Finite Group Databasebeta

← #33013620

Subgroups — #33013620

Order 18688.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988477C211yesmaximal, characteristic
2C2×#17988458C211yesmaximal, characteristic
3C2×#17988449C211yesmaximal, characteristic
4C2×#17988444C211yesmaximal, characteristic
5#22608197C211yesmaximal, characteristic, complemented
6#22608190C211yesmaximal, characteristic, complemented
7#22608184C211yesmaximal, characteristic, complemented
8#22608181C211yesmaximal, characteristic, complemented
9#22608179C211yesmaximal, characteristic
10#22608173C211yesmaximal, characteristic
11#22608169C211yesmaximal, characteristic
12#22608165C211yesmaximal, characteristic, complemented
13#22608163C211yesmaximal, characteristic, complemented
14#22608158C211yesmaximal, characteristic, complemented
15C2×#389×C73C211yesmaximal, characteristic, complemented
16C23×C4×D73C2211yescharacteristic
17C22×C4⋊Dic73C2211yescharacteristic
18C22×#11924007C2211yescharacteristic
19C22×#11924005C2211yescharacteristic
20C22×#11924005C2211yescharacteristic
21C22×#11924005C2211yescharacteristic
22C22×#11924005C2211yescharacteristic
23C22×#11924005C2211yescharacteristic
24C22×#11924005C2211yescharacteristic
25C22×C4×Dic73C2211yescharacteristic
26#17988477—24no—
27#17988458C418yescomplemented
28#17988449—24no—
29#17988444—24no—
30C2×#14556498C2211yescharacteristic
31C2×#14556498C2211yescharacteristic
32C2×#14556498C2211yescharacteristic
33C2×#14556498C2211yescharacteristic
34C2×#14556498C2211yescharacteristic
35C2×#14556498C2211yescharacteristic
36C2×#14556498C2211yescharacteristic
37C2×#14556498C2211yescharacteristic
38C2×#14556498C2211yescharacteristic
39C2×#14556498C2211yescharacteristic
40C2×#14556498C2211yescharacteristic
41C2×#14556498C2211yescharacteristic
42C2×#14556498C2211yescharacteristic
43C2×#14556498C2211yescharacteristic
44C2×#14556498C2211yescharacteristic
45C2×#14556498C2211yescharacteristic
46C2×#14556498C2211yescharacteristic
47C2×#14556498C2211yescharacteristic
48C22×C4⋊C4×C73C2211yescharacteristic
49C22×C4⋊C4×C73C2211yescharacteristic
50C22×C4⋊C4×C73C2211yescharacteristic
51C22×C4⋊C4×C73C2211yescharacteristic
52C22×C42×C73C2211yescharacteristic
53#389×C73—24no—
54C2×#95×C73C2211yescharacteristic
55C2×#95×C73C2211yescharacteristic
56C24×D73C2311yescharacteristic
57C23×Dic73C2311yescharacteristic
58C23×Dic73C2311yescharacteristic
59C23×Dic73C2311yescharacteristic
60C23×Dic73C2311yescharacteristic
61C23×Dic73C2311yescharacteristic
62C23×Dic73C2311yescharacteristic
63C23×Dic73C2311yescharacteristic
64C22×C4×D73—22no—
65C22×C4×D73—22no—
66C22×C4×D73—22no—
67C22×C4×D73—22no—
68C22×C4×D73—41no—
69C22×C4×D73—41no—
70C22×C4×D73C2×C414yes—
71C2×C4⋊Dic73—22no—
72C2×C4⋊Dic73—22no—
73C2×C4⋊Dic73—41no—
74C2×#11924007—41no—
75C2×#11924007—41no—
76C2×#11924007C2×C414yes—
77C2×#11924005—22no—
78C2×#11924005—22no—
79C2×#11924005—22no—
80C2×#11924005—22no—
81C2×#11924005—22no—
82C2×#11924005—22no—
83C2×#11924005—22no—
84C2×#11924005—22no—
85C2×#11924005—22no—
86C2×#11924005—41no—
87C2×#11924005—41no—
88C2×#11924005—41no—
89C2×#11924005—41no—
90C2×#11924005—41no—
91C2×#11924005—41no—
92C2×#11924005C2×C414yes—
93C2×#11924005C2×C414yes—
94C2×#11924005D414yes—
95C2×C4×Dic73—22no—
96C2×C4×Dic73—41no—
97C2×C4×Dic73—41no—
98#14556498—22no—
99#14556498—22no—
100#14556498—22no—
101#14556498—22no—
102#14556498—22no—
103#14556498—22no—
104#14556498—22no—
105#14556498—22no—
106#14556498—22no—
107#14556498—41no—
108#14556498—41no—
109#14556498—41no—
110#14556498—41no—
111#14556498—41no—
112#14556498—41no—
113#14556498—41no—
114#14556498C2×C414yes—
115#14556498C2×C414yes—
116C23×C4×C73C2311yescharacteristic
117C23×C4×C73C2311yescharacteristic
118C23×C4×C73C2311yescharacteristic
119C23×C4×C73C2311yescharacteristic
120C23×C4×C73C2311yescharacteristic
121C23×C4×C73C2311yescharacteristic
122C23×C4×C73C2311yescharacteristic
123C2×C4⋊C4×C73—22no—
124C2×C4⋊C4×C73—22no—
125C2×C4⋊C4×C73—22no—
126C2×C4⋊C4×C73—22no—
127C2×C4⋊C4×C73—22no—
128C2×C4⋊C4×C73—22no—
129C2×C4⋊C4×C73—22no—
130C2×C4⋊C4×C73—22no—
131C2×C4⋊C4×C73—41no—
132C2×C4⋊C4×C73—41no—
133C2×C4⋊C4×C73—41no—
134C2×C4⋊C4×C73C2×C414yes—
135C2×C42×C73—22no—
136C2×C42×C73—22no—
137C2×C42×C73—41no—
138#95×C73—22no—
139#95×C73D414yes—
140C23×D73—21no—
141C23×D73—21no—
142C23×D73—21no—
143C23×D73—21no—
144C23×D73—21no—
145C23×D73—21no—
146C23×D73—21no—
147C23×D73—21no—
148C23×D73—21no—
149C23×D73—21no—
150C23×D73—21no—
151C23×D73—21no—
152C23×D73C22×C412yes—
153C23×D73C2×D412yes—
154C23×D73#4112yes—
155C22×Dic73—21no—
156C22×Dic73—21no—
157C22×Dic73—21no—
158C22×Dic73—21no—
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73—21no—
170C22×Dic73—21no—
171C22×Dic73—21no—
172C22×Dic73—21no—
173C22×Dic73—21no—
174C22×Dic73—21no—
175C22×Dic73—21no—
176C22×Dic73—21no—
177C22×Dic73—21no—
178C22×Dic73—21no—
179C22×Dic73—21no—
180C22×Dic73—21no—
181C22×Dic73—21no—
182C22×Dic73—21no—
183C22×Dic73—21no—
184C22×Dic73—21no—
185C22×Dic73—21no—
186C22×Dic73—21no—
187C22×Dic73—21no—
188C22×Dic73—21no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73—21no—
200C22×Dic73C22×C412yes—
201C22×Dic73C22×C412yes—
202C22×Dic73C22×C412yes—
203C22×Dic73C2×D412yes—
204C2×C4×D73—28no—
205C2×C4×D73—28no—
206C2×C4×D73—44no—
207C2×C4×D73—44no—
208C2×C4×D73—44no—
209C2×C4×D73—44no—
210C2×C4×D73—44no—
211C4⋊Dic73—44no—
212#11924007—44no—
213#11924005—28no—
214#11924005—28no—
215#11924005—44no—
216#11924005—44no—
217#11924005—44no—
218#11924005—44no—
219C4×Dic73—44no—
220C24×C73C2411yescharacteristic
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73C22×C412yes—
261C22×C4×C73C22×C412yes—
262C22×C4×C73C22×C412yes—
263C22×C4×C73C2×D412yes—
264C22×C4×C73C2×D412yes—
265C22×C4×C73C2×D412yes—
266C22×C4×C73C2×D412yes—
267C22×C4×C73#4112yes—
268C22×C4×C73#4112yes—
269C22×C4×C73#4112yes—
270C4⋊C4×C73—28no—
271C4⋊C4×C73—44no—
272C4⋊C4×C73—44no—
273C4⋊C4×C73—44no—
274C42×C73—44no—
275C23×C73C23×C411yescharacteristic
276C23×C73C22×D411yescharacteristic
277C23×C73C22×D411yescharacteristic
278C23×C73C2×#4111yescharacteristic
279C23×C73C2×#4111yescharacteristic
280C23×C73C2×#4111yescharacteristic
281C23×C73C2×#4111yescharacteristic
282C23×C73H(5,𝔽2)11yescharacteristic
283C23×C73H(5,𝔽2)11yescharacteristic
284C23×C73H(5,𝔽2)11yescharacteristic
285C23×C73H(5,𝔽2)11yescharacteristic
286C23×C732−1+411yescharacteristic
287C23×C732−1+411yescharacteristic
288C23×C732−1+411yescharacteristic
289C23×C732−1+411yescharacteristic
290C22×D73—22no—
291C22×D73—22no—
292C22×D73—22no—
293C22×D73—22no—
294C22×D73—22no—
295C22×D73—22no—
296C22×D73—22no—
297C22×D73—22no—
298C22×D73—22no—
299C22×D73—22no—
300C22×D73—22no—
301C22×D73—22no—
302C22×D73—22no—
303C22×D73—22no—
304C22×D73—22no—
305C22×D73—22no—
306C22×D73—22no—
307C22×D73—22no—
308C22×D73—41no—
309C22×D73—41no—
310C22×D73—41no—
311C22×D73—41no—
312C22×D73—41no—
313C22×D73—41no—
314C22×D73—41no—
315C22×D73—41no—
316C22×D73—41no—
317C22×D73—41no—
318C22×D73—41no—
319C22×D73—41no—
320C22×D73—41no—
321C22×D73—41no—
322C22×D73—41no—
323C22×D73—41no—
324C22×D73C4×D414yes—
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73—22no—
335C2×C4×C73—22no—
336C2×C4×C73—22no—
337C2×C4×C73—22no—
338C2×C4×C73—22no—
339C2×C4×C73—22no—
340C2×C4×C73—22no—
341C2×C4×C73—22no—
342C2×C4×C73—22no—
343C2×C4×C73—22no—
344C2×C4×C73—22no—
345C2×C4×C73—22no—
346C2×C4×C73—22no—
347C2×C4×C73—22no—
348C2×C4×C73—22no—
349C2×C4×C73—41no—
350C2×C4×C73—41no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—41no—
354C2×C4×C73—41no—
355C2×C4×C73—41no—
356C2×C4×C73—41no—
357C2×C4×C73—41no—
358C2×C4×C73—41no—
359C2×C4×C73—41no—
360C2×C4×C73—41no—
361C2×C4×C73—41no—
362C2×C4×C73—41no—
363C2×C4×C73—41no—
364C2×C4×C73—41no—
365C2×C4×C73—41no—
366C2×C4×C73—41no—
367C2×C4×C73—41no—
368C2×C4×C73—41no—
369C2×C4×C73—41no—
370C2×C4×C73—41no—
371C2×C4×C73—41no—
372C2×C4×C73#11714yes—
373C2×C4×C73C4×D414yes—
374C2×Dic73—22no—
375C2×Dic73—22no—
376C2×Dic73—22no—
377C2×Dic73—22no—
378C2×Dic73—22no—
379C2×Dic73—22no—
380C2×Dic73—22no—
381C2×Dic73—22no—
382C2×Dic73—22no—
383C2×Dic73—22no—
384C2×Dic73—22no—
385C2×Dic73—22no—
386C2×Dic73—41no—
387C2×Dic73—41no—
388C2×Dic73—41no—
389C2×Dic73—41no—
390C2×Dic73—41no—
391C2×Dic73—41no—
392C2×Dic73—41no—
393C2×Dic73—41no—
394C2×Dic73—41no—
395C2×Dic73—41no—
396C2×Dic73—41no—
397C2×Dic73—41no—
398C2×Dic73—41no—
399C2×Dic73—41no—
400C2×Dic73—41no—
401C2×Dic73—41no—
402C2×Dic73—41no—
403C2×Dic73—41no—
404C2×Dic73—41no—
405C2×Dic73—41no—
406C2×Dic73—41no—
407C2×Dic73—41no—
408C2×Dic73—41no—
409C2×Dic73—41no—
410C2×Dic73—41no—
411C2×Dic73—41no—
412C2×Dic73—41no—
413C2×Dic73—41no—
414C2×Dic73—41no—
415C2×Dic73—41no—
416C2×Dic73—41no—
417C2×Dic73—41no—
418C2×Dic73—41no—
419C2×Dic73—41no—
420C2×Dic73—41no—
421C2×Dic73—41no—
422C2×Dic73—41no—
423C4×D73—416no—
424C22×C73C2×#11711yescharacteristic
425C22×C73C2×C4×D411yescharacteristic
426C22×C73C2×C4×D411yescharacteristic
427C22×C73#51811yescharacteristic
428C22×C73#51911yescharacteristic
429C22×C73#52011yescharacteristic
430C22×C73#52011yescharacteristic
431C22×C73#53411yescharacteristic
432C22×C73#53611yescharacteristic
433C22×C73#53611yescharacteristic
434C22×C73#53711yescharacteristic
435C22×C73#53911yescharacteristic
436C22×C73#53911yescharacteristic
437C22×C73#54011yescharacteristic
438C22×C73#54011yescharacteristic
439C22×C73#54111yescharacteristic
440C22×C73#54211yescharacteristic
441C22×C73#54211yescharacteristic
442C22×C73#54211yescharacteristic
443C22×C73D4211yescharacteristic
444C22×C73#54611yescharacteristic
445C22×C73#54611yescharacteristic
446C22×C73#54611yescharacteristic
447C22×C73#54711yescharacteristic
448C22×C73#54711yescharacteristic
449C22×C73#54811yescharacteristic
450C22×C73#55111yescharacteristic
451C22×C73#55211yescharacteristic
452C22×C73#55211yescharacteristic
453C22×C73#55211yescharacteristic
454C22×C73#55311yescharacteristic
455C22×C73#56211yescharacteristic
456C22×C73#56211yescharacteristic
457C22×C73#56311yescharacteristic
458C22×C73#56311yescharacteristic
459C2×D73—24no—
460C2×D73—24no—
461C2×D73—24no—
462C2×D73—42no—
463C2×D73—42no—
464C2×D73—42no—
465C2×D73—42no—
466C2×D73—42no—
467C2×D73—42no—
468C2×D73—42no—
469C2×D73—42no—
470C2×D73—42no—
471C2×D73—42no—
472C2×D73—42no—
473C2×D73—42no—
474C4×C73—24no—
475C4×C73—24no—
476C4×C73—42no—
477C4×C73—42no—
478C4×C73—42no—
479C4×C73—42no—
480C4×C73—81no—
481Dic73—42no—
482Dic73—42no—
483Dic73—42no—
484Dic73—42no—
485Dic73—81no—
486Dic73—81no—
487Dic73—81no—
488#14382—731nomaximal, Sylow
489C2×C73#231911yescharacteristic
490C2×C73#232211yescharacteristic
491C2×C73#232311yescharacteristic
492C2×C73#234411yescharacteristic
493C2×C73#235211yescharacteristic
494C2×C73#235811yescharacteristic
495C2×C73#237811yescharacteristic
496C2×C73#267111yescharacteristic
497C2×C73#267411yescharacteristic
498C2×C73#268711yescharacteristic
499C2×C73#269811yescharacteristic
500C2×C73#270111yescharacteristic
501C2×C73#270711yescharacteristic
502C2×C73#273811yescharacteristic
503C2×C73#273911yescharacteristic
504D73—44no—
505C2×#389D7311yescharacteristic, complemented
506C2×#388—731no—
507C2×#385—731no—
508C2×#381—731no—
509C2×#380—731no—
510#1445—731no—
511#1442—731no—
512#1441—731no—
513#1441—731no—
514#1440—731no—
515#1439—731no—
516#1437—731no—
517#1436—731no—
518#1436—731no—
519#1434—731no—
520C73#1438211yescharacteristic, complemented, Sylow
521C24×C4—731no—
522C22×C4⋊C4—731no—
523C22×C4⋊C4—731no—
524C22×C4⋊C4C2×D7311yescharacteristic
525C22×C4⋊C4C2×D7311yescharacteristic
526C22×C4⋊C4C2×D7311yescharacteristic
527C22×C4⋊C4C2×D7311yescharacteristic
528C22×C22⋊C4—731no—
529C22×C22⋊C4—731no—
530C22×C22⋊C4—731no—
531C22×C22⋊C4—731no—
532C22×C22⋊C4—731no—
533C22×C22⋊C4—731no—
534C22×C42—731no—
535C22×C42C2×D7311yescharacteristic
536#389—24no—
537#388—1464no—
538#385—738no—
539#381—1464no—
540#380—1464no—
541C2×#95—731no—
542C2×#95—731no—
543C2×#95—731no—
544C2×#95—731no—
545C2×#95—731no—
546C2×#95—731no—
547C2×#95—731no—
548C2×#95—731no—
549C2×#95—731no—
550C2×#95—731no—
551C2×#95—731no—
552C2×#95—731no—
553C2×#95—731no—
554C2×#95—731no—
555C2×#95—731no—
556C2×#95—731no—
557C2×#95—731no—
558C2×#95—731no—
559C2×#95C2×D7311yescharacteristic
560C2×#95C2×D7311yescharacteristic
561C25—731no—
562C23×C4—2921no—
563C23×C4—2921no—
564C23×C4—734no—
565C23×C4—731no—
566C23×C4—731no—
567C23×C4—731no—
568C23×C4—731no—
569C23×C4—731no—
570C23×C4—731no—
571C23×C4—731no—
572C23×C4—1462no—
573C23×C4—1462no—
574C23×C4—1462no—
575C23×C4—1462no—
576C23×C4C22×D7311yescharacteristic
577C23×C4C22×D7311yescharacteristic
578C23×C4C22×D7311yescharacteristic
579C23×C4C22×D7311yescharacteristic
580C23×C4C22×D7311yescharacteristic
581C23×C4C22×D7311yescharacteristic
582C23×C4C22×D7311yescharacteristic
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—2921no—
595C2×C4⋊C4—2921no—
596C2×C4⋊C4—2921no—
597C2×C4⋊C4—734no—
598C2×C4⋊C4—1462no—
599C2×C4⋊C4—1462no—
600C2×C4⋊C4C4×D7314yes—
601C2×C22⋊C4—2921no—
602C2×C22⋊C4—2921no—
603C2×C22⋊C4—2921no—
604C2×C22⋊C4—2921no—
605C2×C22⋊C4—2921no—
606C2×C22⋊C4—2921no—
607C2×C22⋊C4—734no—
608C2×C22⋊C4—734no—
609C2×C22⋊C4—734no—
610C2×C22⋊C4—1462no—
611C2×C22⋊C4—1462no—
612C2×C22⋊C4—1462no—
613C2×C22⋊C4—1462no—
614C2×C22⋊C4—1462no—
615C2×C22⋊C4—1462no—
616C2×C22⋊C4—1462no—
617C2×C22⋊C4—1462no—
618C2×C22⋊C4—1462no—
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—41no—
622C2×C42—2921no—
623C2×C42—2921no—
624C2×C42—1462no—
625#95—22no—
626#95—2921no—
627#95—2921no—
628#95—2921no—
629#95—2921no—
630#95—2921no—
631#95—2921no—
632#95—2921no—
633#95—734no—
634#95—734no—
635#95—1462no—
636#95—1462no—
637#95—1462no—
638#95—1462no—
639#95—1462no—
640#95—1462no—
641#95—1462no—
642#95—1462no—
643#95—1462no—
644#95C22⋊D7314yes—
645C24—732no—
646C24—732no—
647C24—732no—
648C24—1461no—
649C24—1461no—
650C24—1461no—
651C24—1461no—
652C24—1461no—
653C24—1461no—
654C24—1461no—
655C24—1461no—
656C24—1461no—
657C24—1461no—
658C24—1461no—
659C24—1461no—
660C24C23×D7311yescharacteristic
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—2924no—
701C22×C4—2924no—
702C22×C4—2924no—
703C22×C4—2924no—
704C22×C4—2924no—
705C22×C4—732no—
706C22×C4—732no—
707C22×C4—732no—
708C22×C4—732no—
709C22×C4—1468no—
710C22×C4—1461no—
711C22×C4—1461no—
712C22×C4—1461no—
713C22×C4—1461no—
714C22×C4—1461no—
715C22×C4—1461no—
716C22×C4—1461no—
717C22×C4—1461no—
718C22×C4—1461no—
719C22×C4—1461no—
720C22×C4—1461no—
721C22×C4—1461no—
722C22×C4—1461no—
723C22×C4—1461no—
724C22×C4—1461no—
725C22×C4—1461no—
726C22×C4—1461no—
727C22×C4—1461no—
728C22×C4—1461no—
729C22×C4—1461no—
730C22×C4—1461no—
731C22×C4—1461no—
732C22×C4—1461no—
733C22×C4—1461no—
734C22×C4—1461no—
735C22×C4—1461no—
736C22×C4—1461no—
737C22×C4—1461no—
738C22×C4—1461no—
739C22×C4—1461no—
740C22×C4—1461no—
741C22×C4—1461no—
742C22×C4—1461no—
743C22×C4—1461no—
744C22×C4—1461no—
745C22×C4—1461no—
746C22×C4—1461no—
747C22×C4—1461no—
748C22×C4—1461no—
749C22×C4—1461no—
750C22×C4—1461no—
751C22×C4—1461no—
752C22×C4—1461no—
753C22×C4—1461no—
754C22×C4—1461no—
755C22×C4—1468no—
756C22×C4C2×C4×D7312yes—
757C22×C4C2×C4×D7312yes—
758C22×C4C2×C4×D7312yes—
759C22×C4D4×D7312yes—
760C22×C4C2×C22⋊D7312yes—
761C22×C4C2×C22⋊D7312yes—
762C22×C4C2×C22⋊D7312yes—
763C22×C4#1192402712yes—
764C22×C4#1192402812yes—
765C22×C4#1192402912yes—
766C4⋊C4—28no—
767C4⋊C4—44no—
768C4⋊C4—44no—
769C4⋊C4—44no—
770C4⋊C4—2924no—
771C4⋊C4—2924no—
772C22⋊C4—2924no—
773C22⋊C4—2924no—
774C22⋊C4—2924no—
775C22⋊C4—2924no—
776C22⋊C4—1468no—
777C22⋊C4—1468no—
778C42—44no—
779C42—2924no—
780C23—2921no—
781C23—2921no—
782C23—2921no—
783C23—2921no—
784C23—2921no—
785C23—2921no—
786C23—2921no—
787C23—2921no—
788C23—2921no—
789C23—2921no—
790C23—2921no—
791C23—2921no—
792C23—2921no—
793C23—2921no—
794C23—2921no—
795C23—2921no—
796C23—734no—
797C23—1462no—
798C23—1462no—
799C23—1462no—
800C23—1462no—
801C23—1462no—
802C23—1462no—
803C23—1462no—
804C23—1462no—
805C23—1462no—
806C23—1462no—
807C23—1462no—
808C23—1462no—
809C23—1462no—
810C23—1462no—
811C23—1462no—
812C23—1462no—
813C23—1462no—
814C23—1462no—
815C23C22×C4×D7311yescharacteristic
816C23C2×D4×D7311yescharacteristic
817C23C22×C22⋊D7311yescharacteristic
818C23#41×D7311yescharacteristic
819C23C2×#1192402711yescharacteristic
820C23C2×#1192402811yescharacteristic
821C23C2×#1192402911yescharacteristic
822C23#1455663611yescharacteristic
823C23#1455663611yescharacteristic
824C23#1455663711yescharacteristic
825C23#1455663711yescharacteristic
826C23#1455663811yescharacteristic
827C23#1455663911yescharacteristic
828C23#1455663911yescharacteristic
829C23#1455663911yescharacteristic
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—29216no—
878C2×C4—2921no—
879C2×C4—2921no—
880C2×C4—2921no—
881C2×C4—2921no—
882C2×C4—2921no—
883C2×C4—2921no—
884C2×C4—2921no—
885C2×C4—2921no—
886C2×C4—2921no—
887C2×C4—2921no—
888C2×C4—2921no—
889C2×C4—2921no—
890C2×C4—2921no—
891C2×C4—2921no—
892C2×C4—2921no—
893C2×C4—2921no—
894C2×C4—2921no—
895C2×C4—2921no—
896C2×C4—2921no—
897C2×C4—2921no—
898C2×C4—2921no—
899C2×C4—2921no—
900C2×C4—2921no—
901C2×C4—2921no—
902C2×C4—2921no—
903C2×C4—2921no—
904C2×C4—2921no—
905C2×C4—2921no—
906C2×C4—2921no—
907C2×C4—2921no—
908C2×C4—2921no—
909C2×C4—2921no—
910C2×C4—2921no—
911C2×C4—2921no—
912C2×C4—2921no—
913C2×C4—2921no—
914C2×C4—2921no—
915C2×C4—1462no—
916C2×C4—1462no—
917C2×C4—1462no—
918C2×C4—1462no—
919C2×C4—1462no—
920C2×C4—1462no—
921C2×C4—1462no—
922C2×C4—1462no—
923C2×C4—1462no—
924C2×C4—1462no—
925C2×C4—1462no—
926C2×C4—1462no—
927C2×C4#1455654914yes—
928C2×C4C4×C22⋊D7314yes—
929C22—2922no—
930C22—2922no—
931C22—2922no—
932C22—2922no—
933C22—2922no—
934C22—2922no—
935C22—2922no—
936C22—2922no—
937C22—2922no—
938C22—2922no—
939C22—2922no—
940C22—2922no—
941C22—1464no—
942C22—1464no—
943C22—1464no—
944C22C2×#1455654911yescharacteristic
945C22C4×D4×D7311yescharacteristic
946C22C2×C4×C22⋊D7311yescharacteristic
947C22#1798905911yescharacteristic
948C22#1798906311yescharacteristic
949C22#1798906811yescharacteristic
950C22#1798906911yescharacteristic
951C22#1798914511yescharacteristic
952C22#1798916111yescharacteristic
953C22#1798916211yescharacteristic
954C22#1798916511yescharacteristic
955C22#1798918311yescharacteristic
956C22#1798918511yescharacteristic
957C22#1798919011yescharacteristic
958C22#1798919311yescharacteristic
959C22#1798919511yescharacteristic
960C22#1798920911yescharacteristic
961C22#1798921011yescharacteristic
962C22#1798921111yescharacteristic
963C22D4×C22⋊D7311yescharacteristic
964C22#1798922511yescharacteristic
965C22#1798923111yescharacteristic
966C22#1798923311yescharacteristic
967C22#1798923711yescharacteristic
968C22#1798924011yescharacteristic
969C22#1798924811yescharacteristic
970C22#1798926611yescharacteristic
971C22#1798927111yescharacteristic
972C22#1798927211yescharacteristic
973C22#1798927511yescharacteristic
974C22#1798928511yescharacteristic
975C22#1798933211yescharacteristic
976C22#1798933311yescharacteristic
977C22#1798933611yescharacteristic
978C22#1798934111yescharacteristic
979C4—24no—
980C4—24no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—2922no—
987C4—2922no—
988C4—2922no—
989C4—2922no—
990C4—5841no—
991C4—5841no—
992C4—5841no—
993C2—2924no—
994C2#2261257011yescharacteristic
995C2#2261259511yescharacteristic
996C2#2261260711yescharacteristic
997C2#2261279911yescharacteristic
998C2#2261285611yescharacteristic
999C2#2261290811yescharacteristic
1000C2#2261309311yescharacteristic
1001C2#2261616211yescharacteristic
1002C2#2261620711yescharacteristic
1003C2#2261634811yescharacteristic
1004C2#2261650011yescharacteristic
1005C2#2261653911yescharacteristic
1006C2#2261662811yescharacteristic
1007C2#2261700411yescharacteristic
1008C2#2261701911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×#389×C73C2
socle, cosocleC24×C73C24
prime radicalC24×D73C23
hypercenterC2×#389D73
hypocenterC73#14382
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
5. #22608197C2semidirect
6. #22608190C2semidirect
7. #22608184C2semidirect
8. #22608181C2semidirect
12. #22608165C2semidirect
13. #22608163C2semidirect
14. #22608158C2semidirect
15. C2×#389×C73C2semidirect
27. #17988458C4semidirect
505. C2×#389D73semidirect
520. C73#14382semidirect

Maximal subgroups

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

subgroupindex
C2×#179884772
C2×#179884582
C2×#179884492
C2×#179884442
#226081972
#226081902
#226081842
#226081812
#226081792
#226081732
#226081692
#226081652
#226081632
#226081582
C2×#389×C732
#1438273