Finite Group Databasebeta

← #33104138

Subgroups — #33104138

Order 18688.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988629C211yesmaximal, characteristic, complemented
2C22×#14556523C211yesmaximal, characteristic, complemented
3#22612860C211yesmaximal, characteristic
4D4×C4⋊Dic73C211yesmaximal, characteristic
5#22610701C211yesmaximal, characteristic, complemented
6#22610695C211yesmaximal, characteristic, complemented
7#22610132C211yesmaximal, characteristic, complemented
8#22610126C211yesmaximal, characteristic, complemented
9#22610126C211yesmaximal, characteristic, complemented
10#22610121C211yesmaximal, characteristic, complemented
11#22610099C211yesmaximal, characteristic, complemented
12#22609964C211yesmaximal, characteristic, complemented
13#22609960C211yesmaximal, characteristic, complemented
14#22609828C211yesmaximal, characteristic, complemented
15C2×#435×C73C211yesmaximal, characteristic
16C2×D4×Dic73—21no—
17C2×#14556550C2211yescharacteristic
18C22×C4⋊Dic73C2211yescharacteristic
19C22×C4⋊Dic73C2211yescharacteristic
20C22×C4⋊Dic73C2211yescharacteristic
21#17988629—24no—
22C2×#14556525C2211yescharacteristic
23C2×#14556525C2211yescharacteristic
24C2×#14556525C2211yescharacteristic
25C2×#14556525C2211yescharacteristic
26C2×#14556523—24no—
27C2×#14556523C2211yescharacteristic
28C2×#14556523C2211yescharacteristic
29C2×#14556523C2211yescharacteristic
30C2×#14556523C2211yescharacteristic
31C2×#14556523C2211yescharacteristic
32C2×#14556523C2211yescharacteristic
33#17988486—21no—
34#17988480—21no—
35#17988473—21no—
36#17988467—21no—
37#17988462—21no—
38#17988462—21no—
39#17988457C2211yescharacteristic
40#17988453C2211yescharacteristic
41#17988447C2211yescharacteristic
42#17988447C2211yescharacteristic
43#17988447C2211yescharacteristic
44#17988447C2211yescharacteristic
45C4×C4⋊Dic73C2211yescharacteristic
46C4×C4⋊Dic73C2211yescharacteristic
47C22⋊C4×Dic73—21no—
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988350C2211yescharacteristic
51#17988350C2211yescharacteristic
52#17988350C2211yescharacteristic
53#17988350C2211yescharacteristic
54C22×M16×C73C2211yescharacteristic
55C23×C8×C73C2211yescharacteristic
56C2×C4×D4×C73C2211yescharacteristic
57#435×C73C418yescomplemented
58C2×C4⋊C8×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60C2×C22⋊C8×C73C2211yescharacteristic
61C2×#97×C73C2211yescharacteristic
62C23×Dic73—21no—
63C23×Dic73—21no—
64C23×Dic73—21no—
65D4×Dic73—44no—
66#14556550—22no—
67#14556550—41no—
68C2×C4⋊Dic73—22no—
69C2×C4⋊Dic73—22no—
70C2×C4⋊Dic73—22no—
71C2×C4⋊Dic73—21no—
72C2×C4⋊Dic73—21no—
73C2×C4⋊Dic73—21no—
74C2×C4⋊Dic73—21no—
75C2×C4⋊Dic73—21no—
76C2×C4⋊Dic73—41no—
77C2×C4⋊Dic73—41no—
78C2×C4⋊Dic73—41no—
79C2×C4⋊Dic73C2311yescharacteristic
80C2×C4⋊Dic73C2311yescharacteristic
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×C4⋊Dic73C2311yescharacteristic
86C2×C4⋊Dic73C2311yescharacteristic
87C2×C22⋊Dic73—21no—
88C2×C22⋊Dic73—21no—
89C2×C22⋊Dic73—21no—
90C2×C22⋊Dic73—21no—
91C2×C22⋊Dic73—21no—
92C2×C4×Dic73—21no—
93C2×C4×Dic73—21no—
94C2×C4×Dic73—21no—
95#14556525—22no—
96#14556525—22no—
97#14556525—22no—
98#14556525—41no—
99#14556523—22no—
100#14556523—22no—
101#14556523—22no—
102#14556523—22no—
103#14556523—41no—
104#14556523D414yescomplemented
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110#14556498—21no—
111#14556498—21no—
112#14556498—21no—
113C22×D4×C73D411yescharacteristic
114C23×C4×C73C2311yescharacteristic
115C23×C4×C73C2311yescharacteristic
116C2×M16×C73—22no—
117C2×M16×C73—22no—
118C2×M16×C73C2×C414yescomplemented
119C22×C8×C73—22no—
120C22×C8×C73—22no—
121C22×C8×C73C2×C414yescomplemented
122C22×C8×C73C2311yescharacteristic
123C22×C8×C73C2311yescharacteristic
124C22×C8×C73C2311yescharacteristic
125C22×C8×C73C2311yescharacteristic
126C4×D4×C73C2×C414yes—
127C4×D4×C73Q814yes—
128C2×C4⋊C4×C73D411yescharacteristic
129C2×C22⋊C4×C73D411yescharacteristic
130C2×C22⋊C4×C73D411yescharacteristic
131C2×C42×C73C2311yescharacteristic
132C4⋊C8×C73C2×C414yescomplemented
133C22⋊C8×C73C2×C414yescomplemented
134C22⋊C8×C73C2×C414yescomplemented
135#97×C73C2×C414yescomplemented
136C22×Dic73—21no—
137C22×Dic73—21no—
138C22×Dic73—21no—
139C22×Dic73—21no—
140C22×Dic73—21no—
141C22×Dic73—21no—
142C22×Dic73—21no—
143C22×Dic73—21no—
144C22×Dic73—42no—
145C22×Dic73—42no—
146C22×Dic73—42no—
147C22×Dic73—42no—
148C22×Dic73—42no—
149C22×Dic73—42no—
150C22×Dic73—81no—
151C22×Dic73—81no—
152C22×Dic73—81no—
153C4⋊Dic73—21no—
154C4⋊Dic73—21no—
155C4⋊Dic73—21no—
156C4⋊Dic73—21no—
157C4⋊Dic73—21no—
158C4⋊Dic73—21no—
159C4⋊Dic73—21no—
160C4⋊Dic73—21no—
161C4⋊Dic73—21no—
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—42no—
168C4⋊Dic73—42no—
169C4⋊Dic73—42no—
170C4⋊Dic73—42no—
171C4⋊Dic73—81no—
172C4⋊Dic73C2×D412yes—
173C4⋊Dic73C2×D412yes—
174C22⋊Dic73—42no—
175C22⋊Dic73—42no—
176C22⋊Dic73—42no—
177C22⋊Dic73—42no—
178C22⋊Dic73—81no—
179C4×Dic73—42no—
180C4×Dic73—42no—
181C4×Dic73—81no—
182C24×C73C2×D411yescharacteristic
183C24×C73C2×D411yescharacteristic
184C2×D4×C73—22no—
185C2×D4×C73—22no—
186C2×D4×C73C4⋊C414yes—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73C22×C412yes—
196C22×C4×C73C22×C412yes—
197C22×C4×C73C2×D411yescharacteristic
198C22×C4×C73C2×D411yescharacteristic
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×Q812yes—
202C22×C4×C73C2×Q812yes—
203C22×C4×C73C2411yescharacteristic
204M16×C73—28no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—28no—
212C2×C8×C73C22×C412yes—
213C2×C8×C73C22×C412yes—
214C2×C8×C73C22×C412yes—
215C2×C8×C73C22×C412yes—
216C2×C8×C73C2×D412yes—
217C2×C8×C73#4112yes—
218C4⋊C4×C73C4⋊C414yes—
219C22⋊C4×C73C4⋊C414yes—
220C22⋊C4×C73C4⋊C414yes—
221C42×C73C22×C412yes—
222C42×C73C2×Q812yes—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73C2×C4⋊C412yes—
234C23×C73C2×C4⋊C412yes—
235C23×C73AGL(1,ℤ/8)12yes—
236C23×C73#13712yes—
237C23×C73C22×D411yescharacteristic
238D4×C73—28no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—22no—
248C2×C4×C73—22no—
249C2×C4×C73—22no—
250C2×C4×C73—22no—
251C2×C4×C73—22no—
252C2×C4×C73—22no—
253C2×C4×C73—22no—
254C2×C4×C73—22no—
255C2×C4×C73C2×C4⋊C412yes—
256C2×C4×C73C2×C4⋊C412yes—
257C2×C4×C73C2×C4⋊C412yes—
258C2×C4×C73C2×C4⋊C412yes—
259C2×C4×C73C23×C411yescharacteristic
260C2×C4×C73C22×D411yescharacteristic
261C2×C4×C73C22×Q811yescharacteristic
262C2×C4×C73C2×#4111yescharacteristic
263C2×C4×C73H(5,𝔽2)11yescharacteristic
264C2×C4×C732−1+411yescharacteristic
265C2×Dic73—22no—
266C2×Dic73—22no—
267C2×Dic73—41no—
268C2×Dic73—41no—
269C2×Dic73—41no—
270C2×Dic73—41no—
271C2×Dic73—41no—
272C2×Dic73—41no—
273C2×Dic73—41no—
274C2×Dic73—41no—
275C2×Dic73—41no—
276C2×Dic73—41no—
277C2×Dic73—41no—
278C2×Dic73—41no—
279C2×Dic73—41no—
280C2×Dic73—41no—
281C2×Dic73—41no—
282C2×Dic73—41no—
283C2×Dic73—41no—
284C2×Dic73—41no—
285C2×Dic73—41no—
286C2×Dic73—41no—
287C2×Dic73—41no—
288C2×Dic73—41no—
289C2×Dic73—84no—
290C2×Dic73—84no—
291C2×Dic73—84no—
292C8×C73—22no—
293C8×C73—22no—
294C8×C73—22no—
295C8×C73C4×D414yescomplemented
296C22×C73—22no—
297C22×C73—22no—
298C22×C73—22no—
299C22×C73—22no—
300C22×C73—22no—
301C22×C73—22no—
302C22×C73—22no—
303C22×C73—22no—
304C22×C73—22no—
305C22×C73—41no—
306C22×C73—41no—
307C22×C73—41no—
308C22×C73—41no—
309C22×C73#42814yescomplemented
310C22×C73C22×C4⋊C411yescharacteristic
311C22×C73D4211yescharacteristic
312C22×C73#54711yescharacteristic
313C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C73C2×#13711yescharacteristic
315C22×C73#57711yescharacteristic
316C22×C73#57711yescharacteristic
317C4×C73—22no—
318C4×C73—22no—
319C4×C73—22no—
320C4×C73—22no—
321C4×C73C2×C4×D411yescharacteristic
322C4×C73#52011yescharacteristic
323C4×C73D4×Q811yescharacteristic
324C4×C73#55411yescharacteristic
325Dic73—42no—
326Dic73—42no—
327Dic73—81no—
328Dic73—81no—
329Dic73—81no—
330Dic73—81no—
331Dic73—81no—
332Dic73—81no—
333#22659—731nomaximal, Sylow
334C2×C73—24no—
335C2×C73—42no—
336C2×C73D4×C4⋊C411yescharacteristic
337C2×C73C2×#42811yescharacteristic
338C2×C73#291211yescharacteristic
339C2×C73#326511yescharacteristic
340C2×C73#326611yescharacteristic
341C2×C73#334411yescharacteristic
342C2×C73#334511yescharacteristic
343C2×#435D7311yescharacteristic
344C2×#428—731no—
345C22×#106—731no—
346#2352—731no—
347D4×C4⋊C4—731no—
348#1949—731no—
349#1948—731no—
350#1854—731no—
351#1853—731no—
352#1853—731no—
353#1852—731no—
354#1847—731no—
355#1809—731no—
356#1808—731no—
357#1776—731no—
358C73#2265911yescharacteristic, complemented, Sylow
359C22×M16C2×D7311yescharacteristic
360C23×C8C2×D7311yescharacteristic
361C2×C4×D4—1461no—
362C2×C4×D4C2×D7311yescharacteristic
363C2×#117—731no—
364C22×C4⋊C4—731no—
365C22×C4⋊C4—731no—
366C22×C4⋊C4—731no—
367#435Dic7318yescomplemented
368#428—1464no—
369C2×#107—731no—
370C2×#107—731no—
371C2×#107—731no—
372C2×#107—731no—
373C2×#106—731no—
374C2×#106—731no—
375C2×#106—731no—
376C2×#106—731no—
377C2×#106—731no—
378C2×#106—731no—
379C2×#106—1464no—
380C2×C4⋊C8C2×D7311yescharacteristic
381C2×C22⋊C8C2×D7311yescharacteristic
382C2×C22⋊C8C2×D7311yescharacteristic
383C2×#97C2×D7311yescharacteristic
384#389—1461no—
385#388—1461no—
386#387—1461no—
387#386—1461no—
388#385—1461no—
389#385—1461no—
390#384—731no—
391#382—731no—
392#380—731no—
393#380—731no—
394#380—731no—
395#380—731no—
396C4×C4⋊C4—731no—
397C4×C4⋊C4—731no—
398C4×C22⋊C4—1461no—
399#340—731no—
400#340—731no—
401#340—731no—
402#340—731no—
403#340—731no—
404#340—731no—
405C22×D4D29211yescharacteristic
406C23×C4—1461no—
407C23×C4—1461no—
408C23×C4—1461no—
409C23×C4C22×D7311yescharacteristic
410C23×C4C22×D7311yescharacteristic
411C2×M16—22no—
412C2×M16—22no—
413C2×M16C2×Dic7314yescomplemented
414C22×C8—22no—
415C22×C8—22no—
416C22×C8C2×Dic7314yescomplemented
417C22×C8C22×D7311yescharacteristic
418C22×C8C22×D7311yescharacteristic
419C22×C8C22×D7311yescharacteristic
420C22×C8C22×D7311yescharacteristic
421C4×D4—2924no—
422C4×D4Dic14614yes—
423C4×D4C2×Dic7314yes—
424#117—2921no—
425#117—1462no—
426C2×C4⋊C4—2921no—
427C2×C4⋊C4—2921no—
428C2×C4⋊C4—2921no—
429C2×C4⋊C4—731no—
430C2×C4⋊C4—731no—
431C2×C4⋊C4—731no—
432C2×C4⋊C4—731no—
433C2×C4⋊C4—731no—
434C2×C4⋊C4—731no—
435C2×C4⋊C4—731no—
436C2×C4⋊C4—731no—
437C2×C4⋊C4—1461no—
438C2×C4⋊C4—1461no—
439C2×C4⋊C4—1461no—
440C2×C4⋊C4—1461no—
441C2×C4⋊C4—1462no—
442C2×C4⋊C4—1462no—
443C2×C4⋊C4—1462no—
444C2×C4⋊C4—1461no—
445C2×C4⋊C4D29211yescharacteristic
446C2×C22⋊C4—1461no—
447C2×C22⋊C4—1461no—
448C2×C22⋊C4—1461no—
449C2×C22⋊C4—1461no—
450C2×C22⋊C4—1461no—
451C2×C22⋊C4D29211yescharacteristic
452C2×C22⋊C4D29211yescharacteristic
453C2×C42—1461no—
454C2×C42—1461no—
455C2×C42—1461no—
456C2×C42C22×D7311yescharacteristic
457#107—2921no—
458#107—1462no—
459#107—1462no—
460#107—1462no—
461#106—2921no—
462#106—734no—
463#106—1462no—
464#106—1462no—
465#106—1462no—
466#106—1462no—
467C4⋊C8C2×Dic7314yescomplemented
468C22⋊C8C2×Dic7314yescomplemented
469C22⋊C8C2×Dic7314yescomplemented
470#97C2×Dic7314yescomplemented
471#95—1461no—
472#95—1461no—
473#95—1461no—
474#95—1461no—
475#95—1461no—
476#95—1461no—
477#95—1461no—
478#95—1461no—
479C24C2×D29211yescharacteristic
480C24C2×D29211yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4C4⋊Dic7314yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—2922no—
493C22×C4—2922no—
494C22×C4—2922no—
495C22×C4—2922no—
496C22×C4—2922no—
497C22×C4—2922no—
498C22×C4—5841no—
499C22×C4—5841no—
500C22×C4—5841no—
501C22×C4—1461no—
502C22×C4—1461no—
503C22×C4—1461no—
504C22×C4—1461no—
505C22×C4—1461no—
506C22×C4—1461no—
507C22×C4—1461no—
508C22×C4—1461no—
509C22×C4C22×Dic7312yes—
510C22×C4C22×Dic7312yes—
511C22×C4C2×D29211yescharacteristic
512C22×C4C2×D29211yescharacteristic
513C22×C4C2×D29211yescharacteristic
514C22×C4C2×D29211yescharacteristic
515C22×C4C2×Dic14612yes—
516C22×C4C2×Dic14612yes—
517C22×C4C23×D7311yescharacteristic
518M16—28no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—28no—
526C2×C8C22×Dic7312yes—
527C2×C8C22×Dic7312yes—
528C2×C8C22×Dic7312yes—
529C2×C8C22×Dic7312yes—
530C2×C8D4×D7312yes—
531C2×C8#1192402712yes—
532C4⋊C4—2922no—
533C4⋊C4—2922no—
534C4⋊C4—2922no—
535C4⋊C4—2922no—
536C4⋊C4—5841no—
537C4⋊C4—732no—
538C4⋊C4—732no—
539C4⋊C4—1461no—
540C4⋊C4—1461no—
541C4⋊C4—1461no—
542C4⋊C4—1461no—
543C4⋊C4—1461no—
544C4⋊C4—1461no—
545C4⋊C4—1461no—
546C4⋊C4—1461no—
547C4⋊C4—1461no—
548C4⋊C4—1461no—
549C4⋊C4—1461no—
550C4⋊C4—1461no—
551C4⋊C4—1461no—
552C4⋊C4—1461no—
553C4⋊C4C4⋊Dic7314yes—
554C22⋊C4—2922no—
555C22⋊C4—2922no—
556C22⋊C4—2922no—
557C22⋊C4—2922no—
558C22⋊C4—5841no—
559C22⋊C4C4⋊Dic7314yes—
560C22⋊C4C4⋊Dic7314yes—
561C42—2922no—
562C42—2922no—
563C42—5841no—
564C42C22×Dic7312yes—
565C42C2×Dic14612yes—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C2×C4⋊Dic7312yes—
577C23C2×C4⋊Dic7312yes—
578C23#1455661912yes—
579C23#1455662412yes—
580C23C22×D29211yescharacteristic
581D4—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—2921no—
599C2×C4—2921no—
600C2×C4—2921no—
601C2×C4—2921no—
602C2×C4—2921no—
603C2×C4—2921no—
604C2×C4—2921no—
605C2×C4—2921no—
606C2×C4—2921no—
607C2×C4—2921no—
608C2×C4—2921no—
609C2×C4—2921no—
610C2×C4—2921no—
611C2×C4—2921no—
612C2×C4—2921no—
613C2×C4—2921no—
614C2×C4—2921no—
615C2×C4—2921no—
616C2×C4—2921no—
617C2×C4—2921no—
618C2×C4—2921no—
619C2×C4—2921no—
620C2×C4—5844no—
621C2×C4—5844no—
622C2×C4—5844no—
623C2×C4—1462no—
624C2×C4—1462no—
625C2×C4C2×C4⋊Dic7312yes—
626C2×C4C2×C4⋊Dic7312yes—
627C2×C4C2×C4⋊Dic7312yes—
628C2×C4C2×C4⋊Dic7312yes—
629C2×C4C23×Dic7311yescharacteristic
630C2×C4C2×D4×D7311yescharacteristic
631C2×C4C22×Dic14611yescharacteristic
632C2×C4C2×#1192402711yescharacteristic
633C2×C4#1455663711yescharacteristic
634C2×C4#1455663811yescharacteristic
635C8—22no—
636C8—22no—
637C8—22no—
638C8D4×Dic7314yescomplemented
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22#1798862914yescomplemented
653C22C22×C4⋊Dic7311yescharacteristic
654C22D4×D29211yescharacteristic
655C22#1798924111yescharacteristic
656C22C2×#1455661911yescharacteristic
657C22C2×#1455662411yescharacteristic
658C22#1798939911yescharacteristic
659C22#1798939911yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—2922no—
665C4—2922no—
666C4—5841no—
667C4—5841no—
668C4—5841no—
669C4—5841no—
670C4—5841no—
671C4—5841no—
672C4C2×D4×Dic7311yescharacteristic
673C4#1798907011yescharacteristic
674C4D4×Dic14611yescharacteristic
675C4#1798929411yescharacteristic
676C2—24no—
677C2—42no—
678C2D4×C4⋊Dic7311yescharacteristic
679C2C2×#1798862911yescharacteristic
680C2#2261852611yescharacteristic
681C2#2262143111yescharacteristic
682C2#2262144611yescharacteristic
683C2#2262238811yescharacteristic
684C2#2262240311yescharacteristic
subgroupG/H
centerC23C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#435×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×C73D4
cosocleC22×C4×C73C24
hypercenterC2×#435D73
hypocenterC73#22659
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#17988629C2semidirect
2. C22×#14556523C2semidirect
5. #22610701C2semidirect
6. #22610695C2semidirect
7. #22610132C2semidirect
8. #22610126C2semidirect
9. #22610126C2semidirect
10. #22610121C2semidirect
11. #22610099C2semidirect
12. #22609964C2semidirect
13. #22609960C2semidirect
14. #22609828C2semidirect
57. #435×C73C4semidirect
104. #14556523D4semidirect
118. C2×M16×C73C2×C4semidirect
121. C22×C8×C73C2×C4semidirect
132. C4⋊C8×C73C2×C4semidirect
133. C22⋊C8×C73C2×C4semidirect
134. C22⋊C8×C73C2×C4semidirect
135. #97×C73C2×C4semidirect
295. C8×C73C4×D4semidirect
309. C22×C73#428semidirect
358. C73#22659semidirect
367. #435Dic73semidirect
413. C2×M16C2×Dic73semidirect
416. C22×C8C2×Dic73semidirect
467. C4⋊C8C2×Dic73semidirect
468. C22⋊C8C2×Dic73semidirect
469. C22⋊C8C2×Dic73semidirect
470. #97C2×Dic73semidirect
638. C8D4×Dic73semidirect
652. C22#17988629semidirect

Maximal subgroups

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

subgroupindex
C2×#179886292
C22×#145565232
#226128602
D4×C4⋊Dic732
#226107012
#226106952
#226101322
#226101262
#226101212
#226100992
#226099642
#226099602
#226098282
C2×#435×C732
#2265973