Finite Group Databasebeta

← #33102453

Subgroups — #33102453

Order 18688.

1182 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×#17989308C211yesmaximal, characteristic
2C2×#17988662C211yesmaximal, characteristic
3C4⋊C4×C22⋊D73C211yesmaximal, characteristic
4#22610890C211yesmaximal, characteristic, complemented
5#22610881C211yesmaximal, characteristic, complemented
6#22610365C211yesmaximal, characteristic, complemented
7#22610361C211yesmaximal, characteristic, complemented
8#22610235C211yesmaximal, characteristic, complemented
9#22610027C211yesmaximal, characteristic, complemented
10#22610025C211yesmaximal, characteristic, complemented
11#22609934C211yesmaximal, characteristic, complemented
12#103×Dic73C211yesmaximal, characteristic, complemented
13#22609650C211yesmaximal, characteristic, complemented
14#22609649C211yesmaximal, characteristic, complemented
15C73×#1872C211yesmaximal, characteristic, complemented
16C22×#11924012C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18#17989308—24no—
19#17989308C418yescomplemented
20C2×#14556590C2211yescharacteristic
21C2×#14556586—21no—
22C2×#14556584—21no—
23C2×#14556577—21no—
24C2×#14556567C2211yescharacteristic
25C2×Q8×Dic73C2211yescharacteristic
26C2×#14556556—21no—
27C2×C4×C22⋊D73—21no—
28C2×C4×C22⋊D73C2211yescharacteristic
29C2×#14556550C2211yescharacteristic
30C2×#14556549C2211yescharacteristic
31C2×C4⋊C4×D73C2211yescharacteristic
32#17988662—24no—
33C2×#14556520C2211yescharacteristic
34C2×#14556515C2211yescharacteristic
35C2×#14556515C2211yescharacteristic
36C2×#14556503C2211yescharacteristic
37C2×C8×Dic73C2211yescharacteristic
38#17988482—21no—
39#17988460—21no—
40#17988458—21no—
41#17988456C2211yescharacteristic
42#17988447C2211yescharacteristic
43#17988444C2211yescharacteristic
44C4⋊C4×Dic73C2211yescharacteristic
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55C2×C22⋊Q8×C73C2211yescharacteristic
56C22×C4⋊C4×C73C2211yescharacteristic
57C2×#103×C73C2211yescharacteristic
58C2×#103×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62C22×Dic146—21no—
63C22×C22⋊D73D411yescharacteristic
64C22×C4×D73—21no—
65C22×C4×D73C2311yescharacteristic
66C2×#11924012—22no—
67C2×#11924012—22no—
68C2×#11924012—41no—
69C2×#11924011—22no—
70C2×#11924011—22no—
71C2×#11924011—41no—
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74#14556590—22no—
75#14556590C2×C414yescomplemented
76#14556586—28no—
77#14556584—28no—
78#14556577—28no—
79#14556567—22no—
80#14556567C2×C414yescomplemented
81Q8×Dic73—22no—
82Q8×Dic73C2×C414yescomplemented
83#14556556—28no—
84C4×C22⋊D73—44no—
85C4×C22⋊D73C2×C414yes—
86C4×C22⋊D73D414yes—
87#14556550—22no—
88#14556550C2×C414yescomplemented
89#14556549—22no—
90#14556549C2×C414yescomplemented
91C2×C4⋊Dic73—21no—
92C2×C4⋊Dic73C2311yescharacteristic
93C2×C4⋊Dic73C2311yescharacteristic
94C2×C4⋊Dic73C2311yescharacteristic
95C2×C4⋊Dic73C2311yescharacteristic
96C2×#11924007—21no—
97C2×#11924007—21no—
98C2×#11924007—21no—
99C2×#11924007—21no—
100C2×#11924007—21no—
101C2×#11924007D411yescharacteristic
102C4⋊C4×D73—22no—
103C4⋊C4×D73—41no—
104C2×C22⋊Dic73—21no—
105C2×C22⋊Dic73—21no—
106C2×C22⋊Dic73D411yescharacteristic
107C2×#11924005—21no—
108C2×#11924005—21no—
109C2×#11924005—21no—
110C2×#11924005D411yescharacteristic
111C2×C4×Dic73—21no—
112C2×C4×Dic73—21no—
113C2×C4×Dic73—21no—
114C2×C4×Dic73—21no—
115C2×C4×Dic73C2311yescharacteristic
116#14556520—22no—
117#14556515—22no—
118#14556515—41no—
119#14556503—22no—
120C8×Dic73—22no—
121#14556498—21no—
122#14556498—21no—
123#14556498—21no—
124C22×Q8×C73C2311yescharacteristic
125C23×C4×C73—21no—
126C23×C4×C73C2311yescharacteristic
127C22×C8×C73C2311yescharacteristic
128C22×C8×C73C2311yescharacteristic
129C22⋊Q8×C73—22no—
130C22⋊Q8×C73C2×C414yescomplemented
131C2×C4⋊C4×C73—21no—
132C2×C4⋊C4×C73—22no—
133C2×C4⋊C4×C73—21no—
134C2×C4⋊C4×C73—41no—
135C2×C4⋊C4×C73C2311yescharacteristic
136C2×C4⋊C4×C73C2311yescharacteristic
137C2×C4⋊C4×C73C2311yescharacteristic
138C2×C22⋊C4×C73—21no—
139#103×C73—22no—
140#103×C73—41no—
141C22⋊C8×C73—22no—
142C23×D73C2×D411yescharacteristic
143C2×Dic146—24no—
144C2×Dic146—42no—
145C2×Dic146—42no—
146C2×C22⋊D73—22no—
147C2×C22⋊D73—22no—
148C2×C22⋊D73C22⋊C414yes—
149C22×Dic73—21no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73C2×D411yescharacteristic
154C22×Dic73C2×D411yescharacteristic
155C22×Dic73C2×D411yescharacteristic
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—42no—
161C2×C4×D73—42no—
162C2×C4×D73—81no—
163C2×C4×D73C22×C412yes—
164C2×C4×D73C2×D412yes—
165#11924012—44no—
166#11924011—44no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831#4112yes—
173C4⋊Dic73—21no—
174C4⋊Dic73—21no—
175C4⋊Dic73—24no—
176C4⋊Dic73—21no—
177C4⋊Dic73—21no—
178C4⋊Dic73—21no—
179C4⋊Dic73—21no—
180C4⋊Dic73C22×C412yes—
181C4⋊Dic73C22×C412yes—
182#11924007—24no—
183#11924007—24no—
184#11924007—42no—
185#11924007—42no—
186#11924007—81no—
187#11924007C22⋊C414yes—
188C22⋊Dic73—24no—
189C22⋊Dic73—42no—
190C22⋊Dic73C22⋊C414yes—
191#11924005—24no—
192#11924005—24no—
193#11924005—42no—
194#11924005C22⋊C414yes—
195C4×Dic73—24no—
196C4×Dic73—24no—
197C4×Dic73—24no—
198C4×Dic73—42no—
199C4×Dic73C22×C412yes—
200C4×Dic73C2×D412yes—
201C24×C73C2×D411yescharacteristic
202C2×Q8×C73—21no—
203C2×Q8×C73—21no—
204C2×Q8×C73—21no—
205C2×Q8×C73—21no—
206C2×Q8×C73—21no—
207C2×Q8×C73C22×C412yes—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—42no—
217C22×C4×C73—42no—
218C22×C4×C73—81no—
219C22×C4×C73C22×C412yes—
220C22×C4×C73C2×D411yescharacteristic
221C22×C4×C73C2×D412yes—
222C22×C4×C73C2411yescharacteristic
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C4⋊C4×C73—24no—
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×C73#4112yes—
237C22⋊C4×C73—24no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73C2×C22⋊C412yes—
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—
253Q8×C73—22no—
254Q8×C73—22no—
255Q8×C73—41no—
256Q8×C73—41no—
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—41no—
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×C73C23×C411yescharacteristic
278C2×C4×C73C22×D411yescharacteristic
279C2×C4×C73C2×#4111yescharacteristic
280C2×C4×C73C2×#4111yescharacteristic
281C2×C4×C73H(5,𝔽2)11yescharacteristic
282C2×C4×C732−1+411yescharacteristic
283C22⋊D73—28no—
284C2×Dic73—21no—
285C2×Dic73—21no—
286C2×Dic73—21no—
287C2×Dic73—21no—
288C2×Dic73—22no—
289C2×Dic73—22no—
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×Dic73—41no—
300C2×Dic73C2×C22⋊C412yes—
301C2×Dic73C2×C22⋊C412yes—
302C2×Dic73C2×C22⋊C412yes—
303C2×Dic73AGL(1,ℤ/8)12yes—
304C2×Dic73#13712yes—
305C4×D73—22no—
306C4×D73—22no—
307C4×D73—22no—
308C4×D73—22no—
309C4×D73—84no—
310Dic146—48no—
311C8×C73—41no—
312C8×C73—41no—
313#10596831—22no—
314#10596831—41no—
315C22×C73—22no—
316C22×C73—22no—
317C22×C73—22no—
318C22×C73—41no—
319C22×C73—41no—
320C22×C73—41no—
321C22×C73—41no—
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—42no—
348Dic73—42no—
349Dic73—81no—
350Dic73—81no—
351Dic73#41714yes—
352#22504—731nomaximal, Sylow
353C2×C73—42no—
354C2×C73#233911yescharacteristic
355C2×C73C2×#41711yescharacteristic
356C2×C73#289811yescharacteristic
357C2×C73#332411yescharacteristic
358C2×C73#332811yescharacteristic
359C2×C73#335311yescharacteristic
360C2×C73#335611yescharacteristic
361D73—42no—
362C2×#556—731no—
363C2×#436—731no—
364D4×C4⋊C4—731no—
365#1990—731no—
366#1988—731no—
367#1894—731no—
368#1894—731no—
369#1872—731no—
370#1872D7311yescharacteristic, complemented
371#1825—731no—
372#1825—731no—
373#1803—731no—
374C4×#103—731no—
375#1736—731no—
376#1736—731no—
377C73#2250411yescharacteristic, complemented, Sylow
378C22×M16—731no—
379C22×M16—731no—
380#556—738no—
381#556—1464no—
382C2×C4⋊Q8—731no—
383C2×#126—1461no—
384C2×#126—1461no—
385C2×#124—1461no—
386C2×C22⋊Q8—731no—
387C2×C22⋊Q8C2×D7311yescharacteristic
388C2×C4×Q8—731no—
389C2×C4×Q8—1461no—
390C2×C4×D4—731no—
391C2×C4×D4—1461no—
392C2×#117—731no—
393C2×#117—731no—
394C22×C4⋊C4—731no—
395C22×C4⋊C4C2×D7311yescharacteristic
396#436—1464no—
397C2×C4⋊C8—731no—
398C2×#103—731no—
399C2×#103—731no—
400C2×#103C2×D7311yescharacteristic
401C2×#103C2×D7311yescharacteristic
402C2×C22⋊C8—731no—
403C2×C22⋊C8C2×D7311yescharacteristic
404C2×C4×C8—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#340—731no—
421#340—731no—
422#340C2×D7311yescharacteristic
423#340C2×D7311yescharacteristic
424C22×Q8—1461no—
425C22×Q8C22×D7311yescharacteristic
426C22×D4—731no—
427C23×C4—21no—
428C23×C4—731no—
429C23×C4—1461no—
430C23×C4C22×D7311yescharacteristic
431C2×M16—2921no—
432C2×M16—2921no—
433C2×M16—1462no—
434C2×M16—1462no—
435C2×M16—1462no—
436C2×M16—1462no—
437C22×C8—731no—
438C22×C8—731no—
439C22×C8C22×D7311yescharacteristic
440C22×C8C22×D7311yescharacteristic
441C4⋊Q8—734no—
442C4⋊Q8—1462no—
443#126—1468no—
444#126—1468no—
445#124—1468no—
446C22⋊Q8—22no—
447C22⋊Q8—734no—
448C22⋊Q8—1462no—
449C22⋊Q8C4×D7314yescomplemented
450C4×Q8—734no—
451C4×Q8—1462no—
452C4×Q8—1468no—
453C4×D4—2924no—
454C4×D4—734no—
455C4×D4—734no—
456#117—734no—
457#117—734no—
458#117—1462no—
459#117—1462no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—41no—
464C2×C4⋊C4—2921no—
465C2×C4⋊C4—731no—
466C2×C4⋊C4—731no—
467C2×C4⋊C4—731no—
468C2×C4⋊C4—731no—
469C2×C4⋊C4—731no—
470C2×C4⋊C4—1461no—
471C2×C4⋊C4—1461no—
472C2×C4⋊C4—1462no—
473C2×C4⋊C4—1461no—
474C2×C4⋊C4—1461no—
475C2×C4⋊C4—1461no—
476C2×C4⋊C4—1461no—
477C2×C4⋊C4C22×D7311yescharacteristic
478C2×C4⋊C4C22×D7311yescharacteristic
479C2×C4⋊C4C22×D7311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—731no—
482C2×C22⋊C4—731no—
483C2×C22⋊C4—1461no—
484C2×C22⋊C4—1461no—
485C2×C22⋊C4—1461no—
486C2×C22⋊C4—1461no—
487C2×C22⋊C4—1461no—
488C2×C42—731no—
489C2×C42—1461no—
490C2×C42—1461no—
491C2×C42—1461no—
492C2×C42—1461no—
493C4⋊C8—1462no—
494#103—22no—
495#103—41no—
496#103—2921no—
497#103—1462no—
498C22⋊C8—22no—
499C22⋊C8—1462no—
500C4×C8—1462no—
501#95—1461no—
502#95—1461no—
503#95—1461no—
504C24—731no—
505C24D4×D7311yescharacteristic
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—2922no—
512C2×Q8—2922no—
513C2×Q8—1464no—
514C2×Q8C2×C4×D7312yes—
515C2×D4—734no—
516C2×D4—1462no—
517C2×D4—1462no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
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—
550M16—2924no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—732no—
558C2×C8—1461no—
559C2×C8—1461no—
560C2×C8—1461no—
561C2×C8—1461no—
562C2×C8—1461no—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—42no—
569C4⋊C4—2922no—
570C4⋊C4—2922no—
571C4⋊C4—5841no—
572C4⋊C4—734no—
573C4⋊C4—732no—
574C4⋊C4—732no—
575C4⋊C4—1464no—
576C4⋊C4—1464no—
577C4⋊C4—1464no—
578C4⋊C4—1461no—
579C4⋊C4—1461no—
580C4⋊C4—1461no—
581C4⋊C4—1461no—
582C4⋊C4—1461no—
583C4⋊C4—1461no—
584C4⋊C4C2×C4×D7312yes—
585C4⋊C4#1192402712yes—
586C22⋊C4—24no—
587C22⋊C4—2922no—
588C22⋊C4—2922no—
589C22⋊C4—734no—
590C22⋊C4—734no—
591C22⋊C4—1464no—
592C22⋊C4—1464no—
593C22⋊C4—1464no—
594C42—2922no—
595C42—732no—
596C42—732no—
597C42—1464no—
598C42—1464no—
599C42—1464no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—732no—
607C23—1461no—
608C23—1461no—
609C23—1461no—
610C23—1461no—
611C23—1461no—
612C23—1461no—
613C23C22⋊C4×D7312yes—
614C23C2×D4×D7311yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619Q8—2928no—
620D4—1468no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
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—732no—
655C2×C4—732no—
656C2×C4—1462no—
657C2×C4—1462no—
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×C4#41×D7311yescharacteristic
670C2×C4C2×#1192402711yescharacteristic
671C2×C4#1455663611yescharacteristic
672C2×C4#1455663811yescharacteristic
673C8—41no—
674C8—41no—
675C8—2921no—
676C8—1462no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—2921no—
685C22—2921no—
686C22—2921no—
687C22—2921no—
688C22—1462no—
689C22—1462no—
690C22—1462no—
691C22C2×C22⋊C4×D7311yescharacteristic
692C22#1798922411yescharacteristic
693C22#1798923511yescharacteristic
694C22AGL(1,ℤ/8)×D7311yescharacteristic
695C22#137×D7311yescharacteristic
696C22#1798939311yescharacteristic
697C22#1798940011yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—2922no—
704C4—2922no—
705C4—5841no—
706C4—5841no—
707C4—734no—
708C4—1462no—
709C4—1462no—
710C4C4×#1192402711yescharacteristic
711C4#1798906611yescharacteristic
712C4#1798922611yescharacteristic
713C4#1798923711yescharacteristic
714C2—42no—
715C2—2922no—
716C2#2261275711yescharacteristic
717C2#417×D7311yescharacteristic
718C2#2261845911yescharacteristic
719C2#2262215511yescharacteristic
720C2#2262220711yescharacteristic
721C2#2262250811yescharacteristic
722C2#2262253911yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1872C2
socleC23×C73C22×D4
prime radicalC22×C22⋊D73D4
cosocleC22×C4×C73C24
hypercenter#1872D73
hypocenterC73#22504
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
4. #22610890C2semidirect
5. #22610881C2semidirect
6. #22610365C2semidirect
7. #22610361C2semidirect
8. #22610235C2semidirect
9. #22610027C2semidirect
10. #22610025C2semidirect
11. #22609934C2semidirect
12. #103×Dic73C2semidirect
13. #22609650C2semidirect
14. #22609649C2semidirect
15. C73×#1872C2semidirect
19. #17989308C4semidirect
75. #14556590C2×C4semidirect
80. #14556567C2×C4semidirect
82. Q8×Dic73C2×C4semidirect
88. #14556550C2×C4semidirect
90. #14556549C2×C4semidirect
130. C22⋊Q8×C73C2×C4semidirect
370. #1872D73semidirect
377. C73#22504semidirect
449. C22⋊Q8C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179893082
C2×#179886622
C4⋊C4×C22⋊D732
#226108902
#226108812
#226103652
#226103612
#226102352
#226100272
#226100252
#226099342
#103×Dic732
#226096502
#226096492
C73×#18722
#2250473