Finite Group Databasebeta

← #33092513

Subgroups — #33092513

Order 18688.

1066 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×#17988821C211yesmaximal, characteristic
2C2×C4×#11924013C211yesmaximal, characteristic, complemented
3C2×#17988543C211yesmaximal, characteristic, complemented
4#22612624C211yesmaximal, characteristic, complemented
5#22610796C211yesmaximal, characteristic, complemented
6#22610661C211yesmaximal, characteristic, complemented
7#22610631C211yesmaximal, characteristic, complemented
8#22610627C211yesmaximal, characteristic, complemented
9#22610370C211yesmaximal, characteristic, complemented
10#22610367C211yesmaximal, characteristic, complemented
11#22609958C211yesmaximal, characteristic, complemented
12C4×#14556524C211yesmaximal, characteristic, complemented
13#22609759C211yesmaximal, characteristic, complemented
14#22609756C211yesmaximal, characteristic, complemented
15C73×#2324C211yesmaximal, characteristic, complemented
16C22×#11924013C2211yescharacteristic
17C22×#11924012C2211yescharacteristic
18C23×#10596831C2211yescharacteristic
19C2×#14556565C2211yescharacteristic
20C2×C4×D292C2211yescharacteristic
21#17988821C418yescomplemented
22C4×#11924013—24no—
23C2×#14556524C2211yescharacteristic
24C2×#14556524C2211yescharacteristic
25C2×#14556524C2211yescharacteristic
26C2×#14556512C2211yescharacteristic
27C2×#14556512C2211yescharacteristic
28C2×#14556512C2211yescharacteristic
29C2×#14556511C2211yescharacteristic
30C2×#14556511C2211yescharacteristic
31C2×#14556511C2211yescharacteristic
32#17988543—24no—
33C2×#14556502C2211yescharacteristic
34C2×#14556502C2211yescharacteristic
35C2×C4×#10596831C2211yescharacteristic
36C2×C4×#10596831C2211yescharacteristic
37#17988489C2211yescharacteristic
38#17988487—21no—
39#17988485C2211yescharacteristic
40#17988477—21no—
41#17988463—21no—
42#17988458—21no—
43#17988447C2211yescharacteristic
44C4×C4⋊Dic73C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51C2×#121×C73C2211yescharacteristic
52C2×C4×D4×C73C2211yescharacteristic
53C2×#117×C73C2211yescharacteristic
54#390×C73—21no—
55#390×C73C2211yescharacteristic
56#389×C73C2211yescharacteristic
57#388×C73—21no—
58#386×C73—21no—
59#385×C73—21no—
60#380×C73C2211yescharacteristic
61C4×C4⋊C4×C73C2211yescharacteristic
62C22×D292C2311yescharacteristic
63C22×C22⋊D73—21no—
64C22×C4×D73—21no—
65C2×#11924013—22no—
66C2×#11924013—22no—
67C2×#11924013C2×C414yes—
68C2×#11924012—22no—
69C2×#11924012—22no—
70C2×#11924012—22no—
71C22×#10596831—22no—
72C22×#10596831—22no—
73C22×#10596831C2×C414yescomplemented
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78#14556565—22no—
79#14556565C2×C414yescomplemented
80C4×D292—22no—
81C4×D292—22no—
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×#11924007—21no—
86C2×C22⋊Dic73—21no—
87C2×#11924005—21no—
88C2×#11924005—21no—
89C2×#11924005—21no—
90C2×#11924005—21no—
91C2×C4×Dic73—21no—
92#14556524—22no—
93#14556524—22no—
94#14556524C2×C414yescomplemented
95#14556512—22no—
96#14556512—22no—
97#14556512C2×C414yescomplemented
98#14556511—22no—
99#14556511—22no—
100#14556511C2×C414yescomplemented
101#14556502—22no—
102#14556502—22no—
103C4×#10596831—22no—
104C4×#10596831D414yescomplemented
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108C22×D4×C73—21no—
109C22×D4×C73C2311yescharacteristic
110C23×C4×C73—21no—
111C23×C4×C73C2311yescharacteristic
112#121×C73—22no—
113#121×C73C2×C414yescomplemented
114C4×D4×C73—22no—
115C4×D4×C73—22no—
116#117×C73—22no—
117#117×C73—22no—
118C2×C4⋊C4×C73—21no—
119C2×C4⋊C4×C73D411yescharacteristic
120C2×C4⋊C4×C73D411yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C4⋊C4×C73C2311yescharacteristic
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73D411yescharacteristic
130C2×C22⋊C4×C73D411yescharacteristic
131C2×C42×C73—21no—
132C2×C42×C73C2311yescharacteristic
133C2×C42×C73C2311yescharacteristic
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137C23×D73—21no—
138C2×D292—21no—
139C2×D292—21no—
140C2×D292—21no—
141C2×D292—21no—
142C2×D292—21no—
143C2×D292C22×C412yes—
144C2×C22⋊D73—24no—
145C2×C22⋊D73—81no—
146C2×C22⋊D73—81no—
147C22×Dic73—21no—
148C22×Dic73—21no—
149C22×Dic73—21no—
150C2×C4×D73—42no—
151C2×C4×D73—81no—
152C2×C4×D73—81no—
153#11924013—28no—
154#11924012—28no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—28no—
162C2×#10596831C22×C412yes—
163C2×#10596831C22×C412yes—
164C2×#10596831C2×D412yes—
165C2×#10596831C2×D412yes—
166C2×#10596831#4112yes—
167C2×#10596831#4112yes—
168C4⋊Dic73—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73C22×C412yes—
174#11924007—81no—
175C22⋊Dic73—81no—
176#11924005—24no—
177#11924005—42no—
178#11924005—81no—
179#11924005—81no—
180C4×Dic73—81no—
181C24×C73—21no—
182C24×C73C2×D411yescharacteristic
183C2×D4×C73—24no—
184C2×D4×C73—21no—
185C2×D4×C73—21no—
186C2×D4×C73—21no—
187C2×D4×C73—21no—
188C2×D4×C73—21no—
189C2×D4×C73—81no—
190C2×D4×C73—81no—
191C2×D4×C73C22×C412yes—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—42no—
200C22×C4×C73—81no—
201C22×C4×C73—81no—
202C22×C4×C73C22×C412yes—
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2×D411yescharacteristic
205C22×C4×C73C2×D411yescharacteristic
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73#4112yes—
209C22×C4×C73C2411yescharacteristic
210C4⋊C4×C73—22no—
211C4⋊C4×C73—22no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—81no—
218C4⋊C4×C73C22×C412yes—
219C22⋊C4×C73—24no—
220C22⋊C4×C73—22no—
221C22⋊C4×C73—22no—
222C22⋊C4×C73—42no—
223C22⋊C4×C73—81no—
224C22⋊C4×C73—81no—
225C22⋊C4×C73—81no—
226C42×C73—21no—
227C42×C73—21no—
228C42×C73—81no—
229C42×C73C2×D412yes—
230C42×C73#4112yes—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—22no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73C4×D412yes—
245C23×C73C22×D411yescharacteristic
246C22×D73—22no—
247C22×D73—41no—
248C22×D73—41no—
249C22×D73—41no—
250C22×D73—41no—
251C22×D73—41no—
252C22×D73—41no—
253D4×C73—22no—
254D4×C73—22no—
255D4×C73—41no—
256D4×C73—41no—
257D4×C73—84no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—84no—
284C2×C4×C73C4×D412yes—
285C2×C4×C73#12112yes—
286C2×C4×C73#12112yes—
287C2×C4×C73C23×C411yescharacteristic
288C2×C4×C73C22×D411yescharacteristic
289C2×C4×C73C2×#4111yescharacteristic
290C2×C4×C73C2×#4111yescharacteristic
291C2×C4×C73C2×#4111yescharacteristic
292C2×C4×C73C2×#4111yescharacteristic
293C22⋊D73—84no—
294C2×Dic73—22no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297C2×Dic73—41no—
298C2×Dic73—41no—
299C2×Dic73—41no—
300C2×Dic73—41no—
301C2×Dic73—41no—
302C2×Dic73—41no—
303D292—22no—
304D292—22no—
305D292—41no—
306D292—41no—
307C4×D73—84no—
308#10596831—22no—
309#10596831—22no—
310#10596831—22no—
311#10596831C4×D414yes—
312C22×C73—22no—
313C22×C73—22no—
314C22×C73—22no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73—41no—
319C22×C73—42no—
320C22×C73—42no—
321C22×C73—42no—
322C22×C73—81no—
323C22×C73—81no—
324C22×C73—81no—
325C22×C73—81no—
326C22×C73C2×C4×D411yescharacteristic
327C22×C73C2×#12111yescharacteristic
328C22×C73#53211yescharacteristic
329C22×C73#57611yescharacteristic
330C22×C73#57611yescharacteristic
331C22×C73#57611yescharacteristic
332C22×C73#57811yescharacteristic
333C2×D73—42no—
334C2×D73—42no—
335C2×D73—42no—
336C2×D73—81no—
337C2×D73—81no—
338C2×D73—81no—
339C2×D73—81no—
340C4×C73—22no—
341C4×C73—22no—
342C4×C73—22no—
343C4×C73—42no—
344C4×C73—41no—
345C4×C73—41no—
346C4×C73—81no—
347C4×C73—81no—
348C4×C73C2×C4×D411yescharacteristic
349C4×C73C4×#4111yescharacteristic
350C4×C73#52511yescharacteristic
351C4×C73#52911yescharacteristic
352Dic73—42no—
353Dic73—81no—
354Dic73—81no—
355#21524—731nomaximal, Sylow
356C2×C73—42no—
357C2×C73—82no—
358C2×C73C4×#12111yescharacteristic
359C2×C73#294811yescharacteristic
360C2×C73#295111yescharacteristic
361C2×C73#305811yescharacteristic
362C2×C73#306111yescharacteristic
363C2×C73#317511yescharacteristic
364C2×C73#317611yescharacteristic
365D73—82no—
366C2×#466—731no—
367C2×C4×D8—731no—
368C2×#405—731no—
369#2324—731no—
370#2324D7311yescharacteristic, complemented
371#1970—731no—
372#1942—731no—
373#1936—731no—
374#1936—731no—
375#1895—731no—
376#1895—731no—
377#1808—731no—
378C4×#107—731no—
379#1762—731no—
380#1762—731no—
381C73#2152411yescharacteristic, complemented, Sylow
382C22×D8—731no—
383C22×M16—731no—
384C23×C8—731no—
385C2×#121—731no—
386C2×#121C2×D7311yescharacteristic
387C2×C4×D4—731no—
388C2×C4×D4C2×D7311yescharacteristic
389C2×#117C2×D7311yescharacteristic
390#466—738no—
391C4×D8—1464no—
392C2×#107—731no—
393C2×#107—731no—
394C2×#107—731no—
395C2×#102—731no—
396C2×#102—731no—
397C2×#102—731no—
398C2×#102—731no—
399C2×#102—731no—
400C2×#102—731no—
401#405—1464no—
402C2×#97—731no—
403C2×#97—731no—
404C2×C4×C8—731no—
405C2×C4×C8—731no—
406#390—21no—
407#390—731no—
408#390—1461no—
409#390C2×D7311yescharacteristic
410#389—731no—
411#389C2×D7311yescharacteristic
412#388—21no—
413#388—1461no—
414#386—21no—
415#386—1461no—
416#385—21no—
417#385—1461no—
418#380—731no—
419#380C2×D7311yescharacteristic
420C4×C4⋊C4—731no—
421C4×C4⋊C4C2×D7311yescharacteristic
422#340—731no—
423#340—731no—
424#340—731no—
425#340—731no—
426#340—731no—
427#340—731no—
428C22×D4—21no—
429C22×D4—731no—
430C22×D4—1461no—
431C22×D4C22×D7311yescharacteristic
432C23×C4—21no—
433C23×C4—1461no—
434C23×C4C22×D7311yescharacteristic
435C2×D8—734no—
436C2×D8—1462no—
437C2×D8—1462no—
438C2×M16—1462no—
439C2×M16—1462no—
440C2×M16—1462no—
441C22×C8—731no—
442C22×C8—734no—
443C22×C8—731no—
444C22×C8—731no—
445C22×C8—731no—
446C22×C8—1462no—
447C22×C8—1462no—
448#121—22no—
449#121—734no—
450#121—1462no—
451#121C4×D7314yescomplemented
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—1462no—
455C4×D4—1462no—
456#117—22no—
457#117—22no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—731no—
460C2×C4⋊C4—731no—
461C2×C4⋊C4—731no—
462C2×C4⋊C4—1461no—
463C2×C4⋊C4C22⋊D7311yescharacteristic
464C2×C4⋊C4C22⋊D7311yescharacteristic
465C2×C4⋊C4C22×D7311yescharacteristic
466C2×C4⋊C4C22×D7311yescharacteristic
467C2×C4⋊C4C22×D7311yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—1461no—
474C2×C22⋊C4—1461no—
475C2×C22⋊C4—1461no—
476C2×C22⋊C4—1461no—
477C2×C22⋊C4—1461no—
478C2×C22⋊C4C22⋊D7311yescharacteristic
479C2×C22⋊C4C22⋊D7311yescharacteristic
480C2×C42—21no—
481C2×C42—1461no—
482C2×C42C22×D7311yescharacteristic
483C2×C42C22×D7311yescharacteristic
484#107—734no—
485#107—1462no—
486#107—1462no—
487#102—734no—
488#102—734no—
489#102—1462no—
490#102—1462no—
491#102—1462no—
492#102—1462no—
493#97—1462no—
494#97—1462no—
495C4×C8—734no—
496C4×C8—1462no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—1461no—
501#95—1461no—
502#95—1461no—
503C24—21no—
504C24—1461no—
505C24C2×C22⋊D7311yescharacteristic
506C2×D4—24no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4—5841no—
515C2×D4—5841no—
516C2×D4—732no—
517C2×D4—1464no—
518C2×D4—1461no—
519C2×D4—1461no—
520C2×D4—1461no—
521C2×D4—1461no—
522C2×D4—1461no—
523C2×D4C2×C4×D7312yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—2922no—
535C22×C4—5841no—
536C22×C4—5841no—
537C22×C4—1461no—
538C22×C4—1461no—
539C22×C4—1461no—
540C22×C4C2×C4×D7312yes—
541C22×C4C2×C22⋊D7311yescharacteristic
542C22×C4C2×C22⋊D7311yescharacteristic
543C22×C4C2×C22⋊D7311yescharacteristic
544C22×C4C2×C22⋊D7311yescharacteristic
545C22×C4C2×C22⋊D7311yescharacteristic
546C22×C4#1192402812yes—
547C22×C4C23×D7311yescharacteristic
548D8—1468no—
549M16—1468no—
550C2×C8—732no—
551C2×C8—732no—
552C2×C8—732no—
553C2×C8—732no—
554C2×C8—732no—
555C2×C8—732no—
556C2×C8—1468no—
557C2×C8—1461no—
558C2×C8—1461no—
559C2×C8—1461no—
560C2×C8—1461no—
561C2×C8—1461no—
562C2×C8—1461no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—81no—
571C4⋊C4—5841no—
572C4⋊C4—732no—
573C4⋊C4—1461no—
574C4⋊C4—1461no—
575C4⋊C4—1461no—
576C4⋊C4—1461no—
577C4⋊C4—1461no—
578C4⋊C4C2×C4×D7312yes—
579C22⋊C4—24no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C22⋊C4—2922no—
587C22⋊C4—5841no—
588C22⋊C4—5841no—
589C22⋊C4—5841no—
590C22⋊C4—1464no—
591C42—21no—
592C42—21no—
593C42—81no—
594C42—5841no—
595C42D4×D7312yes—
596C42#1192402712yes—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—2921no—
611C23—2921no—
612C23—2921no—
613C23—2921no—
614C23—2921no—
615C23—2921no—
616C23—1462no—
617C23C4×C22⋊D7312yes—
618C23C22×C22⋊D7311yescharacteristic
619D4—22no—
620D4—22no—
621D4—41no—
622D4—41no—
623D4—84no—
624D4—2921no—
625D4—2921no—
626D4—5844no—
627D4—1462no—
628D4—1462no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—84no—
655C2×C4—2921no—
656C2×C4—2921no—
657C2×C4—2921no—
658C2×C4—2921no—
659C2×C4—2921no—
660C2×C4—2921no—
661C2×C4—2921no—
662C2×C4—2921no—
663C2×C4—5844no—
664C2×C4—1462no—
665C2×C4C4×C22⋊D7312yes—
666C2×C4#1455656312yes—
667C2×C4#1455656312yes—
668C2×C4C22×C4×D7311yescharacteristic
669C2×C4C2×D4×D7311yescharacteristic
670C2×C4#41×D7311yescharacteristic
671C2×C4#41×D7311yescharacteristic
672C2×C4C2×#1192402711yescharacteristic
673C2×C4C2×#1192402811yescharacteristic
674C8—734no—
675C8—1462no—
676C8—1462no—
677C8—1462no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—2922no—
693C22—2922no—
694C22—2922no—
695C22—5841no—
696C22—5841no—
697C22—5841no—
698C22—5841no—
699C22C2×C4×C22⋊D7311yescharacteristic
700C22C2×#1455656311yescharacteristic
701C22#1798913311yescharacteristic
702C22#1798939011yescharacteristic
703C22#1798939011yescharacteristic
704C22#1798939011yescharacteristic
705C22#1798940211yescharacteristic
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—41no—
711C4—41no—
712C4—81no—
713C4—81no—
714C4—2922no—
715C4—5841no—
716C4—5841no—
717C4C4×D4×D7311yescharacteristic
718C4C4×#1192402711yescharacteristic
719C4#1798909611yescharacteristic
720C4#1798911711yescharacteristic
721C2—42no—
722C2—82no—
723C2—5842no—
724C2C4×#1455656311yescharacteristic
725C2#2261878111yescharacteristic
726C2#2261880411yescharacteristic
727C2#2261957611yescharacteristic
728C2#2261959811yescharacteristic
729C2#2262056411yescharacteristic
730C2#2262057511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2324C2
socleC23×C73C22×D4
prime radicalC2×#17988821C2
cosocleC22×C4×C73C24
hypercenter#2324D73
hypocenterC73#21524
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11924013C2semidirect
3. C2×#17988543C2semidirect
4. #22612624C2semidirect
5. #22610796C2semidirect
6. #22610661C2semidirect
7. #22610631C2semidirect
8. #22610627C2semidirect
9. #22610370C2semidirect
10. #22610367C2semidirect
11. #22609958C2semidirect
12. C4×#14556524C2semidirect
13. #22609759C2semidirect
14. #22609756C2semidirect
15. C73×#2324C2semidirect
21. #17988821C4semidirect
73. C22×#10596831C2×C4semidirect
79. #14556565C2×C4semidirect
94. #14556524C2×C4semidirect
97. #14556512C2×C4semidirect
100. #14556511C2×C4semidirect
104. C4×#10596831D4semidirect
113. #121×C73C2×C4semidirect
370. #2324D73semidirect
381. C73#21524semidirect
451. #121C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179888212
C2×C4×#119240132
C2×#179885432
#226126242
#226107962
#226106612
#226106312
#226106272
#226103702
#226103672
#226099582
C4×#145565242
#226097592
#226097562
C73×#23242
#2152473