Finite Group Databasebeta

← #33106237

Subgroups — #33106237

Order 18688.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988738C211yesmaximal, characteristic
2C2×#17988687C211yesmaximal, characteristic, complemented
3C22×#14556512C211yesmaximal, characteristic
4#22612934C211yesmaximal, characteristic, complemented
5#22610811C211yesmaximal, characteristic, complemented
6#22610631C211yesmaximal, characteristic, complemented
7#22610548C211yesmaximal, characteristic, complemented
8#22610352C211yesmaximal, characteristic, complemented
9#22610289C211yesmaximal, characteristic, complemented
10#22610265C211yesmaximal, characteristic, complemented
11#22610178C211yesmaximal, characteristic, complemented
12#22610118C211yesmaximal, characteristic, complemented
13#22609756C211yesmaximal, characteristic, complemented
14#22609709C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C73C211yesmaximal, characteristic
16C22×#11924016C2211yescharacteristic
17C22×#11924016C2211yescharacteristic
18C23×#10596831C2211yescharacteristic
19C2×#14556570C2211yescharacteristic
20C2×C4×Dic146C2211yescharacteristic, complemented
21C22×C4⋊Dic73C2211yescharacteristic
22#17988738C418yescomplemented
23#17988687—24no—
24C2×#14556524C2211yescharacteristic, complemented
25C2×#14556524C2211yescharacteristic, complemented
26C2×#14556514C2211yescharacteristic, complemented
27C2×#14556514C2211yescharacteristic, complemented
28C2×#14556512—24no—
29C2×#14556512C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×#14556512C2211yescharacteristic
32C2×#14556512C2211yescharacteristic
33C2×#14556512C2211yescharacteristic
34C2×#14556512C2211yescharacteristic
35C2×C22⋊#10596831C2211yescharacteristic
36C2×#14556502C2211yescharacteristic, complemented
37C2×#14556502C2211yescharacteristic, complemented
38#17988493C2211yescharacteristic, complemented
39#17988485C2211yescharacteristic, complemented
40#17988484—21no—
41#17988474—21no—
42#17988459—21no—
43C4×C4⋊Dic73C2211yescharacteristic, complemented
44C22⋊C4×Dic73—21no—
45#17988349C2211yescharacteristic, complemented
46#17988349C2211yescharacteristic, complemented
47#17988349C2211yescharacteristic, complemented
48#17988349C2211yescharacteristic, complemented
49#17988342C2211yescharacteristic, complemented
50#17988342C2211yescharacteristic, complemented
51C23×D4×C73C2211yescharacteristic
52C2×C4×D4×C73C2211yescharacteristic
53C2×C4×D4×C73C2211yescharacteristic
54C22×C22⋊C4×C73—21no—
55#390×C73C2211yescharacteristic
56#390×C73C2211yescharacteristic
57#386×C73—21no—
58#386×C73—21no—
59#380×C73C2211yescharacteristic
60#379×C73—21no—
61C4×C22⋊C4×C73C2211yescharacteristic
62C22×Dic146C2311yescharacteristic
63C23×Dic73—21no—
64C2×#11924016—22no—
65C2×#11924016—22no—
66C2×#11924016—41no—
67C2×#11924016—41no—
68C2×#11924016C2×C414yescomplemented
69C2×#11924016C2×C414yescomplemented
70C22×#10596831—22no—
71C22×#10596831—22no—
72C22×#10596831—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#14556514—22no—
96#14556514—41no—
97#14556512—22no—
98#14556512—22no—
99#14556512—22no—
100#14556512C2×C414yescomplemented
101#14556512C2×C414yescomplemented
102#14556512D414yes—
103C22⋊#10596831C2×C414yescomplemented
104#14556502—22no—
105#14556502—41no—
106#14556498—21no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110C25×C73—21no—
111C22×D4×C73—22no—
112C22×D4×C73—22no—
113C22×D4×C73—21no—
114C22×D4×C73—22no—
115C22×D4×C73—41no—
116C22×D4×C73—41no—
117C22×D4×C73C2×C414yes—
118C22×D4×C73C2311yescharacteristic
119C22×D4×C73C2311yescharacteristic
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×C73—21no—
133C2×C22⋊C4×C73—21no—
134C2×C22⋊C4×C73—21no—
135C2×C22⋊C4×C73—21no—
136C2×C22⋊C4×C73—44no—
137C2×C22⋊C4×C73D411yescharacteristic
138C2×C22⋊C4×C73D411yescharacteristic
139C2×C42×C73C2311yescharacteristic
140C2×C42×C73C2311yescharacteristic
141#95×C73—21no—
142#95×C73D411yescharacteristic
143#95×C73D411yescharacteristic
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146—21no—
147C2×Dic146—21no—
148C2×Dic146—21no—
149C2×Dic146C22×C412yes—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73—21no—
154C22×Dic73—42no—
155C22×Dic73—42no—
156C22×Dic73—81no—
157#11924016—28no—
158#11924016—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×#10596831—44no—
169C2×#10596831C22×C412yes—
170C2×#10596831C22×C412yes—
171C2×#10596831C2×D412yes—
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73—21no—
175C4⋊Dic73—21no—
176C4⋊Dic73—42no—
177C4⋊Dic73C22×C412yes—
178C4⋊Dic73C2×D412yes—
179#11924007—24no—
180#11924007—42no—
181#11924007—81no—
182C22⋊Dic73—24no—
183C4×Dic73—42no—
184C4×Dic73—81no—
185C24×C73—21no—
186C24×C73—21no—
187C24×C73—24no—
188C24×C73—42no—
189C24×C73—42no—
190C24×C73—42no—
191C24×C73—42no—
192C24×C73—81no—
193C24×C73—81no—
194C24×C73C2×D411yescharacteristic
195C2×D4×C73—28no—
196C2×D4×C73—24no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—21no—
202C2×D4×C73—21no—
203C2×D4×C73—21no—
204C2×D4×C73—21no—
205C2×D4×C73—44no—
206C2×D4×C73—44no—
207C2×D4×C73—44no—
208C2×D4×C73—42no—
209C2×D4×C73—42no—
210C2×D4×C73C22×C412yes—
211C2×D4×C73C22×C412yes—
212C2×D4×C73C2×D412yes—
213C2×D4×C73#4112yes—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—42no—
221C22×C4×C73—42no—
222C22×C4×C73—42no—
223C22×C4×C73—42no—
224C22×C4×C73—81no—
225C22×C4×C73—81no—
226C22×C4×C73C22×C412yes—
227C22×C4×C73C2×D411yescharacteristic
228C22×C4×C73C2×D411yescharacteristic
229C22×C4×C73C2×D411yescharacteristic
230C22×C4×C73C2×D411yescharacteristic
231C22×C4×C73C2×D411yescharacteristic
232C22×C4×C73#4112yes—
233C22×C4×C73C2411yescharacteristic
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C22⋊C4×C73—22no—
239C22⋊C4×C73—22no—
240C22⋊C4×C73—42no—
241C22⋊C4×C73—42no—
242C22⋊C4×C73—42no—
243C22⋊C4×C73—42no—
244C22⋊C4×C73—42no—
245C22⋊C4×C73—81no—
246C22⋊C4×C73—81no—
247C42×C73—21no—
248C42×C73—21no—
249C42×C73—21no—
250C42×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—22no—
256C23×C73—22no—
257C23×C73—22no—
258C23×C73—22no—
259C23×C73—48no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73—41no—
263C23×C73—41no—
264C23×C73—41no—
265C23×C73—41no—
266C23×C73—41no—
267C23×C73—41no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—48no—
271C23×C73—84no—
272C23×C73—84no—
273C23×C73—84no—
274C23×C73—84no—
275C23×C73—84no—
276C23×C73C4×D412yes—
277C23×C73AGL(1,ℤ/8)12yes—
278C23×C73#13712yes—
279C23×C73C22×D411yescharacteristic
280D4×C73—22no—
281D4×C73—22no—
282D4×C73—22no—
283D4×C73—22no—
284D4×C73—22no—
285D4×C73—48no—
286D4×C73—41no—
287D4×C73—41no—
288D4×C73C4×D414yes—
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—21no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
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—84no—
314C2×C4×C73—84no—
315C2×C4×C73C4×D412yes—
316C2×C4×C73C23×C411yescharacteristic
317C2×C4×C73C22×D411yescharacteristic
318C2×C4×C73C2×#4111yescharacteristic
319C2×C4×C73C2×#4111yescharacteristic
320C2×C4×C73H(5,𝔽2)11yescharacteristic
321C2×C4×C73H(5,𝔽2)11yescharacteristic
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—41no—
326C2×Dic73—41no—
327C2×Dic73—41no—
328C2×Dic73—41no—
329C2×Dic73—41no—
330C2×Dic73—41no—
331C2×Dic73—41no—
332C2×Dic73—41no—
333C2×Dic73—41no—
334C2×Dic73—84no—
335Dic146—22no—
336Dic146—22no—
337Dic146—41no—
338Dic146—41no—
339#10596831—22no—
340#10596831—22no—
341#10596831—22no—
342#10596831—41no—
343C22×C73—22no—
344C22×C73—22no—
345C22×C73—22no—
346C22×C73—22no—
347C22×C73—22no—
348C22×C73—22no—
349C22×C73—24no—
350C22×C73—42no—
351C22×C73—42no—
352C22×C73—42no—
353C22×C73—42no—
354C22×C73—42no—
355C22×C73—42no—
356C22×C73—42no—
357C22×C73—42no—
358C22×C73—42no—
359C22×C73—816no—
360C22×C73—81no—
361C22×C73—81no—
362C22×C73—81no—
363C22×C73—81no—
364C22×C73#44014yescomplemented
365C22×C73C2×C4×D411yescharacteristic
366C22×C73D4211yescharacteristic
367C22×C73#54611yescharacteristic
368C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C73C2×#13711yescharacteristic
370C22×C73#57611yescharacteristic
371C22×C73#57711yescharacteristic
372C4×C73—22no—
373C4×C73—41no—
374C4×C73—41no—
375C4×C73—41no—
376C4×C73—41no—
377C4×C73—81no—
378C4×C73—81no—
379C4×C73C2×C4×D411yescharacteristic
380C4×C73#51811yescharacteristic
381C4×C73#54611yescharacteristic
382C4×C73#55111yescharacteristic
383Dic73—42no—
384Dic73—42no—
385Dic73—42no—
386Dic73—81no—
387#22854—731nomaximal, Sylow
388C2×C73—24no—
389C2×C73—44no—
390C2×C73—82no—
391C2×C73#235811yescharacteristic
392C2×C73C2×#44011yescharacteristic
393C2×C73#294611yescharacteristic
394C2×C73#326411yescharacteristic
395C2×C73#326611yescharacteristic
396C2×C73#331011yescharacteristic
397C2×C73#331411yescharacteristic
398C2×#450—731no—
399C2×#440—731no—
400C22×#102—731no—
401#2360—731no—
402D4×C22⋊C4D7311yescharacteristic
403#1973—731no—
404#1936—731no—
405#1925—731no—
406#1892—731no—
407#1880—731no—
408#1877—731no—
409#1862—731no—
410#1852—731no—
411#1762—731no—
412#1752—731no—
413C73#2285411yescharacteristic, complemented, Sylow
414C23×D4C2×D7311yescharacteristic
415C22×SD16—731no—
416C22×SD16—731no—
417C23×C8—731no—
418C2×C22⋊Q8—731no—
419C2×C4×Q8—731no—
420C2×C4×D4C2×D7311yescharacteristic
421C2×C4×D4C2×D7311yescharacteristic
422C22×C4⋊C4—731no—
423C22×C22⋊C4—21no—
424#450—738no—
425#440—1464no—
426C2×#107—731no—
427C2×#107—731no—
428C2×#103—731no—
429C2×#103—731no—
430C2×#102—731no—
431C2×#102—731no—
432C2×#102—731no—
433C2×#102—731no—
434C2×#102—731no—
435C2×#102—731no—
436C2×#102—1464no—
437C2×C22⋊C8—731no—
438C2×#97—731no—
439C2×#97—731no—
440#391—731no—
441#390C2×D7311yescharacteristic
442#390C2×D7311yescharacteristic
443#389—731no—
444#389—1461no—
445#387—1461no—
446#386—21no—
447#386—21no—
448#385—1461no—
449#380C2×D7311yescharacteristic
450#379—21no—
451C4×C4⋊C4—731no—
452C4×C22⋊C4—1461no—
453C4×C22⋊C4C2×D7311yescharacteristic
454#340—731no—
455#340—731no—
456#340—731no—
457#340—731no—
458#336—731no—
459#336—731no—
460C25—21no—
461C22×Q8—731no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4C4×D7314yes—
469C22×D4C22×D7311yescharacteristic
470C22×D4C22×D7311yescharacteristic
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—1461no—
474C23×C4C22×D7311yescharacteristic
475C2×SD16—2921no—
476C2×SD16—2921no—
477C2×SD16—734no—
478C2×SD16—734no—
479C2×SD16—1462no—
480C2×SD16—1462no—
481C22×C8—2921no—
482C22×C8—731no—
483C22×C8—731no—
484C22×C8—731no—
485C22×C8—731no—
486C22×C8—1462no—
487C22×C8—1462no—
488C22⋊Q8—734no—
489C22⋊Q8—1462no—
490C4×Q8—2921no—
491C4×Q8—1462no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—41no—
495C4×D4—41no—
496C2×C4⋊C4—2921no—
497C2×C4⋊C4—731no—
498C2×C4⋊C4—731no—
499C2×C4⋊C4—731no—
500C2×C4⋊C4—1461no—
501C2×C4⋊C4—1461no—
502C2×C4⋊C4—1462no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4—1461no—
505C2×C4⋊C4C22×D7311yescharacteristic
506C2×C4⋊C4C22×D7311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—44no—
515C2×C22⋊C4—1461no—
516C2×C22⋊C4C22⋊D7311yescharacteristic
517C2×C22⋊C4C22⋊D7311yescharacteristic
518C2×C42—1461no—
519C2×C42—1461no—
520C2×C42C22×D7311yescharacteristic
521C2×C42C22×D7311yescharacteristic
522#107—2921no—
523#107—1462no—
524#103—2921no—
525#103—1462no—
526#102—734no—
527#102—734no—
528#102—734no—
529#102—1462no—
530#102—1462no—
531#102—1462no—
532C22⋊C8—734no—
533#97—2921no—
534#97—1462no—
535#95—21no—
536#95—1461no—
537#95—1461no—
538#95—1461no—
539#95—1461no—
540#95C22⋊D7311yescharacteristic
541#95C22⋊D7311yescharacteristic
542C24—21no—
543C24—21no—
544C24—24no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—81no—
550C24—81no—
551C24C2×C22⋊D7311yescharacteristic
552C2×Q8—732no—
553C2×Q8—1461no—
554C2×Q8—1461no—
555C2×Q8—1461no—
556C2×Q8—1461no—
557C2×Q8—1461no—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4C2×C4×D7312yes—
574C2×D4C2×C4×D7312yes—
575C2×D4D4×D7312yes—
576C2×D4#1192402712yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—2922no—
590C22×C4—2922no—
591C22×C4—5841no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1461no—
596C22×C4C2×C4×D7312yes—
597C22×C4C2×C22⋊D7311yescharacteristic
598C22×C4C2×C22⋊D7311yescharacteristic
599C22×C4C2×C22⋊D7311yescharacteristic
600C22×C4C2×C22⋊D7311yescharacteristic
601C22×C4C2×C22⋊D7311yescharacteristic
602C22×C4#1192402812yes—
603C22×C4C23×D7311yescharacteristic
604SD16—2924no—
605SD16—1468no—
606C2×C8—2924no—
607C2×C8—732no—
608C2×C8—732no—
609C2×C8—732no—
610C2×C8—1461no—
611C2×C8—1461no—
612C2×C8—1461no—
613C2×C8—1461no—
614C2×C8—1461no—
615C2×C8—1461no—
616C2×C8—1461no—
617C2×C8—1461no—
618C2×C8—1461no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—2922no—
624C4⋊C4—2922no—
625C4⋊C4—5841no—
626C4⋊C4—732no—
627C4⋊C4—732no—
628C4⋊C4—1461no—
629C4⋊C4—1461no—
630C4⋊C4—1464no—
631C4⋊C4—1461no—
632C4⋊C4—1461no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—1464no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—2922no—
648C42—5841no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23C4×C22⋊D7312yes—
675C23#1455661712yes—
676C23#1455662112yes—
677C23C22×C22⋊D7311yescharacteristic
678Q8—2921no—
679Q8—2921no—
680Q8—1462no—
681Q8—1462no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4#1455655114yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—84no—
716C2×C4—84no—
717C2×C4—2921no—
718C2×C4—2921no—
719C2×C4—2921no—
720C2×C4—2921no—
721C2×C4—2921no—
722C2×C4—2921no—
723C2×C4—2921no—
724C2×C4—2921no—
725C2×C4—2921no—
726C2×C4—5844no—
727C2×C4—1462no—
728C2×C4—1462no—
729C2×C4—1462no—
730C2×C4C4×C22⋊D7312yes—
731C2×C4C22×C4×D7311yescharacteristic
732C2×C4C2×D4×D7311yescharacteristic
733C2×C4C2×#1192402711yescharacteristic
734C2×C4C2×#1192402811yescharacteristic
735C2×C4#1455663611yescharacteristic
736C2×C4#1455663611yescharacteristic
737C8—2921no—
738C8—1462no—
739C8—1462no—
740C8—1462no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22#1798868714yescomplemented
763C22C2×C4×C22⋊D7311yescharacteristic
764C22D4×C22⋊D7311yescharacteristic
765C22#1798923111yescharacteristic
766C22C2×#1455661711yescharacteristic
767C22C2×#1455662111yescharacteristic
768C22#1798939011yescharacteristic
769C22#1798939811yescharacteristic
770C4—22no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4—81no—
777C4—2922no—
778C4—2922no—
779C4—2922no—
780C4—5841no—
781C4C2×#1455655111yescharacteristic
782C4#1798906011yescharacteristic
783C4#1798922711yescharacteristic
784C4#1798926311yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2#2261291011yescharacteristic
789C2C2×#1798868711yescharacteristic
790C2#2261876311yescharacteristic
791C2#2262140711yescharacteristic
792C2#2262143711yescharacteristic
793C2#2262195211yescharacteristic
794C2#2262201211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingD4×C22⋊C4×C73C2
socleC23×C73C22×D4
prime radicalC23×D4×C73C22
cosocleC22×C4×C73C24
hypercenterD4×C22⋊C4D73
hypocenterC73#22854
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#17988687C2semidirect
4. #22612934C2semidirect
5. #22610811C2semidirect
6. #22610631C2semidirect
7. #22610548C2semidirect
8. #22610352C2semidirect
9. #22610289C2semidirect
10. #22610265C2semidirect
11. #22610178C2semidirect
12. #22610118C2semidirect
13. #22609756C2semidirect
14. #22609709C2semidirect
20. C2×C4×Dic146C22semidirect
22. #17988738C4semidirect
24. C2×#14556524C22semidirect
25. C2×#14556524C22semidirect
26. C2×#14556514C22semidirect
27. C2×#14556514C22semidirect
36. C2×#14556502C22semidirect
37. C2×#14556502C22semidirect
38. #17988493C22semidirect
39. #17988485C22semidirect
43. C4×C4⋊Dic73C22semidirect
45. #17988349C22semidirect
46. #17988349C22semidirect
47. #17988349C22semidirect
48. #17988349C22semidirect
49. #17988342C22semidirect
50. #17988342C22semidirect
68. C2×#11924016C2×C4semidirect
69. C2×#11924016C2×C4semidirect
78. #14556570C2×C4semidirect
100. #14556512C2×C4semidirect
101. #14556512C2×C4semidirect
103. C22⋊#10596831C2×C4semidirect
364. C22×C73#440semidirect
413. C73#22854semidirect
762. C22#17988687semidirect

Maximal subgroups

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

subgroupindex
C2×#179887382
C2×#179886872
C22×#145565122
#226129342
#226108112
#226106312
#226105482
#226103522
#226102892
#226102652
#226101782
#226101182
#226097562
#226097092
D4×C22⋊C4×C732
#2285473