D4C22×D7311yescharacteristic
443C23×C4—21no—
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—1461no—
447C23×C4C22×D7311yescharacteristic
448C2×Q16—2921no—
449C2×Q16—2921no—
450C2×Q16—734no—
451C2×SD16—734no—
452C2×SD16—1462no—
453C2×SD16—1462no—
454C2×M16—2921no—
455C2×M16—1462no—
456C2×M16—1462no—
457C22×C8—731no—
458C22×C8—731no—
459C22×C8—731no—
460C22×C8—731no—
461C22⋊Q8—734no—
462C22⋊Q8—1462no—
463C4×Q8—2921no—
464C4×Q8—1462no—
465C4×D4—22no—
466C4×D4—22no—
467C4×D4—41no—
468C4×D4—41no—
469C2×C4⋊C4—2921no—
470C2×C4⋊C4—731no—
471C2×C4⋊C4—731no—
472C2×C4⋊C4—731no—
473C2×C4⋊C4—1461no—
474C2×C4⋊C4—1461no—
475C2×C4⋊C4—1462no—
476C2×C4⋊C4—1461no—
477C2×C4⋊C4—1461no—
478C2×C4⋊C4C22×D7311yescharacteristic
479C2×C4⋊C4C22×D7311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—1461no—
484C2×C22⋊C4C22⋊D7311yescharacteristic
485C2×C22⋊C4C22⋊D7311yescharacteristic
486C2×C42—1461no—
487C2×C42—1461no—
488C2×C42C22×D7311yescharacteristic
489C2×C42C22×D7311yescharacteristic
490#107—2921no—
491#107—1462no—
492#103—2921no—
493#103—734no—
494#103—1462no—
495#103—1462no—
496#103—1462no—
497#102—734no—
498#102—734no—
499#102—1462no—
500C22⋊C8—734no—
501#97—1462no—
502C4×C8—2921no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—1461no—
509#95—1461no—
510#95—1461no—
511#95—1461no—
512#95C22⋊D7311yescharacteristic
513#95C22⋊D7311yescharacteristic
514C24—21no—
515C24C2×C22⋊D7311yescharacteristic
516#41—28no—
517#41—44no—
518#41—44no—
519#41—44no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—732no—
526C2×Q8—1461no—
527C2×Q8—1461no—
528C2×Q8—1461no—
529C2×Q8—1461no—
530C2×Q8—1461no—
531C2×Q8C2×C4×D7312yes—
532C2×D4—24no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4C2×C4×D7312yes—
539C2×D4D4×D7312yes—
540C2×D4#1192402712yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—2922no—
558C22×C4—2922no—
559C22×C4—5841no—
560C22×C4—1461no—
561C22×C4—1461no—
562C22×C4—1461no—
563C22×C4—1461no—
564C22×C4C2×C4×D7312yes—
565C22×C4C2×C22⋊D7311yescharacteristic
566C22×C4C2×C22⋊D7311yescharacteristic
567C22×C4C2×C22⋊D7311yescharacteristic
568C22×C4C2×C22⋊D7311yescharacteristic
569C22×C4C2×C22⋊D7311yescharacteristic
570C22×C4#1192402812yes—
571C22×C4C23×D7311yescharacteristic
572Q16—2924no—
573SD16—1468no—
574M16—2924no—
575C2×C8—732no—
576C2×C8—732no—
577C2×C8—732no—
578C2×C8—1461no—
579C2×C8—1461no—
580C2×C8—1461no—
581C2×C8—1461no—
582C2×C8—1461no—
583C2×C8—1461no—
584C2×C8—1461no—
585C2×C8—1461no—
586C2×C8—1461no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—2922no—
592C4⋊C4—2922no—
593C4⋊C4—5841no—
594C4⋊C4—732no—
595C4⋊C4—732no—
596C4⋊C4—1461no—
597C4⋊C4—1461no—
598C4⋊C4—1464no—
599C4⋊C4—1461no—
600C4⋊C4—1461no—
601C22⋊C4—22no—
602C22⋊C4—41no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—1464no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—2922no—
612C42—5841no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—21no—
619C23—22no—
620C23—21no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23C4×C22⋊D7312yes—
627C23C22×C22⋊D7311yescharacteristic
628Q8—22no—
629Q8—22no—
630Q8—41no—
631Q8—41no—
632Q8—2921no—
633Q8—2921no—
634Q8—1462no—
635Q8—1462no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4—48no—
640D4#1455655114yes—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—48no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—84no—
669C2×C4—84no—
670C2×C4—2921no—
671C2×C4—2921no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—2921no—
675C2×C4—2921no—
676C2×C4—2921no—
677C2×C4—2921no—
678C2×C4—2921no—
679C2×C4—5844no—
680C2×C4—1462no—
681C2×C4—1462no—
682C2×C4—1462no—
683C2×C4C4×C22⋊D7312yes—
684C2×C4#1455662112yes—
685C2×C4C22×C4×D7311yescharacteristic
686C2×C4C2×D4×D7311yescharacteristic
687C2×C4C2×#1192402711yescharacteristic
688C2×C4C2×#1192402811yescharacteristic
689C2×C4#1455663611yescharacteristic
690C2×C4#1455663611yescharacteristic
691C8—2921no—
692C8—1462no—
693C8—1462no—
694C8—1462no—
695C22—22no—
696C22—22no—
697C22—24no—
698C22—22no—
699C22—42no—
700C22—41no—
701C22—41no—
702C22—42no—
703C22—42no—
704C22—41no—
705C22—42no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22C2×C4×C22⋊D7311yescharacteristic
710C22D4×C22⋊D7311yescharacteristic
711C22#1798923111yescharacteristic
712C22C2×#1455662111yescharacteristic
713C22#1798938511yescharacteristic
714C22#1798939011yescharacteristic
715C22#1798940211yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—42no—
722C4—81no—
723C4—81no—
724C4—2922no—
725C4—2922no—
726C4—2922no—
727C4—5841no—
728C4C2×#1455655111yescharacteristic
729C4#1798906011yescharacteristic
730C4#1798922711yescharacteristic
731C4#1798926311yescharacteristic
732C2—42no—
733C2—44no—
734C2#2261291011yescharacteristic
735C2C4×#1455662111yescharacteristic
736C2#2261880411yescharacteristic
737C2#2262153811yescharacteristic
738C2#2262157311yescharacteristic
739C2#2262201211yescharacteristic
740C2#2262202711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2339C2
socleC23×C73C22×D4
prime radicalC22×#41×C73C22
cosocleC22×C4×C73C24
hypercenter#2339D73
hypocenterC73#22862
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. C2×#17988687C2semidirect
4. #22612934C2semidirect
5. #22610791C2semidirect
6. #22610624C2semidirect
7. #22610569C2semidirect
8. #22610362C2semidirect
9. #22610275C2semidirect
10. #22610265C2semidirect
11. #22610178C2semidirect
12. #22610118C2semidirect
13. C4×#14556512C2semidirect
14. #22609715C2semidirect
22. #17988749C4semidirect
66. C2×#11924018C2×C4semidirect
69. C2×#11924016C2×C4semidirect
78. #14556570C2×C4semidirect
97. #14556515C2×C4semidirect
101. #14556512C2×C4semidirect
103. C22⋊#10596831C2×C4semidirect
386. C73#22862semidirect

Maximal subgroups

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

subgroupindex
C2×#179887492
C2×#179886872
C2×#179885882
#226129342
#226107912
#226106242
#226105692
#226103622
#226102752
#226102652
#226101782
#226101182
C4×#145565122
#226097152
C73×#23392
#2286273