Finite Group Databasebeta

← #33102268

Subgroups — #33102268

Order 18688.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989272C211yesmaximal, characteristic
2C2×#17988658C211yesmaximal, characteristic
3C4⋊C4×C22⋊D73C211yesmaximal, characteristic
4#22610898C211yesmaximal, characteristic, complemented
5#22610885C211yesmaximal, characteristic, complemented
6#22610363C211yesmaximal, characteristic, complemented
7#22610354C211yesmaximal, characteristic, complemented
8#22610238C211yesmaximal, characteristic, complemented
9#22610237C211yesmaximal, characteristic, complemented
10#22610025C211yesmaximal, characteristic, complemented
11#22610017C211yesmaximal, characteristic, complemented
12#22609935C211yesmaximal, characteristic, complemented
13#22609760C211yesmaximal, characteristic, complemented
14#22609649C211yesmaximal, characteristic, complemented
15C2×#340×C73C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17#17989272—24no—
18#17989272C418yescomplemented
19C2×#14556586—21no—
20C2×#14556582C2211yescharacteristic
21C2×#14556581—21no—
22C2×#14556574—21no—
23C2×#14556571C2211yescharacteristic
24C2×#14556570C2211yescharacteristic
25C2×#14556556C2211yescharacteristic
26C2×C4×C22⋊D73—21no—
27C2×C4×C22⋊D73C2211yescharacteristic
28C2×#14556550—21no—
29C2×#14556549C2211yescharacteristic
30C2×C4⋊C4×D73C2211yescharacteristic
31#17988658—24no—
32C2×#14556520C2211yescharacteristic
33C2×#14556516C2211yescharacteristic
34C2×#14556516C2211yescharacteristic
35C2×#14556514C2211yescharacteristic
36C2×#14556514C2211yescharacteristic
37C2×C22⋊#10596831C2211yescharacteristic
38C2×#14556503C2211yescharacteristic
39C2×#14556501C2211yescharacteristic
40#17988482—21no—
41#17988460—21no—
42#17988458—21no—
43#17988456C2211yescharacteristic
44#17988447C2211yescharacteristic
45#17988444C2211yescharacteristic
46C4⋊C4×Dic73C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55C23×C8×C73C2211yescharacteristic
56C22×C4⋊C4×C73C2211yescharacteristic
57C22×C4⋊C4×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62C22×Dic146C2311yescharacteristic
63C22×C22⋊D73D411yescharacteristic
64C22×C4×D73—21no—
65C22×C4×D73C2311yescharacteristic
66C2×#11924011—22no—
67C2×#11924011—22no—
68C2×#11924011—41no—
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71#14556586—28no—
72#14556582—22no—
73#14556582C2×C414yescomplemented
74#14556581—28no—
75#14556574—28no—
76#14556571—22no—
77#14556571C2×C414yescomplemented
78#14556570—22no—
79#14556570C2×C414yescomplemented
80#14556556—22no—
81#14556556C2×C414yescomplemented
82C4×C22⋊D73—44no—
83C4×C22⋊D73C2×C414yes—
84C4×C22⋊D73D414yes—
85#14556550—28no—
86#14556549—22no—
87#14556549C2×C414yescomplemented
88C2×C4⋊Dic73—21no—
89C2×C4⋊Dic73—21no—
90C2×C4⋊Dic73C2311yescharacteristic
91C2×C4⋊Dic73C2311yescharacteristic
92C2×C4⋊Dic73C2311yescharacteristic
93C2×#11924007—21no—
94C2×#11924007—21no—
95C2×#11924007—21no—
96C2×#11924007—21no—
97C2×#11924007—21no—
98C2×#11924007—21no—
99C2×#11924007D411yescharacteristic
100C4⋊C4×D73—22no—
101C4⋊C4×D73—41no—
102C2×C22⋊Dic73—21no—
103C2×C22⋊Dic73—21no—
104C2×C22⋊Dic73D411yescharacteristic
105C2×#11924005—21no—
106C2×#11924005—21no—
107C2×#11924005—21no—
108C2×#11924005D411yescharacteristic
109C2×C4×Dic73—21no—
110C2×C4×Dic73—21no—
111C2×C4×Dic73—21no—
112C2×C4×Dic73C2311yescharacteristic
113#14556520—22no—
114#14556516—22no—
115#14556516—41no—
116#14556514—22no—
117#14556514—41no—
118C22⋊#10596831—22no—
119#14556503—22no—
120#14556501—22no—
121#14556498—21no—
122#14556498—21no—
123#14556498—21no—
124C23×C4×C73—21no—
125C23×C4×C73—21no—
126C23×C4×C73C2311yescharacteristic
127C22×C8×C73—22no—
128C22×C8×C73—22no—
129C22×C8×C73—41no—
130C22×C8×C73C2311yescharacteristic
131C22×C8×C73C2311yescharacteristic
132C2×C4⋊C4×C73—22no—
133C2×C4⋊C4×C73—21no—
134C2×C4⋊C4×C73—22no—
135C2×C4⋊C4×C73—21no—
136C2×C4⋊C4×C73—41no—
137C2×C4⋊C4×C73C2×C414yescomplemented
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C4⋊C4×C73C2311yescharacteristic
140C2×C4⋊C4×C73C2311yescharacteristic
141C2×C4⋊C4×C73C2311yescharacteristic
142C23×D73C2×D411yescharacteristic
143C2×Dic146—21no—
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146—21no—
147C2×Dic146—21no—
148C2×Dic146C22×C412yes—
149C2×C22⋊D73—22no—
150C2×C22⋊D73—22no—
151C2×C22⋊D73C22⋊C414yes—
152C22×Dic73—21no—
153C22×Dic73—21no—
154C22×Dic73—21no—
155C22×Dic73—21no—
156C22×Dic73C2×D411yescharacteristic
157C22×Dic73C2×D411yescharacteristic
158C22×Dic73C2×D411yescharacteristic
159C2×C4×D73—21no—
160C2×C4×D73—21no—
161C2×C4×D73—21no—
162C2×C4×D73—21no—
163C2×C4×D73—42no—
164C2×C4×D73—42no—
165C2×C4×D73—81no—
166C2×C4×D73C22×C412yes—
167C2×C4×D73C2×D412yes—
168#11924011—44no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C4⋊Dic73—21no—
176C4⋊Dic73—24no—
177C4⋊Dic73—24no—
178C4⋊Dic73—21no—
179C4⋊Dic73—21no—
180C4⋊Dic73—21no—
181C4⋊Dic73—21no—
182C4⋊Dic73C22×C412yes—
183#11924007—24no—
184#11924007—24no—
185#11924007—24no—
186#11924007—42no—
187#11924007—42no—
188#11924007—81no—
189#11924007C22⋊C414yes—
190C22⋊Dic73—24no—
191C22⋊Dic73—42no—
192C22⋊Dic73C22⋊C414yes—
193#11924005—24no—
194#11924005—24no—
195#11924005—42no—
196#11924005C22⋊C414yes—
197C4×Dic73—24no—
198C4×Dic73—24no—
199C4×Dic73—42no—
200C4×Dic73C22×C412yes—
201C4×Dic73C2×D412yes—
202C24×C73C2×D411yescharacteristic
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—24no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—42no—
213C22×C4×C73—42no—
214C22×C4×C73—42no—
215C22×C4×C73—42no—
216C22×C4×C73—81no—
217C22×C4×C73C22×C412yes—
218C22×C4×C73C2×D411yescharacteristic
219C22×C4×C73C2×D412yes—
220C22×C4×C73C2411yescharacteristic
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—44no—
227C2×C8×C73#4112yes—
228C4⋊C4×C73—24no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—42no—
235C4⋊C4×C73C22×C412yes—
236C4⋊C4×C73C22×C412yes—
237C4⋊C4×C73#4112yes—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73C2×C22⋊C412yes—
243C23×C73AGL(1,ℤ/8)12yes—
244C23×C73#13712yes—
245C23×C73C22×D411yescharacteristic
246C22×D73—21no—
247C22×D73—21no—
248C22×D73—21no—
249C22×D73—21no—
250C22×D73—21no—
251C22×D73—21no—
252C22×D73C2×C22⋊C412yes—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—22no—
261C2×C4×C73—22no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—48no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—84no—
273C2×C4×C73C2×C22⋊C412yes—
274C2×C4×C73C23×C411yescharacteristic
275C2×C4×C73C22×D411yescharacteristic
276C2×C4×C73C2×#4111yescharacteristic
277C2×C4×C73C2×#4111yescharacteristic
278C2×C4×C73H(5,𝔽2)11yescharacteristic
279C2×C4×C732−1+411yescharacteristic
280C22⋊D73—28no—
281C2×Dic73—21no—
282C2×Dic73—21no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—21no—
286C2×Dic73—21no—
287C2×Dic73—22no—
288C2×Dic73—22no—
289C2×Dic73—41no—
290C2×Dic73—41no—
291C2×Dic73—41no—
292C2×Dic73—41no—
293C2×Dic73—41no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297C2×Dic73—41no—
298C2×Dic73—41no—
299C2×Dic73C2×C22⋊C412yes—
300C2×Dic73C2×C22⋊C412yes—
301C2×Dic73C2×C22⋊C412yes—
302C4×D73—22no—
303C4×D73—22no—
304C4×D73—22no—
305C4×D73—22no—
306C4×D73—84no—
307Dic146—22no—
308Dic146—22no—
309Dic146—41no—
310Dic146—41no—
311C8×C73—22no—
312C8×C73—41no—
313#10596831—41no—
314#10596831—41no—
315C22×C73—22no—
316C22×C73—22no—
317C22×C73—22no—
318C22×C73—22no—
319C22×C73—22no—
320C22×C73—22no—
321C22×C73#41714yes—
322C22×C73C22×C22⋊C411yescharacteristic
323C22×C73#54611yescharacteristic
324C22×C73#54711yescharacteristic
325C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C73C2×#13711yescharacteristic
327C22×C73#57711yescharacteristic
328C22×C73#57811yescharacteristic
329C2×D73—22no—
330C2×D73—22no—
331C2×D73—22no—
332C2×D73—41no—
333C2×D73—41no—
334C2×D73—41no—
335C2×D73—41no—
336C4×C73—22no—
337C4×C73—42no—
338C4×C73—42no—
339C4×C73—42no—
340C4×C73—81no—
341C4×C73C4×#4111yescharacteristic
342C4×C73#52011yescharacteristic
343C4×C73#54611yescharacteristic
344C4×C73#54711yescharacteristic
345Dic73—22no—
346Dic73—22no—
347Dic73—22no—
348Dic73—42no—
349Dic73—42no—
350Dic73—81no—
351Dic73—81no—
352#22491—731nomaximal, Sylow
353C2×C73—24no—
354C2×C73#233911yescharacteristic
355C2×C73C2×#41711yescharacteristic
356C2×C73#289811yescharacteristic
357C2×C73#331011yescharacteristic
358C2×C73#331211yescharacteristic
359C2×C73#334311yescharacteristic
360C2×C73#334411yescharacteristic
361D73—42no—
362C2×#552—731no—
363C2×#435—731no—
364D4×C4⋊C4—731no—
365#1992—731no—
366#1989—731no—
367#1894—731no—
368#1892—731no—
369#1872—731no—
370#1872—731no—
371#1825—731no—
372#1823—731no—
373#1803—731no—
374#1763—731no—
375#1736—731no—
376C2×#340D7311yescharacteristic, complemented
377C73#2249111yescharacteristic, complemented, Sylow
378C22×M16—731no—
379C23×C8C2×D7311yescharacteristic
380#552—738no—
381#552—1464no—
382C2×#126—1461no—
383C2×#125—731no—
384C2×#125—1461no—
385C2×#123—1461no—
386C2×C22⋊Q8—731no—
387C2×C22⋊Q8—731no—
388C2×C4×Q8—731no—
389C2×C4×D4—731no—
390C2×C4×D4—1461no—
391C2×#117—731no—
392C2×#117—1461no—
393C22×C4⋊C4—731no—
394C22×C4⋊C4C2×D7311yescharacteristic
395C22×C4⋊C4C2×D7311yescharacteristic
396#435—1464no—
397C2×C4⋊C8—731no—
398C2×#103—731no—
399C2×#103—731no—
400C2×#103—731no—
401C2×#103—731no—
402C2×C22⋊C8—731no—
403C2×C22⋊C8—731no—
404C2×#97—731no—
405#389—1461no—
406#385—1461no—
407#385—1461no—
408#384—731no—
409#380—731no—
410#380—731no—
411C4×C4⋊C4—731no—
412#340—731no—
413#340—731no—
414#340—731no—
415#340—731no—
416#340—731no—
417#340—731no—
418#340—731no—
419#340—731no—
420#340C2×D7311yescharacteristic
421#340C2×D7311yescharacteristic
422#340C2×D7311yescharacteristic
423#340C2×D7311yescharacteristic
424C22×Q8—731no—
425C22×D4—731no—
426C23×C4—21no—
427C23×C4—21no—
428C23×C4—731no—
429C23×C4—1461no—
430C23×C4C22×D7311yescharacteristic
431C2×M16—2921no—
432C2×M16—1462no—
433C2×M16—1462no—
434C22×C8—22no—
435C22×C8—22no—
436C22×C8—41no—
437C22×C8—731no—
438C22×C8—731no—
439C22×C8C22×D7311yescharacteristic
440C22×C8C22×D7311yescharacteristic
441#126—1468no—
442#125—734no—
443#125—1462no—
444#125—1468no—
445#123—1468no—
446C22⋊Q8—734no—
447C22⋊Q8—734no—
448C22⋊Q8—1462no—
449C22⋊Q8—1462no—
450C4×Q8—734no—
451C4×Q8—1462no—
452C4×D4—2924no—
453C4×D4—734no—
454C4×D4—734no—
455#117—734no—
456#117—1468no—
457#117—1462no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4—2921no—
464C2×C4⋊C4—731no—
465C2×C4⋊C4—731no—
466C2×C4⋊C4—731no—
467C2×C4⋊C4—731no—
468C2×C4⋊C4—1461no—
469C2×C4⋊C4—1461no—
470C2×C4⋊C4—1462no—
471C2×C4⋊C4—1461no—
472C2×C4⋊C4—1461no—
473C2×C4⋊C4—1461no—
474C2×C4⋊C4—1461no—
475C2×C4⋊C4—1461no—
476C2×C4⋊C4—1461no—
477C2×C4⋊C4C4×D7314yescomplemented
478C2×C4⋊C4C22×D7311yescharacteristic
479C2×C4⋊C4C22×D7311yescharacteristic
480C2×C4⋊C4C22×D7311yescharacteristic
481C2×C4⋊C4C22×D7311yescharacteristic
482C2×C22⋊C4—731no—
483C2×C22⋊C4—731no—
484C2×C22⋊C4—1461no—
485C2×C22⋊C4—1461no—
486C2×C22⋊C4—1461no—
487C2×C22⋊C4—1461no—
488C2×C22⋊C4—1461no—
489C2×C42—731no—
490C2×C42—1461no—
491C2×C42—1461no—
492C2×C42—1461no—
493C4⋊C8—1462no—
494#103—2921no—
495#103—2921no—
496#103—1462no—
497#103—1462no—
498C22⋊C8—1462no—
499C22⋊C8—1462no—
500#97—1462no—
501#95—1461no—
502#95—1461no—
503#95—1461no—
504C24—731no—
505C24D4×D7311yescharacteristic
506C2×Q8—732no—
507C2×Q8—1461no—
508C2×Q8—1461no—
509C2×Q8—1461no—
510C2×Q8—1461no—
511C2×Q8—1461no—
512C2×D4—734no—
513C2×D4—1462no—
514C2×D4—1462no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—24no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—81no—
529C22×C4—2922no—
530C22×C4—2922no—
531C22×C4—5841no—
532C22×C4—731no—
533C22×C4—731no—
534C22×C4—731no—
535C22×C4—732no—
536C22×C4—732no—
537C22×C4—1461no—
538C22×C4—1461no—
539C22×C4—1461no—
540C22×C4—1461no—
541C22×C4—1461no—
542C22×C4—1461no—
543C22×C4—1461no—
544C22×C4—1461no—
545C22×C4C2×C4×D7312yes—
546C22×C4D4×D7311yescharacteristic
547C22×C4D4×D7312yes—
548C22×C4C23×D7311yescharacteristic
549M16—2924no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—44no—
556C2×C8—1461no—
557C2×C8—1461no—
558C2×C8—1461no—
559C2×C8—1461no—
560C2×C8—1461no—
561C2×C8—1461no—
562C2×C8#1192402812yes—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—2922no—
571C4⋊C4—2922no—
572C4⋊C4—5841no—
573C4⋊C4—734no—
574C4⋊C4—732no—
575C4⋊C4—1464no—
576C4⋊C4—1464no—
577C4⋊C4—1464no—
578C4⋊C4—1464no—
579C4⋊C4—1461no—
580C4⋊C4—1461no—
581C4⋊C4—1461no—
582C4⋊C4—1461no—
583C4⋊C4—1464no—
584C4⋊C4—1461no—
585C4⋊C4C2×C4×D7312yes—
586C4⋊C4C2×C4×D7312yes—
587C4⋊C4#1192402812yes—
588C22⋊C4—2922no—
589C22⋊C4—2922no—
590C22⋊C4—734no—
591C22⋊C4—734no—
592C22⋊C4—1464no—
593C22⋊C4—1464no—
594C22⋊C4—1464no—
595C42—2922no—
596C42—732no—
597C42—732no—
598C42—1464no—
599C42—1464no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—732no—
605C23—1461no—
606C23—1461no—
607C23—1461no—
608C23—1461no—
609C23—1461no—
610C23—1461no—
611C23C22⋊C4×D7312yes—
612C23#1455661512yes—
613C23#1455662012yes—
614C23C2×D4×D7311yescharacteristic
615Q8—2921no—
616Q8—2921no—
617Q8—1462no—
618Q8—1462no—
619D4—1468no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—48no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—84no—
640C2×C4—2921no—
641C2×C4—2921no—
642C2×C4—2921no—
643C2×C4—2921no—
644C2×C4—2921no—
645C2×C4—2921no—
646C2×C4—2921no—
647C2×C4—2921no—
648C2×C4—2921no—
649C2×C4—2921no—
650C2×C4—5844no—
651C2×C4—732no—
652C2×C4—732no—
653C2×C4—732no—
654C2×C4—1462no—
655C2×C4—1462no—
656C2×C4—1461no—
657C2×C4—1461no—
658C2×C4—1461no—
659C2×C4—1461no—
660C2×C4—1461no—
661C2×C4—1461no—
662C2×C4—1462no—
663C2×C4—1462no—
664C2×C4—1462no—
665C2×C4—1462no—
666C2×C4C22⋊C4×D7312yes—
667C2×C4C22×C4×D7311yescharacteristic
668C2×C4C2×D4×D7311yescharacteristic
669C2×C4C2×#1192402811yescharacteristic
670C2×C4C2×#1192402811yescharacteristic
671C2×C4#1455663611yescharacteristic
672C2×C4#1455663911yescharacteristic
673C8—22no—
674C8—41no—
675C8—2921no—
676C8—2921no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—2921no—
684C22—2921no—
685C22—2921no—
686C22—2921no—
687C22—1462no—
688C22—1462no—
689C22—1462no—
690C22#1798858514yes—
691C22C2×C22⋊C4×D7311yescharacteristic
692C22#1798922711yescharacteristic
693C22#1798923811yescharacteristic
694C22C2×#1455661511yescharacteristic
695C22C2×#1455662011yescharacteristic
696C22#1798939311yescharacteristic
697C22#1798940011yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—2922no—
704C4—2922no—
705C4—5841no—
706C4—5841no—
707C4—1462no—
708C4—1462no—
709C4—1462no—
710C4C4×#1192402811yescharacteristic
711C4#1798906811yescharacteristic
712C4#1798922711yescharacteristic
713C4#1798923811yescharacteristic
714C2—24no—
715C2—2922no—
716C2#2261275811yescharacteristic
717C2C2×#1798858511yescharacteristic
718C2#2261845911yescharacteristic
719C2#2262194811yescharacteristic
720C2#2262197811yescharacteristic
721C2#2262236711yescharacteristic
722C2#2262238211yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#340×C73C2
socleC23×C73C22×D4
prime radicalC22×C22⋊D73D4
cosocleC22×C4×C73C24
hypercenterC2×#340D73
hypocenterC73#22491
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. #22610898C2semidirect
5. #22610885C2semidirect
6. #22610363C2semidirect
7. #22610354C2semidirect
8. #22610238C2semidirect
9. #22610237C2semidirect
10. #22610025C2semidirect
11. #22610017C2semidirect
12. #22609935C2semidirect
13. #22609760C2semidirect
14. #22609649C2semidirect
15. C2×#340×C73C2semidirect
18. #17989272C4semidirect
73. #14556582C2×C4semidirect
77. #14556571C2×C4semidirect
79. #14556570C2×C4semidirect
81. #14556556C2×C4semidirect
87. #14556549C2×C4semidirect
137. C2×C4⋊C4×C73C2×C4semidirect
376. C2×#340D73semidirect
377. C73#22491semidirect
477. C2×C4⋊C4C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179892722
C2×#179886582
C4⋊C4×C22⋊D732
#226108982
#226108852
#226103632
#226103542
#226102382
#226102372
#226100252
#226100172
#226099352
#226097602
#226096492
C2×#340×C732
#2249173