Finite Group Databasebeta

← #33102420

Subgroups — #33102420

Order 18688.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989283C211yesmaximal, characteristic
2#22612860C211yesmaximal, characteristic, complemented
3#22610896C211yesmaximal, characteristic, complemented
4#22610886C211yesmaximal, characteristic, complemented
5#22610369C211yesmaximal, characteristic, complemented
6#22610369C211yesmaximal, characteristic, complemented
7#22610251C211yesmaximal, characteristic, complemented
8#22610246C211yesmaximal, characteristic, complemented
9#22610027C211yesmaximal, characteristic, complemented
10#22610018C211yesmaximal, characteristic, complemented
11#22609942C211yesmaximal, characteristic, complemented
12C4×#14556513C211yesmaximal, characteristic, complemented
13#22609651C211yesmaximal, characteristic, complemented
14#22609651C211yesmaximal, characteristic, complemented
15C2×#436×C73C211yesmaximal, characteristic, complemented
16#17989283—24no—
17#17989283C418yescomplemented
18C2×#14556586—21no—
19C2×#14556583C2211yescharacteristic
20C2×#14556573—21no—
21C2×#14556565C2211yescharacteristic
22C2×#14556565C2211yescharacteristic
23C2×#14556563—21no—
24C2×C4×D292C2211yescharacteristic
25C2×#14556551—21no—
26C2×#14556550C2211yescharacteristic
27C2×#14556550C2211yescharacteristic
28C22×C4⋊Dic73C2211yescharacteristic
29C22×C4⋊Dic73C2211yescharacteristic
30C2×#14556513C2211yescharacteristic
31C2×#14556513C2211yescharacteristic
32C2×#14556513C2211yescharacteristic
33C2×#14556513C2211yescharacteristic
34#17988480—21no—
35#17988473—21no—
36#17988467—21no—
37#17988453C2211yescharacteristic
38#17988447C2211yescharacteristic
39#17988447C2211yescharacteristic
40C4×C4⋊Dic73C2211yescharacteristic
41C22⋊C4×Dic73—21no—
42#17988350C2211yescharacteristic
43#17988350C2211yescharacteristic
44#17988350C2211yescharacteristic
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988350C2211yescharacteristic
51#17988350C2211yescharacteristic
52#17988350C2211yescharacteristic
53#17988350C2211yescharacteristic
54C22×M16×C73C2211yescharacteristic
55C22×M16×C73C2211yescharacteristic
56C2×C4×D4×C73C2211yescharacteristic
57#436×C73—24no—
58C2×C4⋊C8×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60C2×C22⋊C8×C73C2211yescharacteristic
61C2×C4×C8×C73C2211yescharacteristic
62C22×D292C2311yescharacteristic
63C22×C22⋊D73—21no—
64C22×C22⋊D73—21no—
65C23×Dic73—21no—
66C23×Dic73—21no—
67C22×C4×D73—21no—
68#14556586—28no—
69#14556583—22no—
70#14556583C2×C414yescomplemented
71#14556573—28no—
72#14556565—22no—
73#14556565—22no—
74#14556565C2×C414yes—
75#14556565C2×C414yescomplemented
76#14556563—28no—
77C4×D292—22no—
78C4×D292C2×C414yescomplemented
79#14556551—28no—
80#14556550—22no—
81#14556550—22no—
82#14556550—41no—
83#14556550C2×C414yes—
84C2×C4⋊Dic73—22no—
85C2×C4⋊Dic73—22no—
86C2×C4⋊Dic73—21no—
87C2×C4⋊Dic73—21no—
88C2×C4⋊Dic73—41no—
89C2×C4⋊Dic73C2×C414yescomplemented
90C2×C4⋊Dic73C2311yescharacteristic
91C2×C4⋊Dic73C2311yescharacteristic
92C2×C4⋊Dic73C2311yescharacteristic
93C2×C4⋊Dic73C2311yescharacteristic
94C2×C4⋊Dic73C2311yescharacteristic
95C2×C4⋊Dic73C2311yescharacteristic
96C2×C4⋊Dic73C2311yescharacteristic
97C2×#11924007—21no—
98C2×#11924007—21no—
99C2×C22⋊Dic73—21no—
100C2×C22⋊Dic73—21no—
101C2×C22⋊Dic73—21no—
102C2×C22⋊Dic73—21no—
103C2×#11924005—21no—
104C2×#11924005—21no—
105C2×#11924005—21no—
106C2×C4×Dic73—21no—
107C2×C4×Dic73—21no—
108C2×C4×Dic73—21no—
109#14556513—22no—
110#14556513—22no—
111#14556513—41no—
112#14556513—41no—
113#14556498—21no—
114#14556498—21no—
115#14556498—21no—
116#14556498—21no—
117#14556498—21no—
118C22×D4×C73D411yescharacteristic
119C23×C4×C73C2311yescharacteristic
120C23×C4×C73C2311yescharacteristic
121C2×M16×C73—22no—
122C2×M16×C73—22no—
123C2×M16×C73—22no—
124C2×M16×C73—22no—
125C2×M16×C73—41no—
126C2×M16×C73—41no—
127C22×C8×C73C2311yescharacteristic
128C22×C8×C73C2311yescharacteristic
129C22×C8×C73C2311yescharacteristic
130C22×C8×C73C2311yescharacteristic
131C4×D4×C73C2×C414yes—
132C4×D4×C73D414yes—
133C2×C4⋊C4×C73D411yescharacteristic
134C2×C22⋊C4×C73D411yescharacteristic
135C2×C22⋊C4×C73D411yescharacteristic
136C2×C42×C73C2311yescharacteristic
137C4⋊C8×C73—22no—
138C22⋊C8×C73—22no—
139C22⋊C8×C73—22no—
140C4×C8×C73—22no—
141C23×D73—21no—
142C2×D292—21no—
143C2×D292—21no—
144C2×D292—21no—
145C2×D292—21no—
146C2×D292—21no—
147C2×D292C22×C412yes—
148C2×C22⋊D73—24no—
149C2×C22⋊D73—24no—
150C2×C22⋊D73—42no—
151C2×C22⋊D73—42no—
152C2×C22⋊D73—81no—
153C2×C22⋊D73—81no—
154C22×Dic73—21no—
155C22×Dic73—21no—
156C22×Dic73—21no—
157C22×Dic73—21no—
158C22×Dic73—24no—
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—42no—
163C22×Dic73—42no—
164C22×Dic73—81no—
165C22×Dic73—81no—
166C22×Dic73—81no—
167C2×C4×D73—24no—
168C2×C4×D73—81no—
169C2×C4×D73—81no—
170C4⋊Dic73—24no—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73—21no—
175C4⋊Dic73—21no—
176C4⋊Dic73—21no—
177C4⋊Dic73—21no—
178C4⋊Dic73—21no—
179C4⋊Dic73—21no—
180C4⋊Dic73—21no—
181C4⋊Dic73—42no—
182C4⋊Dic73C22×C412yes—
183C4⋊Dic73C22×C412yes—
184C4⋊Dic73C22×C412yes—
185C4⋊Dic73#4112yes—
186#11924007—24no—
187#11924007—24no—
188C22⋊Dic73—24no—
189C22⋊Dic73—42no—
190C22⋊Dic73—42no—
191C22⋊Dic73—81no—
192#11924005—24no—
193#11924005—24no—
194#11924005—24no—
195C4×Dic73—24no—
196C4×Dic73—42no—
197C4×Dic73—81no—
198C24×C73C2×D411yescharacteristic
199C24×C73C2×D411yescharacteristic
200C2×D4×C73—41no—
201C2×D4×C73—41no—
202C2×D4×C73C22⋊C414yes—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73C22×C412yes—
212C22×C4×C73C22×C412yes—
213C22×C4×C73C2×D412yes—
214C22×C4×C73C2×D412yes—
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219C22×C4×C73C2411yescharacteristic
220M16×C73—44no—
221M16×C73—44no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73#4112yes—
234C4⋊C4×C73C22⋊C414yes—
235C22⋊C4×C73C22⋊C414yes—
236C22⋊C4×C73C22⋊C414yes—
237C42×C73C22×C412yes—
238C42×C73C2×D412yes—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73C2×C22⋊C412yes—
252C23×C73C2×C22⋊C412yes—
253C23×C73C22×D411yescharacteristic
254C22×D73—22no—
255C22×D73—41no—
256C22×D73—41no—
257C22×D73—41no—
258C22×D73—41no—
259C22×D73—41no—
260C22×D73—41no—
261D4×C73—44no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73C2×C22⋊C412yes—
279C2×C4×C73C2×C22⋊C412yes—
280C2×C4×C73C2×C22⋊C412yes—
281C2×C4×C73C2×C22⋊C412yes—
282C2×C4×C73C23×C411yescharacteristic
283C2×C4×C73C22×D411yescharacteristic
284C2×C4×C73C2×#4111yescharacteristic
285C2×C4×C73C2×#4111yescharacteristic
286C2×C4×C73H(5,𝔽2)11yescharacteristic
287C2×C4×C732−1+411yescharacteristic
288C22⋊D73—48no—
289C22⋊D73—84no—
290C2×Dic73—22no—
291C2×Dic73—22no—
292C2×Dic73—22no—
293C2×Dic73—22no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297C2×Dic73—41no—
298C2×Dic73—41no—
299C2×Dic73—41no—
300C2×Dic73—41no—
301C2×Dic73—41no—
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—
311C2×Dic73—84no—
312C2×Dic73—84no—
313D292—22no—
314D292—22no—
315D292—41no—
316D292—41no—
317C4×D73—84no—
318C8×C73—22no—
319C8×C73—41no—
320C8×C73—41no—
321C8×C73—41no—
322C22×C73—22no—
323C22×C73—22no—
324C22×C73—22no—
325C22×C73—22no—
326C22×C73—22no—
327C22×C73—22no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—41no—
335C22×C73—41no—
336C22×C73C22×C22⋊C411yescharacteristic
337C22×C73#54611yescharacteristic
338C22×C73#54711yescharacteristic
339C22×C73#57511yescharacteristic
340C22×C73#57511yescharacteristic
341C22×C73#57611yescharacteristic
342C22×C73#57711yescharacteristic
343C2×D73—42no—
344C2×D73—42no—
345C2×D73—42no—
346C2×D73—81no—
347C2×D73—81no—
348C2×D73—81no—
349C2×D73—81no—
350C4×C73—22no—
351C4×C73—22no—
352C4×C73—22no—
353C4×C73—22no—
354C4×C73C4×#4111yescharacteristic
355C4×C73#52011yescharacteristic
356C4×C73#54611yescharacteristic
357C4×C73#54711yescharacteristic
358Dic73—42no—
359Dic73—42no—
360Dic73—42no—
361Dic73—42no—
362Dic73—81no—
363Dic73—81no—
364Dic73—81no—
365#22501—731nomaximal, Sylow
366C2×C73—42no—
367C2×C73—42no—
368C2×C73#233911yescharacteristic
369C2×C73#289611yescharacteristic
370C2×C73#289711yescharacteristic
371C2×C73#332211yescharacteristic
372C2×C73#332611yescharacteristic
373C2×C73#335111yescharacteristic
374C2×C73#335511yescharacteristic
375D73—82no—
376C2×#553—731no—
377C2×#436D7311yescharacteristic, complemented
378#2352—731no—
379#1991—731no—
380#1989—731no—
381#1895—731no—
382#1895—731no—
383#1875—731no—
384#1874—731no—
385#1825—731no—
386#1823—731no—
387#1804—731no—
388C4×#102—731no—
389#1736—731no—
390#1736—731no—
391C73#2250111yescharacteristic, complemented, Sylow
392C22×M16C2×D7311yescharacteristic
393C22×M16C2×D7311yescharacteristic
394#553—738no—
395#553—1464no—
396C2×#126—1461no—
397C2×#125—731no—
398C2×#123—1461no—
399C2×#121—731no—
400C2×#121—731no—
401C2×#121—1461no—
402C2×C4×D4—731no—
403C2×C4×D4—1461no—
404C2×C4×D4C2×D7311yescharacteristic
405C2×#117—731no—
406C2×#117—731no—
407C22×C4⋊C4—731no—
408C22×C4⋊C4—731no—
409#436—24no—
410C2×C4⋊C8C2×D7311yescharacteristic
411C2×#102—731no—
412C2×#102—731no—
413C2×#102—731no—
414C2×#102—731no—
415C2×C22⋊C8C2×D7311yescharacteristic
416C2×C22⋊C8C2×D7311yescharacteristic
417C2×C4×C8C2×D7311yescharacteristic
418#388—1461no—
419#387—1461no—
420#386—1461no—
421#382—731no—
422#380—731no—
423#380—731no—
424C4×C4⋊C4—731no—
425C4×C22⋊C4—1461no—
426#340—731no—
427#340—731no—
428#340—731no—
429#340—731no—
430#340—731no—
431#340—731no—
432#340—731no—
433#340—731no—
434#340—731no—
435#340—731no—
436#340—731no—
437#340—731no—
438C22×D4—731no—
439C22×D4—1461no—
440C22×D4—1461no—
441C22×D4D29211yescharacteristic
442C23×C4—1461no—
443C23×C4—1461no—
444C23×C4—1461no—
445C23×C4C22×D7311yescharacteristic
446C23×C4C22×D7311yescharacteristic
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—41no—
452C2×M16—41no—
453C22×C8C22×D7311yescharacteristic
454C22×C8C22×D7311yescharacteristic
455C22×C8C22×D7311yescharacteristic
456C22×C8C22×D7311yescharacteristic
457#126—1468no—
458#125—734no—
459#125—1462no—
460#123—1468no—
461#121—734no—
462#121—734no—
463#121—1468no—
464#121—1462no—
465#121—1462no—
466C4×D4—734no—
467C4×D4—1468no—
468C4×D4—1462no—
469C4×D4C4×D7314yes—
470C4×D4C22⋊D7314yes—
471#117—2921no—
472#117—734no—
473#117—1462no—
474#117—1462no—
475C2×C4⋊C4—2921no—
476C2×C4⋊C4—734no—
477C2×C4⋊C4—731no—
478C2×C4⋊C4—731no—
479C2×C4⋊C4—731no—
480C2×C4⋊C4—731no—
481C2×C4⋊C4—731no—
482C2×C4⋊C4—731no—
483C2×C4⋊C4—731no—
484C2×C4⋊C4—1461no—
485C2×C4⋊C4—1462no—
486C2×C4⋊C4—1462no—
487C2×C4⋊C4—1461no—
488C2×C4⋊C4—1461no—
489C2×C4⋊C4—1461no—
490C2×C4⋊C4D29211yescharacteristic
491C2×C22⋊C4—1461no—
492C2×C22⋊C4—1461no—
493C2×C22⋊C4—1461no—
494C2×C22⋊C4—1461no—
495C2×C22⋊C4—1461no—
496C2×C22⋊C4—1461no—
497C2×C22⋊C4—1461no—
498C2×C22⋊C4D29211yescharacteristic
499C2×C22⋊C4D29211yescharacteristic
500C2×C42—1461no—
501C2×C42—1461no—
502C2×C42—1461no—
503C2×C42C22×D7311yescharacteristic
504C4⋊C8—22no—
505#102—2921no—
506#102—2921no—
507#102—1462no—
508#102—1462no—
509C22⋊C8—22no—
510C22⋊C8—22no—
511C4×C8—22no—
512#95—1461no—
513#95—1461no—
514#95—1461no—
515#95—1461no—
516#95—1461no—
517C24—1461no—
518C24C2×D29211yescharacteristic
519C24C2×D29211yescharacteristic
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—2922no—
523C2×D4—2922no—
524C2×D4—5841no—
525C2×D4—5841no—
526C2×D4—732no—
527C2×D4—1464no—
528C2×D4—1464no—
529C2×D4—1461no—
530C2×D4—1461no—
531C2×D4—1461no—
532C2×D4—1461no—
533C2×D4—1461no—
534C2×D4#1192400514yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—2922no—
544C22×C4—2922no—
545C22×C4—5841no—
546C22×C4—5841no—
547C22×C4—5841no—
548C22×C4—5841no—
549C22×C4—5841no—
550C22×C4—1461no—
551C22×C4—1461no—
552C22×C4—1461no—
553C22×C4—1461no—
554C22×C4—1461no—
555C22×C4—1461no—
556C22×C4—1461no—
557C22×C4—1464no—
558C22×C4—1464no—
559C22×C4C2×C4×D7312yes—
560C22×C4C2×C4×D7312yes—
561C22×C4C2×C22⋊D7312yes—
562C22×C4C2×C22⋊D7312yes—
563C22×C4C2×D29211yescharacteristic
564C22×C4C2×D29211yescharacteristic
565C22×C4C2×D29211yescharacteristic
566C22×C4C2×D29211yescharacteristic
567C22×C4C23×D7311yescharacteristic
568M16—44no—
569M16—44no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8#1192402712yes—
582C4⋊C4—2922no—
583C4⋊C4—732no—
584C4⋊C4—732no—
585C4⋊C4—732no—
586C4⋊C4—732no—
587C4⋊C4—1461no—
588C4⋊C4—1461no—
589C4⋊C4—1461no—
590C4⋊C4—1461no—
591C4⋊C4—1461no—
592C4⋊C4—1461no—
593C4⋊C4—1464no—
594C4⋊C4—1464no—
595C4⋊C4—1464no—
596C4⋊C4—1461no—
597C4⋊C4—1461no—
598C4⋊C4—1461no—
599C4⋊C4—1461no—
600C4⋊C4#1192400514yes—
601C22⋊C4—2922no—
602C22⋊C4—2922no—
603C22⋊C4—5841no—
604C22⋊C4—1464no—
605C22⋊C4—1464no—
606C22⋊C4—1464no—
607C22⋊C4—1464no—
608C22⋊C4#1192400514yes—
609C22⋊C4#1192400514yes—
610C42—2922no—
611C42—5841no—
612C42—1464no—
613C42C2×C4×D7312yes—
614C42C2×C22⋊D7312yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—2921no—
628C23—2921no—
629C23—2921no—
630C23—2921no—
631C23—2921no—
632C23—2921no—
633C23—1462no—
634C23C2×#1192400512yes—
635C23C2×#1192400512yes—
636C23C22×D29211yescharacteristic
637D4—44no—
638D4—2928no—
639D4—2921no—
640D4—2921no—
641D4—5844no—
642D4—1462no—
643D4—1462no—
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—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—2921no—
661C2×C4—2921no—
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—2921no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—2921no—
675C2×C4—2921no—
676C2×C4—2921no—
677C2×C4—5844no—
678C2×C4—5844no—
679C2×C4—5844no—
680C2×C4—1462no—
681C2×C4—1462no—
682C2×C4—1462no—
683C2×C4—1462no—
684C2×C4C2×#1192400512yes—
685C2×C4C2×#1192400512yes—
686C2×C4C2×#1192400512yes—
687C2×C4C2×#1192400512yes—
688C2×C4C22×C4×D7311yescharacteristic
689C2×C4C22×C22⋊D7311yescharacteristic
690C2×C4#41×D7311yescharacteristic
691C2×C4C2×#1192402711yescharacteristic
692C2×C4#1455663611yescharacteristic
693C2×C4#1455663811yescharacteristic
694C8—22no—
695C8—41no—
696C8—41no—
697C8—41no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—2922no—
713C22—2922no—
714C22—2922no—
715C22—5841no—
716C22—5841no—
717C22—5841no—
718C22—5841no—
719C22C22×#1192400511yescharacteristic
720C22#1798923211yescharacteristic
721C22#1798924111yescharacteristic
722C22#1798938711yescharacteristic
723C22#1798938711yescharacteristic
724C22#1798939211yescharacteristic
725C22#1798939911yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—2922no—
731C4—2922no—
732C4—2922no—
733C4—2922no—
734C4—5841no—
735C4—5841no—
736C4—5841no—
737C4C4×#1192402711yescharacteristic
738C4#1798906611yescharacteristic
739C4#1798923111yescharacteristic
740C4#1798923611yescharacteristic
741C2—42no—
742C2—42no—
743C2—5842no—
744C2#2261275611yescharacteristic
745C2#2261845111yescharacteristic
746C2#2261845811yescharacteristic
747C2#2262213411yescharacteristic
748C2#2262218611yescharacteristic
749C2#2262249311yescharacteristic
750C2#2262253611yescharacteristic
subgroupG/H
centerC23C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#436×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989283C2
cosocleC22×C4×C73C24
hypercenterC2×#436D73
hypocenterC73#22501
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. #22612860C2semidirect
3. #22610896C2semidirect
4. #22610886C2semidirect
5. #22610369C2semidirect
6. #22610369C2semidirect
7. #22610251C2semidirect
8. #22610246C2semidirect
9. #22610027C2semidirect
10. #22610018C2semidirect
11. #22609942C2semidirect
12. C4×#14556513C2semidirect
13. #22609651C2semidirect
14. #22609651C2semidirect
15. C2×#436×C73C2semidirect
17. #17989283C4semidirect
70. #14556583C2×C4semidirect
75. #14556565C2×C4semidirect
78. C4×D292C2×C4semidirect
89. C2×C4⋊Dic73C2×C4semidirect
377. C2×#436D73semidirect
391. C73#22501semidirect

Maximal subgroups

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

subgroupindex
C2×#179892832
#226128602
#226108962
#226108862
#226103692
#226102512
#226102462
#226100272
#226100182
#226099422
C4×#145565132
#226096512
C2×#436×C732
#2250173