Finite Group Databasebeta

← #33102431

Subgroups — #33102431

Order 18688.

1154 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989295C211yesmaximal, characteristic
2C2×#17988662C211yesmaximal, characteristic
3#22612881C211yesmaximal, characteristic
4#22610890C211yesmaximal, characteristic, complemented
5#22610877C211yesmaximal, characteristic, complemented
6#22610365C211yesmaximal, characteristic, complemented
7#22610361C211yesmaximal, characteristic, complemented
8#22610240C211yesmaximal, characteristic, complemented
9#22610018C211yesmaximal, characteristic, complemented
10#22610016C211yesmaximal, characteristic, complemented
11#22609934C211yesmaximal, characteristic, complemented
12#103×Dic73C211yesmaximal, characteristic, complemented
13#22609652C211yesmaximal, characteristic, complemented
14#22609649C211yesmaximal, characteristic, complemented
15C73×#1873C211yesmaximal, characteristic, complemented
16C22×#11924012C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18#17989295—24no—
19#17989295C418yescomplemented
20C2×#14556590C2211yescharacteristic
21C2×#14556581—21no—
22C2×#14556571—21no—
23C2×#14556568—21no—
24C2×#14556567C2211yescharacteristic
25C2×Q8×Dic73C2211yescharacteristic
26C2×C4×C22⋊D73C2211yescharacteristic
27C2×#14556551—21no—
28C2×#14556549C2211yescharacteristic
29C22×C4⋊Dic73C2211yescharacteristic
30C2×C4⋊C4×D73C2211yescharacteristic
31#17988662—24no—
32C2×#14556520C2211yescharacteristic
33C2×#14556515C2211yescharacteristic
34C2×#14556515C2211yescharacteristic
35C2×#14556503C2211yescharacteristic
36C2×C8×Dic73C2211yescharacteristic
37#17988487—21no—
38#17988478—21no—
39#17988475—21no—
40#17988456C2211yescharacteristic
41#17988447C2211yescharacteristic
42#17988444C2211yescharacteristic
43C4⋊C4×Dic73C2211yescharacteristic
44C4×#11924007—21no—
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55C2×C22⋊Q8×C73C2211yescharacteristic
56C2×#117×C73C2211yescharacteristic
57C2×#103×C73C2211yescharacteristic
58C2×#103×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62C22×Dic146—21no—
63C22×C22⋊D73D411yescharacteristic
64C23×Dic73—21no—
65C22×C4×D73—21no—
66C22×C4×D73C2311yescharacteristic
67C2×#11924012—22no—
68C2×#11924012—22no—
69C2×#11924012—41no—
70C2×#11924011—22no—
71C2×#11924011—22no—
72C2×#11924011—41no—
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75#14556590—22no—
76#14556590C2×C414yes—
77#14556581—28no—
78#14556571—28no—
79#14556568—28no—
80#14556567—22no—
81#14556567C2×C414yes—
82Q8×Dic73—22no—
83Q8×Dic73C2×C414yes—
84C4×C22⋊D73C2×C414yes—
85C4×C22⋊D73D414yes—
86#14556551—28no—
87#14556549—22no—
88#14556549—41no—
89C2×C4⋊Dic73—21no—
90C2×C4⋊Dic73—22no—
91C2×C4⋊Dic73—21no—
92C2×C4⋊Dic73C2×C414yes—
93C2×C4⋊Dic73C2311yescharacteristic
94C2×C4⋊Dic73C2311yescharacteristic
95C2×C4⋊Dic73C2311yescharacteristic
96C2×C4⋊Dic73C2311yescharacteristic
97C2×#11924007—21no—
98C2×#11924007—21no—
99C2×#11924007—21no—
100C2×#11924007—21no—
101C2×#11924007—21no—
102C2×#11924007D411yescharacteristic
103C4⋊C4×D73—22no—
104C4⋊C4×D73C2×C414yes—
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×Dic73C2311yescharacteristic
115#14556520—22no—
116#14556515—22no—
117#14556515—41no—
118#14556503—22no—
119C8×Dic73—22no—
120#14556498—21no—
121#14556498—21no—
122#14556498—21no—
123C22×Q8×C73C2311yescharacteristic
124C23×C4×C73C2311yescharacteristic
125C22×C8×C73C2311yescharacteristic
126C22×C8×C73C2311yescharacteristic
127C22⋊Q8×C73—22no—
128C22⋊Q8×C73C2×C414yes—
129#117×C73—22no—
130#117×C73—41no—
131C2×C4⋊C4×C73—21no—
132C2×C4⋊C4×C73C2311yescharacteristic
133C2×C4⋊C4×C73C2311yescharacteristic
134C2×C4⋊C4×C73C2311yescharacteristic
135C2×C22⋊C4×C73—21no—
136C2×C22⋊C4×C73—21no—
137C2×C42×C73—21no—
138#103×C73—22no—
139#103×C73—41no—
140C22⋊C8×C73—22no—
141C23×D73C2×D411yescharacteristic
142C2×Dic146—24no—
143C2×Dic146—81no—
144C2×Dic146—81no—
145C2×C22⋊D73—22no—
146C2×C22⋊D73—22no—
147C2×C22⋊D73C22⋊C414yes—
148C22×Dic73—21no—
149C22×Dic73—21no—
150C22×Dic73—24no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73—81no—
154C22×Dic73—81no—
155C22×Dic73C2×D411yescharacteristic
156C22×Dic73C2×D411yescharacteristic
157C22×Dic73C2×D411yescharacteristic
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—21no—
161C2×C4×D73—21no—
162C2×C4×D73—24no—
163C2×C4×D73—81no—
164C2×C4×D73—81no—
165C2×C4×D73C22×C412yes—
166C2×C4×D73C2×D412yes—
167#11924012—44no—
168#11924011—44no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831#4112yes—
175C4⋊Dic73—24no—
176C4⋊Dic73—21no—
177C4⋊Dic73—21no—
178C4⋊Dic73—24no—
179C4⋊Dic73—21no—
180C4⋊Dic73—21no—
181C4⋊Dic73—21no—
182C4⋊Dic73—21no—
183C4⋊Dic73C22×C412yes—
184C4⋊Dic73C22×C412yes—
185#11924007—24no—
186#11924007—24no—
187#11924007—24no—
188#11924007—42no—
189#11924007—81no—
190#11924007C22⋊C414yes—
191C22⋊Dic73—81no—
192C22⋊Dic73C22⋊C414yes—
193#11924005—24no—
194#11924005—42no—
195#11924005—81no—
196#11924005C22⋊C414yes—
197C4×Dic73—24no—
198C4×Dic73—42no—
199C4×Dic73—42no—
200C4×Dic73C22×C412yes—
201C4×Dic73C2×D412yes—
202C24×C73C2×D411yescharacteristic
203C2×Q8×C73—21no—
204C2×Q8×C73—21no—
205C2×Q8×C73—21no—
206C2×Q8×C73—21no—
207C2×Q8×C73—21no—
208C2×Q8×C73C22×C412yes—
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—21no—
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×C73C22×C412yes—
233C4⋊C4×C73#4112yes—
234C22⋊C4×C73—24no—
235C22⋊C4×C73—42no—
236C42×C73—42no—
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×D73—21no—
250C22×D73—21no—
251C22×D73C2×C22⋊C412yes—
252Q8×C73—22no—
253Q8×C73—22no—
254Q8×C73—41no—
255Q8×C73—41no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—22no—
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—41no—
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×C73C2×C22⋊C412yes—
275C2×C4×C73C23×C411yescharacteristic
276C2×C4×C73C22×D411yescharacteristic
277C2×C4×C73C2×#4111yescharacteristic
278C2×C4×C73C2×#4111yescharacteristic
279C2×C4×C73H(5,𝔽2)11yescharacteristic
280C2×C4×C732−1+411yescharacteristic
281C22⋊D73—28no—
282C2×Dic73—21no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—21no—
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×Dic73—41no—
298C2×Dic73—84no—
299C2×Dic73C2×C22⋊C412yes—
300C2×Dic73C2×C22⋊C412yes—
301C2×Dic73C2×C22⋊C412yes—
302C2×Dic73#13712yes—
303C2×Dic73#13712yes—
304C4×D73—22no—
305C4×D73—22no—
306C4×D73—22no—
307C4×D73—22no—
308C4×D73—84no—
309Dic146—84no—
310C8×C73—41no—
311C8×C73—41no—
312#10596831—22no—
313#10596831—41no—
314C22×C73—22no—
315C22×C73—22no—
316C22×C73—22no—
317C22×C73—41no—
318C22×C73—41no—
319C22×C73—41no—
320C22×C73—41no—
321C22×C73C22×C22⋊C411yescharacteristic
322C22×C73#54611yescharacteristic
323C22×C73#54711yescharacteristic
324C22×C73C2×#13711yescharacteristic
325C22×C73C2×#13711yescharacteristic
326C22×C73#57611yescharacteristic
327C22×C73#57711yescharacteristic
328C2×D73—22no—
329C2×D73—22no—
330C2×D73—22no—
331C2×D73—41no—
332C2×D73—41no—
333C2×D73—41no—
334C2×D73—41no—
335C4×C73—22no—
336C4×C73—42no—
337C4×C73—42no—
338C4×C73—42no—
339C4×C73—81no—
340C4×C73C4×#4111yescharacteristic
341C4×C73#52011yescharacteristic
342C4×C73#54611yescharacteristic
343C4×C73#54711yescharacteristic
344Dic73—22no—
345Dic73—22no—
346Dic73—42no—
347Dic73—42no—
348Dic73—81no—
349Dic73—81no—
350Dic73#41914yes—
351#22502—731nomaximal, Sylow
352C2×C73—42no—
353C2×C73#233911yescharacteristic
354C2×C73C2×#41911yescharacteristic
355C2×C73#289711yescharacteristic
356C2×C73#333111yescharacteristic
357C2×C73#333311yescharacteristic
358C2×C73#335611yescharacteristic
359C2×C73#335711yescharacteristic
360D73—42no—
361C2×#554—731no—
362C2×#436—731no—
363#2354—731no—
364#1990—731no—
365#1987—731no—
366#1894—731no—
367#1894—731no—
368#1873—731no—
369#1873D7311yescharacteristic, complemented
370#1823—731no—
371#1823—731no—
372#1803—731no—
373C4×#103—731no—
374#1736—731no—
375#1736—731no—
376C73#2250211yescharacteristic, complemented, Sylow
377C22×M16—731no—
378C22×M16—731no—
379#554—738no—
380#554—1464no—
381C2×C4⋊Q8—731no—
382C2×#125—1461no—
383C2×C22⋊Q8—731no—
384C2×C22⋊Q8—1461no—
385C2×C22⋊Q8—1461no—
386C2×C22⋊Q8C2×D7311yescharacteristic
387C2×C4×Q8—731no—
388C2×C4×D4—731no—
389C2×C4×D4—1461no—
390C2×#117—731no—
391C2×#117C2×D7311yescharacteristic
392C22×C4⋊C4—731no—
393C22×C4⋊C4—731no—
394#436—1464no—
395C2×C4⋊C8—731no—
396C2×#103—731no—
397C2×#103—731no—
398C2×#103C2×D7311yescharacteristic
399C2×#103C2×D7311yescharacteristic
400C2×C22⋊C8—731no—
401C2×C22⋊C8C2×D7311yescharacteristic
402C2×C4×C8—731no—
403#390—1461no—
404#388—1461no—
405#388—1461no—
406#384—731no—
407#380—731no—
408#380—731no—
409C4×C4⋊C4—731no—
410C4×C4⋊C4—1461no—
411#340—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#340C2×D7311yescharacteristic
422#340C2×D7311yescharacteristic
423C22×Q8—1461no—
424C22×Q8C22×D7311yescharacteristic
425C22×D4—731no—
426C23×C4—731no—
427C23×C4—1461no—
428C23×C4—1461no—
429C23×C4C22×D7311yescharacteristic
430C2×M16—2921no—
431C2×M16—2921no—
432C2×M16—1462no—
433C2×M16—1462no—
434C2×M16—1462no—
435C2×M16—1462no—
436C22×C8—731no—
437C22×C8—731no—
438C22×C8C22×D7311yescharacteristic
439C22×C8C22×D7311yescharacteristic
440C4⋊Q8—734no—
441C4⋊Q8—1462no—
442#125—1468no—
443C22⋊Q8—22no—
444C22⋊Q8—734no—
445C22⋊Q8—1468no—
446C22⋊Q8—1468no—
447C22⋊Q8—1462no—
448C22⋊Q8C4×D7314yes—
449C4×Q8—734no—
450C4×Q8—1462no—
451C4×D4—734no—
452C4×D4—734no—
453C4×D4—1468no—
454#117—22no—
455#117—41no—
456#117—2921no—
457#117—1462no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—731no—
460C2×C4⋊C4—734no—
461C2×C4⋊C4—731no—
462C2×C4⋊C4—731no—
463C2×C4⋊C4—734no—
464C2×C4⋊C4—731no—
465C2×C4⋊C4—731no—
466C2×C4⋊C4—1462no—
467C2×C4⋊C4—1461no—
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⋊C4—1462no—
475C2×C4⋊C4C22×D7311yescharacteristic
476C2×C4⋊C4C22×D7311yescharacteristic
477C2×C4⋊C4C22×D7311yescharacteristic
478C2×C22⋊C4—21no—
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—21no—
487C2×C42—731no—
488C2×C42—1461no—
489C2×C42—1461no—
490C2×C42—1461no—
491C4⋊C8—1462no—
492#103—22no—
493#103—41no—
494#103—2921no—
495#103—1462no—
496C22⋊C8—22no—
497C22⋊C8—1462no—
498C4×C8—1462no—
499#95—1461no—
500#95—1461no—
501#95—1461no—
502C24—731no—
503C24D4×D7311yescharacteristic
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—5841no—
510C2×Q8—5841no—
511C2×Q8—1464no—
512C2×Q8C2×C4×D7312yes—
513C2×D4—734no—
514C2×D4—1462no—
515C2×D4—1462no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—5841no—
525C22×C4—5841no—
526C22×C4—5841no—
527C22×C4—5841no—
528C22×C4—731no—
529C22×C4—731no—
530C22×C4—731no—
531C22×C4—732no—
532C22×C4—732no—
533C22×C4—1464no—
534C22×C4—1461no—
535C22×C4—1461no—
536C22×C4—1461no—
537C22×C4—1461no—
538C22×C4—1464no—
539C22×C4—1461no—
540C22×C4—1461no—
541C22×C4—1461no—
542C22×C4—1461no—
543C22×C4C2×C4×D7312yes—
544C22×C4D4×D7311yescharacteristic
545C22×C4D4×D7312yes—
546C22×C4C23×D7311yescharacteristic
547M16—2924no—
548M16—2924no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—732no—
556C2×C8—1461no—
557C2×C8—1461no—
558C2×C8—1461no—
559C2×C8—1461no—
560C2×C8—1461no—
561C4⋊C4—24no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—2922no—
567C4⋊C4—5841no—
568C4⋊C4—734no—
569C4⋊C4—732no—
570C4⋊C4—732no—
571C4⋊C4—1464no—
572C4⋊C4—1464no—
573C4⋊C4—1464no—
574C4⋊C4—1464no—
575C4⋊C4—1461no—
576C4⋊C4—1461no—
577C4⋊C4—1461no—
578C4⋊C4—1461no—
579C4⋊C4—1464no—
580C4⋊C4—1461no—
581C4⋊C4—1461no—
582C4⋊C4C2×C4×D7312yes—
583C4⋊C4#1192402712yes—
584C22⋊C4—24no—
585C22⋊C4—42no—
586C22⋊C4—2922no—
587C22⋊C4—5841no—
588C22⋊C4—5841no—
589C22⋊C4—734no—
590C22⋊C4—734no—
591C22⋊C4—1464no—
592C42—42no—
593C42—2922no—
594C42—2922no—
595C42—732no—
596C42—732no—
597C42—1464no—
598C23—21no—
599C23—21no—
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—
612C23C2×D4×D7311yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—41no—
616Q8—41no—
617Q8—5844no—
618D4—1468no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
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—2921no—
638C2×C4—2921no—
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—5844no—
648C2×C4—5844no—
649C2×C4—732no—
650C2×C4—732no—
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—1462no—
661C2×C4—1462no—
662C2×C4—1462no—
663C2×C4—1462no—
664C2×C4C22⋊C4×D7312yes—
665C2×C4C22×C4×D7311yescharacteristic
666C2×C4C2×D4×D7311yescharacteristic
667C2×C4#41×D7311yescharacteristic
668C2×C4C2×#1192402711yescharacteristic
669C2×C4#1455663611yescharacteristic
670C2×C4#1455663811yescharacteristic
671C8—41no—
672C8—41no—
673C8—2921no—
674C8—1462no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—2921no—
683C22—2921no—
684C22—2921no—
685C22—2921no—
686C22—1462no—
687C22—1462no—
688C22—1462no—
689C22C2×C22⋊C4×D7311yescharacteristic
690C22#1798922411yescharacteristic
691C22#1798923511yescharacteristic
692C22#137×D7311yescharacteristic
693C22#137×D7311yescharacteristic
694C22#1798938911yescharacteristic
695C22#1798939411yescharacteristic
696C4—22no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—81no—
701C4—2922no—
702C4—2922no—
703C4—5841no—
704C4—5841no—
705C4—734no—
706C4—1462no—
707C4—1462no—
708C4C4×#1192402711yescharacteristic
709C4#1798906611yescharacteristic
710C4#1798922611yescharacteristic
711C4#1798923711yescharacteristic
712C2—42no—
713C2—2922no—
714C2#2261275711yescharacteristic
715C2#419×D7311yescharacteristic
716C2#2261845311yescharacteristic
717C2#2262224011yescharacteristic
718C2#2262226211yescharacteristic
719C2#2262254411yescharacteristic
720C2#2262255511yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1873C2
socleC23×C73C22×D4
prime radicalC22×C22⋊D73D4
cosocleC22×C4×C73C24
hypercenter#1873D73
hypocenterC73#22502
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
4. #22610890C2semidirect
5. #22610877C2semidirect
6. #22610365C2semidirect
7. #22610361C2semidirect
8. #22610240C2semidirect
9. #22610018C2semidirect
10. #22610016C2semidirect
11. #22609934C2semidirect
12. #103×Dic73C2semidirect
13. #22609652C2semidirect
14. #22609649C2semidirect
15. C73×#1873C2semidirect
19. #17989295C4semidirect
369. #1873D73semidirect
376. C73#22502semidirect

Maximal subgroups

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

subgroupindex
C2×#179892952
C2×#179886622
#226128812
#226108902
#226108772
#226103652
#226103612
#226102402
#226100182
#226100162
#226099342
#103×Dic732
#226096522
#226096492
C73×#18732
#2250273