Finite Group Databasebeta

← #33102355

Subgroups — #33102355

Order 18688.

1174 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×#17989292C211yesmaximal, characteristic
2C2×#17988661C211yesmaximal, characteristic
3#22612853C211yesmaximal, characteristic
4#22610902C211yesmaximal, characteristic, complemented
5#22610881C211yesmaximal, characteristic, complemented
6#22610362C211yesmaximal, characteristic, complemented
7#22610353C211yesmaximal, characteristic, complemented
8#22610241C211yesmaximal, characteristic, complemented
9#22610237C211yesmaximal, characteristic, complemented
10#22610020C211yesmaximal, characteristic, complemented
11#22609945C211yesmaximal, characteristic, complemented
12#22609760C211yesmaximal, characteristic, complemented
13#22609650C211yesmaximal, characteristic, complemented
14#340×D73C211yesmaximal, characteristic, complemented
15C73×#1823C211yesmaximal, characteristic, complemented
16C22×#11924012C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18#17989292—24no—
19#17989292C418yescomplemented
20C2×#14556590C2211yescharacteristic
21C2×#14556581—21no—
22C2×#14556571C2211yescharacteristic
23C2×#14556570—21no—
24C2×#14556570C2211yescharacteristic
25C2×#14556569—21no—
26C2×#14556556C2211yescharacteristic
27C2×C4×C22⋊D73—21no—
28C2×C4×C22⋊D73C2211yescharacteristic
29C2×#14556550C2211yescharacteristic
30C2×C4⋊C4×D73C2211yescharacteristic
31C2×C4⋊C4×D73C2211yescharacteristic
32#17988661—24no—
33C2×#14556520C2211yescharacteristic
34C2×#14556516C2211yescharacteristic
35C2×#14556516C2211yescharacteristic
36C2×#14556514C2211yescharacteristic
37C2×#14556514C2211yescharacteristic
38C2×#14556503C2211yescharacteristic
39C2×#14556501C2211yescharacteristic
40#17988475—21no—
41#17988469—21no—
42#17988463—21no—
43#17988452C2211yescharacteristic
44#17988444C2211yescharacteristic
45C4⋊C4×Dic73C2211yescharacteristic
46#17988434—21no—
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55C22×C4⋊C4×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62C22×Dic146—21no—
63C22×Dic146C2311yescharacteristic
64C22×C22⋊D73D411yescharacteristic
65C22×C4×D73—21no—
66C22×C4×D73—21no—
67C22×C4×D73C2311yescharacteristic
68C2×#11924012—22no—
69C2×#11924012—22no—
70C2×#11924012—41no—
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73C2×C8×D73—22no—
74C2×C8×D73—22no—
75C2×C8×D73—41no—
76#14556590—22no—
77#14556590C2×C414yescomplemented
78#14556581—28no—
79#14556571—22no—
80#14556571C2×C414yes—
81#14556570—28no—
82#14556570—22no—
83#14556570C2×C414yescomplemented
84#14556569—28no—
85#14556556—22no—
86#14556556C2×C414yescomplemented
87C4×C22⋊D73—28no—
88C4×C22⋊D73C2×C414yes—
89C4×C22⋊D73D414yes—
90#14556550—22no—
91#14556550—41no—
92C2×C4⋊Dic73—21no—
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—22no—
104C4⋊C4×D73—41no—
105C4⋊C4×D73C2×C414yes—
106C2×C22⋊Dic73—21no—
107C2×C22⋊Dic73—21no—
108C2×C22⋊Dic73D411yescharacteristic
109C2×#11924005—21no—
110C2×#11924005—21no—
111C2×#11924005D411yescharacteristic
112C2×C4×Dic73—21no—
113C2×C4×Dic73—21no—
114C2×C4×Dic73—21no—
115C2×C4×Dic73C2311yescharacteristic
116#14556520—22no—
117#14556516—22no—
118#14556516—41no—
119#14556514—22no—
120#14556514—41no—
121#14556503—22no—
122#14556501—22no—
123#14556498—21no—
124#14556498—21no—
125#14556498—21no—
126#14556498—21no—
127C23×C4×C73—21no—
128C23×C4×C73C2311yescharacteristic
129C22×C8×C73C2311yescharacteristic
130C22×C8×C73C2311yescharacteristic
131C2×C4⋊C4×C73—22no—
132C2×C4⋊C4×C73—21no—
133C2×C4⋊C4×C73C2×C414yescomplemented
134C2×C4⋊C4×C73C2311yescharacteristic
135C2×C4⋊C4×C73C2311yescharacteristic
136C2×C4⋊C4×C73C2311yescharacteristic
137C2×C4⋊C4×C73C2311yescharacteristic
138C2×C22⋊C4×C73—21no—
139C22⋊C8×C73—22no—
140#95×C73—21no—
141C23×D73C2×D411yescharacteristic
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×C22⋊D73—22no—
152C2×C22⋊D73—22no—
153C2×C22⋊D73C22⋊C414yes—
154C22×Dic73—21no—
155C22×Dic73—21no—
156C22×Dic73—21no—
157C22×Dic73—21no—
158C22×Dic73C2×D411yescharacteristic
159C22×Dic73C2×D411yescharacteristic
160C22×Dic73C2×D411yescharacteristic
161C2×C4×D73—21no—
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—24no—
166C2×C4×D73—42no—
167C2×C4×D73—42no—
168C2×C4×D73—81no—
169C2×C4×D73—81no—
170C2×C4×D73—81no—
171C2×C4×D73C22×C412yes—
172C2×C4×D73C2×D412yes—
173#11924012—44no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831#4112yes—
180C8×D73—44no—
181C4⋊Dic73—21no—
182C4⋊Dic73—21no—
183C4⋊Dic73—24no—
184C4⋊Dic73—21no—
185C4⋊Dic73—21no—
186C4⋊Dic73C22×C412yes—
187C4⋊Dic73#4112yes—
188#11924007—24no—
189#11924007—24no—
190#11924007—24no—
191#11924007—24no—
192#11924007—42no—
193#11924007C22⋊C414yes—
194C22⋊Dic73—24no—
195C22⋊Dic73—42no—
196C22⋊Dic73C22⋊C414yes—
197#11924005—24no—
198#11924005—42no—
199#11924005C22⋊C414yes—
200C4×Dic73—24no—
201C4×Dic73—42no—
202C4×Dic73—81no—
203C4×Dic73C22×C412yes—
204C4×Dic73C2×D412yes—
205C24×C73C2×D411yescharacteristic
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—24no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—81no—
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—21no—
227C4⋊C4×C73—24no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73C22×C412yes—
235C4⋊C4×C73C22×C412yes—
236C22⋊C4×C73—81no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73C2×C22⋊C412yes—
244C23×C73C22×D411yescharacteristic
245C22×D73—21no—
246C22×D73—21no—
247C22×D73—21no—
248C22×D73—21no—
249C22×D73C2×C22⋊C412yes—
250C22×D73#13712yes—
251C22×D73#13712yes—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—22no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—41no—
261C2×C4×C73—41no—
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—41no—
269C2×C4×C73—41no—
270C2×C4×C73—84no—
271C2×C4×C73C2×C22⋊C412yes—
272C2×C4×C73C23×C411yescharacteristic
273C2×C4×C73C22×D411yescharacteristic
274C2×C4×C73C2×#4111yescharacteristic
275C2×C4×C73C2×#4111yescharacteristic
276C2×C4×C73H(5,𝔽2)11yescharacteristic
277C2×C4×C732−1+411yescharacteristic
278C22⋊D73—28no—
279C2×Dic73—21no—
280C2×Dic73—21no—
281C2×Dic73—21no—
282C2×Dic73—21no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—22no—
286C2×Dic73—22no—
287C2×Dic73—22no—
288C2×Dic73—41no—
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×Dic73C2×C22⋊C412yes—
298C2×Dic73C2×C22⋊C412yes—
299C2×Dic73C2×C22⋊C412yes—
300C4×D73—22no—
301C4×D73—22no—
302C4×D73—22no—
303C4×D73—22no—
304C4×D73—84no—
305C4×D73—84no—
306Dic146—22no—
307Dic146—22no—
308Dic146—41no—
309Dic146—41no—
310Dic146—84no—
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×#13711yescharacteristic
326C22×C73C2×#13711yescharacteristic
327C22×C73#57611yescharacteristic
328C22×C73#57711yescharacteristic
329C2×D73—22no—
330C2×D73—22no—
331C2×D73—22no—
332C2×D73—22no—
333C2×D73—22no—
334C2×D73—22no—
335C2×D73#41914yes—
336C4×C73—22no—
337C4×C73—42no—
338C4×C73—42no—
339C4×C73—81no—
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—42no—
351Dic73—81no—
352#22497—731nomaximal, Sylow
353C2×C73—42no—
354C2×C73#233911yescharacteristic
355C2×C73C2×#41911yescharacteristic
356C2×C73#289711yescharacteristic
357C2×C73#331411yescharacteristic
358C2×C73#331611yescharacteristic
359C2×C73#334411yescharacteristic
360C2×C73#334611yescharacteristic
361D73—24no—
362C2×#554—731no—
363C2×#435—731no—
364#2352—731no—
365#1993—731no—
366#1988—731no—
367#1894—731no—
368#1892—731no—
369#1873—731no—
370#1872—731no—
371#1824—731no—
372#1823D7311yescharacteristic, complemented
373#1805—731no—
374#1763—731no—
375#1736—731no—
376C2×#340—731no—
377C73#2249711yescharacteristic, complemented, Sylow
378C22×M16—731no—
379C23×C8—731no—
380#554—738no—
381#554—1464no—
382C2×C4⋊Q8—731no—
383C2×#125—1461no—
384C2×C22⋊Q8—731no—
385C2×C22⋊Q8—731no—
386C2×C22⋊Q8—1461no—
387C2×C22⋊Q8—1461no—
388C2×C4×Q8—731no—
389C2×C4×D4—731no—
390C2×C4×D4—1461no—
391C2×#117—731no—
392C22×C4⋊C4—731no—
393C22×C4⋊C4—731no—
394C22×C4⋊C4C2×D7311yescharacteristic
395#435—1464no—
396C2×C4⋊C8—731no—
397C2×#103—731no—
398C2×#103—731no—
399C2×#103—731no—
400C2×#103—731no—
401C2×C22⋊C8—731no—
402C2×C22⋊C8C2×D7311yescharacteristic
403C2×#97—731no—
404#388—1461no—
405#387—1461no—
406#386—1461no—
407#382—731no—
408#380—731no—
409#380C2×D7311yescharacteristic
410C4×C4⋊C4—731no—
411C4×C22⋊C4—1461no—
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×Q8—1461no—
426C22×D4—731no—
427C23×C4—21no—
428C23×C4—731no—
429C23×C4—1461no—
430C23×C4—1461no—
431C23×C4C22×D7311yescharacteristic
432C2×M16—2921no—
433C2×M16—1462no—
434C2×M16—1462no—
435C22×C8—2921no—
436C22×C8—731no—
437C22×C8—731no—
438C22×C8—1462no—
439C22×C8—1462no—
440C22×C8C22×D7311yescharacteristic
441C22×C8C22×D7311yescharacteristic
442C4⋊Q8—734no—
443C4⋊Q8—1462no—
444#125—1468no—
445C22⋊Q8—734no—
446C22⋊Q8—734no—
447C22⋊Q8—1468no—
448C22⋊Q8—1468no—
449C22⋊Q8—1462no—
450C22⋊Q8—1462no—
451C4×Q8—734no—
452C4×Q8—1462no—
453C4×D4—734no—
454C4×D4—734no—
455C4×D4—1468no—
456#117—2921no—
457#117—1462no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—2921no—
461C2×C4⋊C4—731no—
462C2×C4⋊C4—731no—
463C2×C4⋊C4—731no—
464C2×C4⋊C4—734no—
465C2×C4⋊C4—731no—
466C2×C4⋊C4—1462no—
467C2×C4⋊C4—1462no—
468C2×C4⋊C4—1461no—
469C2×C4⋊C4—1461no—
470C2×C4⋊C4—1461no—
471C2×C4⋊C4—1461no—
472C2×C4⋊C4—1461no—
473C2×C4⋊C4—1461no—
474C2×C4⋊C4C4×D7314yescomplemented
475C2×C4⋊C4C22×D7311yescharacteristic
476C2×C4⋊C4C22×D7311yescharacteristic
477C2×C4⋊C4C22×D7311yescharacteristic
478C2×C4⋊C4C22×D7311yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—731no—
481C2×C22⋊C4—731no—
482C2×C22⋊C4—1461no—
483C2×C22⋊C4—1461no—
484C2×C22⋊C4—1461no—
485C2×C22⋊C4—1461no—
486C2×C42—731no—
487C2×C42—1461no—
488C2×C42—1461no—
489C2×C42—1461no—
490C4⋊C8—1462no—
491#103—2921no—
492#103—2921no—
493#103—1462no—
494#103—1462no—
495C22⋊C8—22no—
496C22⋊C8—1462no—
497#97—1462no—
498#95—21no—
499#95—1461no—
500#95—1461no—
501#95—1461no—
502#95—1461no—
503C24—731no—
504C24D4×D7311yescharacteristic
505C2×Q8—5841no—
506C2×Q8—5841no—
507C2×Q8—732no—
508C2×Q8—1464no—
509C2×Q8—1461no—
510C2×Q8—1461no—
511C2×Q8—1461no—
512C2×Q8—1461no—
513C2×Q8—1461no—
514C2×D4—734no—
515C2×D4—1462no—
516C2×D4—1462no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4—2922no—
529C22×C4—2922no—
530C22×C4—5841no—
531C22×C4—5841no—
532C22×C4—5841no—
533C22×C4—731no—
534C22×C4—731no—
535C22×C4—731no—
536C22×C4—732no—
537C22×C4—732no—
538C22×C4—1464no—
539C22×C4—1461no—
540C22×C4—1461no—
541C22×C4—1461no—
542C22×C4—1461no—
543C22×C4—1461no—
544C22×C4—1461no—
545C22×C4—1461no—
546C22×C4—1461no—
547C22×C4C2×C4×D7312yes—
548C22×C4D4×D7311yescharacteristic
549C22×C4D4×D7312yes—
550C22×C4C23×D7311yescharacteristic
551M16—2924no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—2924no—
559C2×C8—732no—
560C2×C8—1461no—
561C2×C8—1461no—
562C2×C8—1461no—
563C2×C8—1461no—
564C2×C8—1461no—
565C4⋊C4—24no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—2922no—
573C4⋊C4—734no—
574C4⋊C4—732no—
575C4⋊C4—732no—
576C4⋊C4—1464no—
577C4⋊C4—1464no—
578C4⋊C4—1464no—
579C4⋊C4—1464no—
580C4⋊C4—1461no—
581C4⋊C4—1461no—
582C4⋊C4—1464no—
583C4⋊C4—1461no—
584C4⋊C4—1461no—
585C4⋊C4C2×C4×D7312yes—
586C4⋊C4C2×C4×D7312yes—
587C22⋊C4—81no—
588C22⋊C4—2922no—
589C22⋊C4—2922no—
590C22⋊C4—734no—
591C22⋊C4—734no—
592C22⋊C4—1464no—
593C22⋊C4—1464no—
594C42—2922no—
595C42—5841no—
596C42—732no—
597C42—732no—
598C42—1464no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—732no—
606C23—732no—
607C23—732no—
608C23—1461no—
609C23—1461no—
610C23—1461no—
611C23—1461no—
612C23C22⋊C4×D7312yes—
613C23C2×D4×D7311yescharacteristic
614Q8—2921no—
615Q8—2921no—
616Q8—5844no—
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—41no—
629C2×C4—41no—
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—84no—
639C2×C4—2921no—
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—5844no—
649C2×C4—5844no—
650C2×C4—732no—
651C2×C4—732no—
652C2×C4—732no—
653C2×C4—1462no—
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×C4#41×D7311yescharacteristic
670C2×C4#41×D7311yescharacteristic
671C2×C4#1455663711yescharacteristic
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—734no—
685C22—1462no—
686C22—1462no—
687C22—1462no—
688C22—1462no—
689C22—1462no—
690C22—1462no—
691C22C2×C22⋊C4×D7311yescharacteristic
692C22#1798922911yescharacteristic
693C22#1798923511yescharacteristic
694C22#137×D7311yescharacteristic
695C22#137×D7311yescharacteristic
696C22#1798938811yescharacteristic
697C22#1798939311yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—2922no—
704C4—2922no—
705C4—2922no—
706C4—5841no—
707C4—1462no—
708C4—1462no—
709C4—1462no—
710C4#1798905511yescharacteristic
711C4#1798906711yescharacteristic
712C4#1798922911yescharacteristic
713C4#1798923511yescharacteristic
714C2—42no—
715C2—1464no—
716C2#2261275511yescharacteristic
717C2#419×D7311yescharacteristic
718C2#2261845211yescharacteristic
719C2#2262201511yescharacteristic
720C2#2262204511yescharacteristic
721C2#2262238911yescharacteristic
722C2#2262241911yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1823C2
socleC23×C73C22×D4
prime radicalC22×C22⋊D73D4
cosocleC22×C4×C73C24
hypercenter#1823D73
hypocenterC73#22497
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #22610902C2semidirect
5. #22610881C2semidirect
6. #22610362C2semidirect
7. #22610353C2semidirect
8. #22610241C2semidirect
9. #22610237C2semidirect
10. #22610020C2semidirect
11. #22609945C2semidirect
12. #22609760C2semidirect
13. #22609650C2semidirect
14. #340×D73C2semidirect
15. C73×#1823C2semidirect
19. #17989292C4semidirect
77. #14556590C2×C4semidirect
83. #14556570C2×C4semidirect
86. #14556556C2×C4semidirect
133. C2×C4⋊C4×C73C2×C4semidirect
372. #1823D73semidirect
377. C73#22497semidirect
474. 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×#179892922
C2×#179886612
#226128532
#226109022
#226108812
#226103622
#226103532
#226102412
#226102372
#226100202
#226099452
#226097602
#226096502
#340×D732
C73×#18232
#2249773