Finite Group Databasebeta

← #33106342

Subgroups — #33106342

Order 18688.

1090 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988749C211yesmaximal, characteristic
2C2×#17988692C211yesmaximal, characteristic, complemented
3C2×#17988583C211yesmaximal, characteristic
4#22612956C211yesmaximal, characteristic, complemented
5#22610811C211yesmaximal, characteristic, complemented
6#22610631C211yesmaximal, characteristic, complemented
7#22610555C211yesmaximal, characteristic, complemented
8#22610352C211yesmaximal, characteristic, complemented
9#22610289C211yesmaximal, characteristic, complemented
10#22610272C211yesmaximal, characteristic, complemented
11#22610185C211yesmaximal, characteristic, complemented
12#22610128C211yesmaximal, characteristic, complemented
13#22609761C211yesmaximal, characteristic, complemented
14#22609709C211yesmaximal, characteristic, complemented
15C73×#2341C211yesmaximal, characteristic
16C22×#11924018C2211yescharacteristic
17C22×#11924016C2211yescharacteristic
18C23×#10596831C2211yescharacteristic
19C2×#14556570C2211yescharacteristic
20C2×C4×Dic146C2211yescharacteristic
21C2×#14556550C2211yescharacteristic
22#17988749C418yescomplemented
23#17988692—24no—
24C2×#14556524C2211yescharacteristic
25C2×#14556522C2211yescharacteristic
26#17988583—24no—
27C2×#14556515C2211yescharacteristic
28C2×#14556515C2211yescharacteristic
29C2×#14556515C2211yescharacteristic
30C2×#14556514C2211yescharacteristic
31C2×#14556514C2211yescharacteristic
32C2×#14556512C2211yescharacteristic
33C2×#14556512C2211yescharacteristic
34C2×#14556512C2211yescharacteristic
35C2×C22⋊#10596831C2211yescharacteristic
36C2×#14556502C2211yescharacteristic
37C2×#14556502C2211yescharacteristic
38#17988493C2211yescharacteristic
39#17988485C2211yescharacteristic
40#17988481—21no—
41#17988475—21no—
42#17988469—21no—
43C4×C4⋊Dic73C2211yescharacteristic
44#17988438—21no—
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988342C2211yescharacteristic
51C22×#41×C73C2211yescharacteristic
52C2×C4×Q8×C73C2211yescharacteristic
53C2×C4×Q8×C73C2211yescharacteristic
54#390×C73—21no—
55#390×C73—21no—
56#390×C73C2211yescharacteristic
57#390×C73C2211yescharacteristic
58#380×C73—21no—
59#380×C73C2211yescharacteristic
60C4×C22⋊C4×C73—21no—
61C4×C22⋊C4×C73C2211yescharacteristic
62C22×Dic146C2311yescharacteristic
63C2×#11924018—22no—
64C2×#11924018—22no—
65C2×#11924018C2×C414yes—
66C2×#11924016—41no—
67C2×#11924016—41no—
68C2×#11924016C2×C414yes—
69C22×#10596831—22no—
70C22×#10596831—22no—
71C22×#10596831—41no—
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76#14556570—22no—
77#14556570C2×C414yes—
78C4×Dic146—22no—
79C4×Dic146—41no—
80#14556550—22no—
81#14556550—41no—
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×#11924007—21no—
86C2×#11924007—21no—
87C2×#11924007—21no—
88C2×C22⋊Dic73—21no—
89C2×C22⋊Dic73—21no—
90C2×C4×Dic73—21no—
91C2×C4×Dic73—21no—
92C2×C4×Dic73—21no—
93#14556524—41no—
94#14556522—22no—
95#14556515—22no—
96#14556515C2×C414yes—
97#14556515D414yes—
98#14556514—22no—
99#14556514—41no—
100#14556512—22no—
101#14556512—22no—
102#14556512C2×C414yes—
103C22⋊#10596831C2×C414yes—
104#14556502—22no—
105#14556502—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×C73C2311yescharacteristic
121C4×Q8×C73—22no—
122C4×Q8×C73—22no—
123C4×Q8×C73—41no—
124C4×Q8×C73—41no—
125C2×C4⋊C4×C73—21no—
126C2×C4⋊C4×C73—21no—
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×C73D411yescharacteristic
135C2×C22⋊C4×C73D411yescharacteristic
136C2×C42×C73—21no—
137C2×C42×C73—21no—
138C2×C42×C73C2311yescharacteristic
139C2×C42×C73C2311yescharacteristic
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—
153#11924018—28no—
154#11924016—44no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—44no—
165C2×#10596831C22×C412yes—
166C2×#10596831C22×C412yes—
167C2×#10596831C2×D412yes—
168C4⋊Dic73—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73C22×C412yes—
173C4⋊Dic73C2×D412yes—
174#11924007—24no—
175#11924007—42no—
176#11924007—42no—
177C22⋊Dic73—24no—
178C22⋊Dic73—42no—
179C4×Dic73—42no—
180C4×Dic73—42no—
181C4×Dic73—42no—
182C24×C73—21no—
183C24×C73C2×D411yescharacteristic
184#41×C73—28no—
185#41×C73—44no—
186#41×C73—44no—
187#41×C73—44no—
188C2×Q8×C73—21no—
189C2×Q8×C73—21no—
190C2×Q8×C73—21no—
191C2×Q8×C73C22×C412yes—
192C2×Q8×C73C2×D412yes—
193C2×Q8×C73#4112yes—
194C2×D4×C73—24no—
195C2×D4×C73—21no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—42no—
201C2×D4×C73—42no—
202C2×D4×C73C22×C412yes—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—24no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—42no—
212C22×C4×C73—42no—
213C22×C4×C73C22×C412yes—
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219C22×C4×C73#4112yes—
220C22×C4×C73C2411yescharacteristic
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—42no—
226C4⋊C4×C73—42no—
227C22⋊C4×C73—41no—
228C22⋊C4×C73—41no—
229C22⋊C4×C73—42no—
230C22⋊C4×C73—42no—
231C22⋊C4×C73—81no—
232C22⋊C4×C73—81no—
233C22⋊C4×C73—81no—
234C42×C73—21no—
235C42×C73—21no—
236C42×C73—21no—
237C42×C73—21no—
238C42×C73—42no—
239C42×C73—42no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—22no—
247C23×C73—41no—
248C23×C73—41no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73C4×D412yes—
254C23×C73C22×D411yescharacteristic
255Q8×C73—22no—
256Q8×C73—22no—
257Q8×C73—22no—
258Q8×C73C4×D414yes—
259D4×C73—22no—
260D4×C73—22no—
261D4×C73—48no—
262D4×C73—41no—
263D4×C73—41no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—21no—
267C2×C4×C73—22no—
268C2×C4×C73—21no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
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—21no—
285C2×C4×C73—48no—
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×C73C4×D412yes—
293C2×C4×C73C23×C411yescharacteristic
294C2×C4×C73C22×D411yescharacteristic
295C2×C4×C73C2×#4111yescharacteristic
296C2×C4×C73C2×#4111yescharacteristic
297C2×C4×C73H(5,𝔽2)11yescharacteristic
298C2×C4×C73H(5,𝔽2)11yescharacteristic
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—41no—
303C2×Dic73—41no—
304C2×Dic73—41no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311Dic146—22no—
312Dic146—22no—
313Dic146—41no—
314Dic146—41no—
315#10596831—22no—
316#10596831—22no—
317#10596831—22no—
318#10596831—41no—
319C22×C73—22no—
320C22×C73—22no—
321C22×C73—22no—
322C22×C73—41no—
323C22×C73—41no—
324C22×C73—41no—
325C22×C73—41no—
326C22×C73—42no—
327C22×C73—42no—
328C22×C73—42no—
329C22×C73—81no—
330C22×C73—81no—
331C22×C73—81no—
332C22×C73—81no—
333C22×C73C2×C4×D411yescharacteristic
334C22×C73D4211yescharacteristic
335C22×C73#54611yescharacteristic
336C22×C73#57511yescharacteristic
337C22×C73#57511yescharacteristic
338C22×C73#57711yescharacteristic
339C22×C73#57811yescharacteristic
340C4×C73—22no—
341C4×C73—24no—
342C4×C73—41no—
343C4×C73—41no—
344C4×C73—41no—
345C4×C73—41no—
346C4×C73—81no—
347C4×C73—81no—
348C4×C73C2×C4×D411yescharacteristic
349C4×C73#51811yescharacteristic
350C4×C73#54611yescharacteristic
351C4×C73#55111yescharacteristic
352Dic73—42no—
353Dic73—42no—
354Dic73—42no—
355Dic73—81no—
356#22861—731nomaximal, Sylow
357C2×C73—42no—
358C2×C73—82no—
359C2×C73#235811yescharacteristic
360C2×C73#294311yescharacteristic
361C2×C73#294711yescharacteristic
362C2×C73#326911yescharacteristic
363C2×C73#327111yescharacteristic
364C2×C73#331311yescharacteristic
365C2×C73#331711yescharacteristic
366C2×#452—731no—
367C2×#441—731no—
368C2×#416—731no—
369#2362—731no—
370#2341D7311yescharacteristic
371#1973—731no—
372#1936—731no—
373#1926—731no—
374#1892—731no—
375#1880—731no—
376#1878—731no—
377#1863—731no—
378#1854—731no—
379#1763—731no—
380#1752—731no—
381C73#2286111yescharacteristic, complemented, Sylow
382C22×#41C2×D7311yescharacteristic
383C22×Q16—731no—
384C22×SD16—731no—
385C23×C8—731no—
386C2×C22⋊Q8—731no—
387C2×C4×Q8—731no—
388C2×C4×Q8C2×D7311yescharacteristic
389C2×C4×Q8C2×D7311yescharacteristic
390C2×#117—731no—
391#452—738no—
392#441—1464no—
393C2×#107—731no—
394C2×#106—731no—
395#416—1464no—
396C2×#103—731no—
397C2×#103—731no—
398C2×#103—731no—
399C2×#103—731no—
400C2×#103—731no—
401C2×#102—731no—
402C2×#102—731no—
403C2×#102—731no—
404C2×C22⋊C8—731no—
405C2×#97—731no—
406C2×#97—731no—
407#391—731no—
408#390—21no—
409#390—21no—
410#390C2×D7311yescharacteristic
411#390C2×D7311yescharacteristic
412#389—731no—
413#388—1461no—
414#388—1461no—
415#387—1461no—
416#380—21no—
417#380C2×D7311yescharacteristic
418C4×C4⋊C4—731no—
419C4×C4⋊C4—1461no—
420C4×C22⋊C4—21no—
421C4×C22⋊C4C2×D7311yescharacteristic
422#340—731no—
423#340—731no—
424#340—731no—
425#340—731no—
426#336—731no—
427#336—731no—
428C2×#41—22no—
429C2×#41—22no—
430C2×#41—22no—
431C2×#41—41no—
432C2×#41—41no—
433C2×#41C4×D7314yes—
434C22×Q8—731no—
435C22×Q8C22×D7311yescharacteristic
436C22×D4—21no—
437C22×D4C22×D7311yescharacteristic
438C23×C4—21no—
439C23×C4C22×D7311yescharacteristic
440C2×Q16—734no—
441C2×Q16—1462no—
442C2×Q16—1462no—
443C2×SD16—2921no—
444C2×SD16—2921no—
445C2×SD16—734no—
446C22×C8—2921no—
447C22×C8—731no—
448C22×C8—731no—
449C22×C8—731no—
450C22×C8—731no—
451C22×C8—1462no—
452C22×C8—1462no—
453C22⋊Q8—734no—
454C22⋊Q8—1462no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×Q8—41no—
458C4×Q8—41no—
459C4×Q8—2921no—
460C4×Q8—1462no—
461#117—2921no—
462#117—1462no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—731no—
466C2×C4⋊C4—731no—
467C2×C4⋊C4—731no—
468C2×C4⋊C4—1461no—
469C2×C4⋊C4—1461no—
470C2×C4⋊C4—1461no—
471C2×C4⋊C4C22×D7311yescharacteristic
472C2×C4⋊C4C22×D7311yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—1461no—
479C2×C22⋊C4—1461no—
480C2×C22⋊C4C22⋊D7311yescharacteristic
481C2×C22⋊C4C22⋊D7311yescharacteristic
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—1461no—
485C2×C42—1461no—
486C2×C42—1461no—
487C2×C42C22×D7311yescharacteristic
488C2×C42C22×D7311yescharacteristic
489#107—2921no—
490#106—1462no—
491#103—2921no—
492#103—734no—
493#103—734no—
494#103—1462no—
495#103—1462no—
496#102—734no—
497#102—1462no—
498#102—1462no—
499C22⋊C8—734no—
500#97—2921no—
501#97—1462no—
502#95—21no—
503#95—1461no—
504#95—1461no—
505#95—1461no—
506#95—1461no—
507#95C22⋊D7311yescharacteristic
508#95C22⋊D7311yescharacteristic
509C24—21no—
510C24C2×C22⋊D7311yescharacteristic
511#41—28no—
512#41—44no—
513#41—44no—
514#41—44no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—732no—
519C2×Q8—1461no—
520C2×Q8—1461no—
521C2×Q8—1461no—
522C2×Q8—1461no—
523C2×Q8—1461no—
524C2×Q8C2×C4×D7312yes—
525C2×Q8D4×D7312yes—
526C2×Q8#1192402712yes—
527C2×D4—24no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4C2×C4×D7312yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—1461no—
547C22×C4—1461no—
548C22×C4—1461no—
549C22×C4—1461no—
550C22×C4C2×C4×D7312yes—
551C22×C4C2×C22⋊D7311yescharacteristic
552C22×C4C2×C22⋊D7311yescharacteristic
553C22×C4C2×C22⋊D7311yescharacteristic
554C22×C4C2×C22⋊D7311yescharacteristic
555C22×C4C2×C22⋊D7311yescharacteristic
556C22×C4#1192402812yes—
557C22×C4C23×D7311yescharacteristic
558Q16—1468no—
559SD16—2924no—
560C2×C8—2924no—
561C2×C8—732no—
562C2×C8—732no—
563C2×C8—732no—
564C2×C8—1461no—
565C2×C8—1461no—
566C2×C8—1461no—
567C2×C8—1461no—
568C2×C8—1461no—
569C2×C8—1461no—
570C2×C8—1461no—
571C2×C8—1461no—
572C2×C8—1461no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—2922no—
580C4⋊C4—2922no—
581C4⋊C4—732no—
582C4⋊C4—732no—
583C4⋊C4—1461no—
584C4⋊C4—1461no—
585C4⋊C4—1464no—
586C4⋊C4—1461no—
587C4⋊C4—1461no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C22⋊C4—81no—
595C22⋊C4—2922no—
596C22⋊C4—1464no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—42no—
602C42—42no—
603C42—2922no—
604C42—2922no—
605C42—2922no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23C4×C22⋊D7312yes—
620C23C22×C22⋊D7311yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—22no—
624Q8—2921no—
625Q8—2921no—
626Q8—1462no—
627Q8—1462no—
628Q8#1455655114yes—
629D4—22no—
630D4—22no—
631D4—48no—
632D4—41no—
633D4—41no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—48no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—2921no—
663C2×C4—2921no—
664C2×C4—2921no—
665C2×C4—2921no—
666C2×C4—2921no—
667C2×C4—2921no—
668C2×C4—2921no—
669C2×C4—2921no—
670C2×C4—2921no—
671C2×C4—1462no—
672C2×C4—1462no—
673C2×C4—1462no—
674C2×C4C4×C22⋊D7312yes—
675C2×C4C22×C4×D7311yescharacteristic
676C2×C4C2×D4×D7311yescharacteristic
677C2×C4C2×#1192402711yescharacteristic
678C2×C4C2×#1192402811yescharacteristic
679C2×C4#1455663611yescharacteristic
680C2×C4#1455663611yescharacteristic
681C8—2921no—
682C8—1462no—
683C8—1462no—
684C8—1462no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22C2×C4×C22⋊D7311yescharacteristic
700C22D4×C22⋊D7311yescharacteristic
701C22#1798923111yescharacteristic
702C22#1798938511yescharacteristic
703C22#1798938511yescharacteristic
704C22#1798939811yescharacteristic
705C22#1798940211yescharacteristic
706C4—22no—
707C4—24no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—81no—
713C4—81no—
714C4—2922no—
715C4—2922no—
716C4—2922no—
717C4—5841no—
718C4C2×#1455655111yescharacteristic
719C4#1798906011yescharacteristic
720C4#1798922711yescharacteristic
721C4#1798926311yescharacteristic
722C2—42no—
723C2—82no—
724C2#2261291011yescharacteristic
725C2#2261872911yescharacteristic
726C2#2261877011yescharacteristic
727C2#2262148711yescharacteristic
728C2#2262151211yescharacteristic
729C2#2262199711yescharacteristic
730C2#2262205711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2341C2
socleC23×C73C22×D4
prime radicalC22×#41×C73C22
cosocleC22×C4×C73C24
hypercenter#2341D73
hypocenterC73#22861
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#17988692C2semidirect
4. #22612956C2semidirect
5. #22610811C2semidirect
6. #22610631C2semidirect
7. #22610555C2semidirect
8. #22610352C2semidirect
9. #22610289C2semidirect
10. #22610272C2semidirect
11. #22610185C2semidirect
12. #22610128C2semidirect
13. #22609761C2semidirect
14. #22609709C2semidirect
22. #17988749C4semidirect
381. C73#22861semidirect

Maximal subgroups

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

subgroupindex
C2×#179887492
C2×#179886922
C2×#179885832
#226129562
#226108112
#226106312
#226105552
#226103522
#226102892
#226102722
#226101852
#226101282
#226097612
#226097092
C73×#23412
#2286173