Finite Group Databasebeta

← #33091128

Subgroups — #33091128

Order 18688.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989208C211yesmaximal, characteristic
2C2×#17988648C211yesmaximal, characteristic, complemented
3#22610883C211yesmaximal, characteristic, complemented
4#22610879C211yesmaximal, characteristic, complemented
5#22610863C211yesmaximal, characteristic, complemented
6#22610863C211yesmaximal, characteristic, complemented
7#22610253C211yesmaximal, characteristic
8#22610248C211yesmaximal, characteristic
9#22610243C211yesmaximal, characteristic, complemented
10#22610238C211yesmaximal, characteristic, complemented
11#22609764C211yesmaximal, characteristic, complemented
12#22609759C211yesmaximal, characteristic, complemented
13C4×#14556514C211yesmaximal, characteristic, complemented
14C4×#14556511C211yesmaximal, characteristic, complemented
15C73×#2274C211yesmaximal, characteristic, complemented
16#17989208—24no—
17#17989208C418yescomplemented
18C2×#14556591C2211yescharacteristic
19C2×#14556586—21no—
20C2×#14556579C2211yescharacteristic
21C2×#14556577—21no—
22C2×#14556573—21no—
23C2×#14556570C2211yescharacteristic
24C2×#14556569—21no—
25C2×#14556565C2211yescharacteristic
26C2×C4×Dic146C2211yescharacteristic
27C2×C4×D292C2211yescharacteristic
28#17988648—24no—
29C2×C4⋊#10596831C2211yescharacteristic
30C2×C4⋊#10596831C2211yescharacteristic
31C2×#14556514C2211yescharacteristic
32C2×#14556514C2211yescharacteristic
33C2×#14556514C2211yescharacteristic
34C2×#14556514C2211yescharacteristic
35C2×#14556511C2211yescharacteristic
36C2×#14556511C2211yescharacteristic
37C2×#14556511C2211yescharacteristic
38C2×#14556511C2211yescharacteristic
39C2×C22⋊#10596831C2211yescharacteristic
40C2×C22⋊#10596831C2211yescharacteristic
41C2×#14556502C2211yescharacteristic
42C2×C4×#10596831C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51C2×#117×C73C2211yescharacteristic
52C2×#117×C73C2211yescharacteristic
53C22×C4⋊C4×C73C2211yescharacteristic
54C4×C4⋊C4×C73—21no—
55C4×C4⋊C4×C73—21no—
56C4×C4⋊C4×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59C4×C4⋊C4×C73C2211yescharacteristic
60C4×C22⋊C4×C73—21no—
61C4×C22⋊C4×C73—21no—
62C22×Dic146—21no—
63C22×Dic146C2311yescharacteristic
64C22×D292C2311yescharacteristic
65C22×C22⋊D73—21no—
66C22×C4×D73—21no—
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71#14556591—22no—
72#14556591C2×C414yescomplemented
73#14556586—28no—
74#14556579—22no—
75#14556579C2×C414yescomplemented
76#14556577—28no—
77#14556573—28no—
78#14556570—22no—
79#14556570C2×C414yes—
80#14556569—28no—
81#14556565—22no—
82#14556565C2×C414yes—
83C4×Dic146—22no—
84C4×Dic146C2×C414yescomplemented
85C4×D292—22no—
86C4×D292C2×C414yescomplemented
87C2×C4⋊Dic73—21no—
88C2×C4⋊Dic73C2311yescharacteristic
89C2×C4⋊Dic73C2311yescharacteristic
90C2×#11924007—21no—
91C2×#11924007—21no—
92C2×C22⋊Dic73—21no—
93C2×#11924005—21no—
94C2×#11924005—21no—
95C2×#11924005—21no—
96C2×#11924005—21no—
97C2×C4×Dic73—21no—
98C4⋊#10596831—22no—
99C4⋊#10596831—22no—
100#14556514—22no—
101#14556514—22no—
102#14556514—22no—
103#14556514—22no—
104#14556511—22no—
105#14556511—22no—
106#14556511—22no—
107#14556511—22no—
108C22⋊#10596831—22no—
109C22⋊#10596831—22no—
110#14556502—22no—
111C4×#10596831—22no—
112C23×C4×C73—21no—
113C23×C4×C73C2311yescharacteristic
114#117×C73—22no—
115#117×C73—22no—
116#117×C73C2×C414yes—
117#117×C73D414yes—
118C2×C4⋊C4×C73—21no—
119C2×C4⋊C4×C73—22no—
120C2×C4⋊C4×C73—22no—
121C2×C4⋊C4×C73D411yescharacteristic
122C2×C4⋊C4×C73D411yescharacteristic
123C2×C4⋊C4×C73C2311yescharacteristic
124C2×C4⋊C4×C73C2311yescharacteristic
125C2×C4⋊C4×C73C2311yescharacteristic
126C2×C4⋊C4×C73C2311yescharacteristic
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73D411yescharacteristic
129C2×C22⋊C4×C73D411yescharacteristic
130C2×C42×C73—21no—
131C2×C42×C73—21no—
132C2×C42×C73—21no—
133C2×C42×C73—21no—
134C2×C42×C73—21no—
135C2×C42×C73C2311yescharacteristic
136C2×C42×C73C2311yescharacteristic
137#95×C73—21no—
138#95×C73—21no—
139#95×C73—21no—
140#95×C73—21no—
141C23×D73—21no—
142C2×Dic146—21no—
143C2×Dic146—21no—
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146—21no—
147C2×Dic146—24no—
148C2×Dic146—81no—
149C2×Dic146—81no—
150C2×Dic146C22×C412yes—
151C2×D292—21no—
152C2×D292—21no—
153C2×D292—21no—
154C2×D292—21no—
155C2×D292—21no—
156C2×D292C22×C412yes—
157C2×C22⋊D73—24no—
158C2×C22⋊D73—81no—
159C2×C22⋊D73—81no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163C2×C4×D73—24no—
164C2×C4×D73—81no—
165C2×C4×D73—81no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C4⋊Dic73—24no—
179C4⋊Dic73—21no—
180C4⋊Dic73—21no—
181C4⋊Dic73C22×C412yes—
182C4⋊Dic73C22×C412yes—
183#11924007—24no—
184#11924007—24no—
185C22⋊Dic73—24no—
186#11924005—24no—
187#11924005—24no—
188#11924005—24no—
189#11924005—24no—
190C4×Dic73—24no—
191C24×C73C2×D411yescharacteristic
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—21no—
200C22×C4×C73—24no—
201C22×C4×C73—81no—
202C22×C4×C73—81no—
203C22×C4×C73C22×C412yes—
204C22×C4×C73C2×D411yescharacteristic
205C22×C4×C73C2×D411yescharacteristic
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73C2×D411yescharacteristic
209C22×C4×C73C2×D412yes—
210C22×C4×C73C2411yescharacteristic
211C4⋊C4×C73—24no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73C22⋊C414yes—
217C4⋊C4×C73C22⋊C414yes—
218C4⋊C4×C73#4112yes—
219C4⋊C4×C73#4112yes—
220C4⋊C4×C73#4112yes—
221C4⋊C4×C73#4112yes—
222C22⋊C4×C73—24no—
223C22⋊C4×C73C22⋊C414yes—
224C22⋊C4×C73C22⋊C414yes—
225C42×C73—24no—
226C42×C73—81no—
227C42×C73—81no—
228C42×C73—81no—
229C42×C73—81no—
230C42×C73C22×C412yes—
231C42×C73C22×C412yes—
232C42×C73C2×D412yes—
233C42×C73C2×D412yes—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73C2×C22⋊C412yes—
241C23×C73C22×D411yescharacteristic
242C22×D73—22no—
243C22×D73—41no—
244C22×D73—41no—
245C22×D73—41no—
246C22×D73—41no—
247C22×D73—41no—
248C22×D73—41no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—22no—
260C2×C4×C73—22no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—84no—
276C2×C4×C73C2×C22⋊C412yes—
277C2×C4×C73C2×C22⋊C412yes—
278C2×C4×C73C2×C22⋊C412yes—
279C2×C4×C73C2×C22⋊C412yes—
280C2×C4×C73C2×C22⋊C412yes—
281C2×C4×C73C23×C411yescharacteristic
282C2×C4×C73C22×D411yescharacteristic
283C2×C4×C73C2×#4111yescharacteristic
284C2×C4×C73C2×#4111yescharacteristic
285C2×C4×C73C2×#4111yescharacteristic
286C2×C4×C73C2×#4111yescharacteristic
287C22⋊D73—84no—
288C2×Dic73—22no—
289C2×Dic73—22no—
290C2×Dic73—22no—
291C2×Dic73—41no—
292C2×Dic73—41no—
293C2×Dic73—41no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297D292—22no—
298D292—22no—
299D292—41no—
300D292—41no—
301C4×D73—84no—
302Dic146—22no—
303Dic146—22no—
304Dic146—41no—
305Dic146—41no—
306Dic146—84no—
307#10596831—41no—
308#10596831—41no—
309#10596831—41no—
310#10596831—41no—
311C22×C73—22no—
312C22×C73—22no—
313C22×C73—22no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73C22×C22⋊C411yescharacteristic
319C22×C73#52511yescharacteristic
320C22×C73#52511yescharacteristic
321C22×C73#57611yescharacteristic
322C22×C73#57711yescharacteristic
323C22×C73#57711yescharacteristic
324C22×C73#57811yescharacteristic
325C2×D73—42no—
326C2×D73—42no—
327C2×D73—42no—
328C2×D73—81no—
329C2×D73—81no—
330C2×D73—81no—
331C2×D73—81no—
332C4×C73—22no—
333C4×C73—22no—
334C4×C73—22no—
335C4×C73—22no—
336C4×C73—22no—
337C4×C73—42no—
338C4×C73—42no—
339C4×C73—42no—
340C4×C73—42no—
341C4×C73C4×#4111yescharacteristic
342C4×C73C4×#4111yescharacteristic
343C4×C73#53211yescharacteristic
344C4×C73#53211yescharacteristic
345Dic73—42no—
346Dic73—42no—
347Dic73—42no—
348#21397—731nomaximal, Sylow
349C2×C73—42no—
350C2×C73#229711yescharacteristic
351C2×C73#289711yescharacteristic
352C2×C73#289811yescharacteristic
353C2×C73#311811yescharacteristic
354C2×C73#312111yescharacteristic
355C2×C73#312411yescharacteristic
356C2×C73#312511yescharacteristic
357D73—82no—
358C2×#542—731no—
359C2×#433—731no—
360#2274D7311yescharacteristic, complemented
361#1988—731no—
362#1987—731no—
363#1983—731no—
364#1983—731no—
365#1875—731no—
366#1874—731no—
367#1873—731no—
368#1872—731no—
369#1763—731no—
370#1762—731no—
371C4×#103—731no—
372C4×#102—731no—
373C73#2139711yescharacteristic, complemented, Sylow
374#542—738no—
375#542—1464no—
376C2×C4⋊Q8—731no—
377C2×#126—1461no—
378C2×#124—731no—
379C2×#124—1461no—
380C2×#123—1461no—
381C2×C22⋊Q8—731no—
382C2×C22⋊Q8—1461no—
383C2×#121—731no—
384C2×C4×Q8—731no—
385C2×C4×D4—731no—
386C2×#117C2×D7311yescharacteristic
387C2×#117C2×D7311yescharacteristic
388C22×C4⋊C4C2×D7311yescharacteristic
389#433—1464no—
390C2×C4⋊C8—731no—
391C2×C4⋊C8—731no—
392C2×#103—731no—
393C2×#103—731no—
394C2×#103—731no—
395C2×#103—731no—
396C2×#102—731no—
397C2×#102—731no—
398C2×#102—731no—
399C2×#102—731no—
400C2×C22⋊C8—731no—
401C2×C22⋊C8—731no—
402C2×#97—731no—
403C2×C4×C8—731no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4C2×D7311yescharacteristic
407C4×C4⋊C4C2×D7311yescharacteristic
408C4×C4⋊C4C2×D7311yescharacteristic
409C4×C4⋊C4C2×D7311yescharacteristic
410C4×C22⋊C4—21no—
411C4×C22⋊C4—21no—
412#340—731no—
413#340—731no—
414#340—731no—
415#340—731no—
416#340—731no—
417#340—731no—
418#340—731no—
419#340—731no—
420C22×Q8—731no—
421C22×Q8—1461no—
422C22×D4—731no—
423C22×D4—1461no—
424C23×C4—21no—
425C23×C4—1461no—
426C23×C4C22×D7311yescharacteristic
427C22×C8—731no—
428C22×C8—731no—
429C22×C8—731no—
430C22×C8—731no—
431C4⋊Q8—734no—
432C4⋊Q8—1462no—
433#126—1468no—
434#124—734no—
435#124—1468no—
436#124—1462no—
437#123—1468no—
438C22⋊Q8—734no—
439C22⋊Q8—1462no—
440C22⋊Q8—1468no—
441#121—734no—
442#121—1462no—
443C4×Q8—734no—
444C4×Q8—1462no—
445C4×D4—734no—
446C4×D4—1462no—
447#117—22no—
448#117—22no—
449#117C4×D7314yes—
450#117D29214yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—731no—
455C2×C4⋊C4—731no—
456C2×C4⋊C4—1461no—
457C2×C4⋊C4—1461no—
458C2×C4⋊C4—1461no—
459C2×C4⋊C4C22⋊D7311yescharacteristic
460C2×C4⋊C4C22⋊D7311yescharacteristic
461C2×C4⋊C4C22×D7311yescharacteristic
462C2×C4⋊C4C22×D7311yescharacteristic
463C2×C4⋊C4C22×D7311yescharacteristic
464C2×C4⋊C4C22×D7311yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—1461no—
467C2×C22⋊C4—1461no—
468C2×C22⋊C4—1461no—
469C2×C22⋊C4—1461no—
470C2×C22⋊C4—1461no—
471C2×C22⋊C4C22⋊D7311yescharacteristic
472C2×C22⋊C4C22⋊D7311yescharacteristic
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—1461no—
479C2×C42C22×D7311yescharacteristic
480C2×C42C22×D7311yescharacteristic
481C4⋊C8—1462no—
482C4⋊C8—1462no—
483#103—1462no—
484#103—1462no—
485#103—1462no—
486#103—1462no—
487#102—1462no—
488#102—1462no—
489#102—1462no—
490#102—1462no—
491C22⋊C8—1462no—
492C22⋊C8—1462no—
493#97—1462no—
494C4×C8—1462no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499C24—1461no—
500C24C2×C22⋊D7311yescharacteristic
501C2×Q8—5841no—
502C2×Q8—5841no—
503C2×Q8—732no—
504C2×Q8—1461no—
505C2×Q8—1461no—
506C2×Q8—1461no—
507C2×Q8—1461no—
508C2×Q8—1464no—
509C2×Q8—1461no—
510C2×D4—5841no—
511C2×D4—5841no—
512C2×D4—732no—
513C2×D4—1464no—
514C2×D4—1461no—
515C2×D4—1461no—
516C2×D4—1461no—
517C2×D4—1461no—
518C2×D4—1461no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—5841no—
531C22×C4—5841no—
532C22×C4—1461no—
533C22×C4—1461no—
534C22×C4—1461no—
535C22×C4—1464no—
536C22×C4C2×C4×D7312yes—
537C22×C4C2×C22⋊D7311yescharacteristic
538C22×C4C2×C22⋊D7311yescharacteristic
539C22×C4C2×C22⋊D7311yescharacteristic
540C22×C4C2×C22⋊D7311yescharacteristic
541C22×C4C2×C22⋊D7311yescharacteristic
542C22×C4C2×D29212yes—
543C22×C4C23×D7311yescharacteristic
544C2×C8—1461no—
545C2×C8—1461no—
546C2×C8—1461no—
547C2×C8—1461no—
548C2×C8—1461no—
549C2×C8—1461no—
550C2×C8—1461no—
551C2×C8—1461no—
552C2×C8—1461no—
553C2×C8—1461no—
554C2×C8—1461no—
555C2×C8—1461no—
556C4⋊C4—24no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—732no—
562C4⋊C4—732no—
563C4⋊C4—1464no—
564C4⋊C4—1464no—
565C4⋊C4—1464no—
566C4⋊C4—1461no—
567C4⋊C4—1461no—
568C4⋊C4#1192400514yes—
569C4⋊C4#1192400514yes—
570C4⋊C4#1192402812yes—
571C4⋊C4#1192402812yes—
572C4⋊C4#1192402812yes—
573C4⋊C4#1192402812yes—
574C22⋊C4—24no—
575C22⋊C4—1464no—
576C22⋊C4—1464no—
577C22⋊C4—1464no—
578C22⋊C4—1464no—
579C22⋊C4—1464no—
580C22⋊C4#1192400514yes—
581C22⋊C4#1192400514yes—
582C42—24no—
583C42—81no—
584C42—81no—
585C42—81no—
586C42—81no—
587C42—1464no—
588C42C2×C4×D7312yes—
589C42C2×C4×D7312yes—
590C42C2×D29212yes—
591C42C2×D29212yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—2921no—
599C23—2921no—
600C23—2921no—
601C23—2921no—
602C23—2921no—
603C23—2921no—
604C23—1462no—
605C23C2×#1192400512yes—
606C23C22×C22⋊D7311yescharacteristic
607Q8—2921no—
608Q8—2921no—
609Q8—5844no—
610Q8—1462no—
611Q8—1462no—
612D4—2921no—
613D4—2921no—
614D4—5844no—
615D4—1462no—
616D4—1462no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4—2921no—
645C2×C4—2921no—
646C2×C4—2921no—
647C2×C4—2921no—
648C2×C4—2921no—
649C2×C4—2921no—
650C2×C4—5844no—
651C2×C4—1462no—
652C2×C4—1462no—
653C2×C4—1462no—
654C2×C4C2×#1192400512yes—
655C2×C4C2×#1192400512yes—
656C2×C4C2×#1192400512yes—
657C2×C4C2×#1192400512yes—
658C2×C4C2×#1192400512yes—
659C2×C4C22×C4×D7311yescharacteristic
660C2×C4C22×D29211yescharacteristic
661C2×C4C2×#1192402811yescharacteristic
662C2×C4C2×#1192402811yescharacteristic
663C2×C4C2×#1192402811yescharacteristic
664C2×C4C2×#1192402811yescharacteristic
665C8—2921no—
666C8—2921no—
667C8—2921no—
668C8—2921no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—2922no—
677C22—2922no—
678C22—2922no—
679C22—5841no—
680C22—5841no—
681C22—5841no—
682C22—5841no—
683C22C22×#1192400511yescharacteristic
684C22#1798909811yescharacteristic
685C22#1798909811yescharacteristic
686C22#1798939011yescharacteristic
687C22#1798939511yescharacteristic
688C22#1798939811yescharacteristic
689C22#1798940211yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—2922no—
700C4—2922no—
701C4—2922no—
702C4C4×#1192402811yescharacteristic
703C4C4×#1192402811yescharacteristic
704C4#1798913711yescharacteristic
705C4#1798913711yescharacteristic
706C2—42no—
707C2—5842no—
708C2#2261242111yescharacteristic
709C2#2261845411yescharacteristic
710C2#2261846111yescharacteristic
711C2#2262011511yescharacteristic
712C2#2262016011yescharacteristic
713C2#2262019311yescharacteristic
714C2#2262020811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2274C2
socleC23×C73C22×D4
prime radicalC2×#14556565C22
cosocleC22×C4×C73C24
hypercenter#2274D73
hypocenterC73#21397
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. C2×#17988648C2semidirect
3. #22610883C2semidirect
4. #22610879C2semidirect
5. #22610863C2semidirect
6. #22610863C2semidirect
9. #22610243C2semidirect
10. #22610238C2semidirect
11. #22609764C2semidirect
12. #22609759C2semidirect
13. C4×#14556514C2semidirect
14. C4×#14556511C2semidirect
15. C73×#2274C2semidirect
17. #17989208C4semidirect
72. #14556591C2×C4semidirect
75. #14556579C2×C4semidirect
84. C4×Dic146C2×C4semidirect
86. C4×D292C2×C4semidirect
360. #2274D73semidirect
373. C73#21397semidirect

Maximal subgroups

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

subgroupindex
C2×#179892082
C2×#179886482
#226108832
#226108792
#226108632
#226102532
#226102482
#226102432
#226102382
#226097642
#226097592
C4×#145565142
C4×#145565112
C73×#22742
#2139773