Finite Group Databasebeta

← #33008604

Subgroups — #33008604

Order 18688.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988480C211yesmaximal, characteristic
2C2×C22⋊C4×Dic73C211yesmaximal, characteristic
3#22608190C211yesmaximal, characteristic, complemented
4#22608187C211yesmaximal, characteristic, complemented
5#22608174C211yesmaximal, characteristic
6#22608174C211yesmaximal, characteristic
7#22608164C211yesmaximal, characteristic, complemented
8#22608162C211yesmaximal, characteristic, complemented
9#22608160C211yesmaximal, characteristic, complemented
10#22608159C211yesmaximal, characteristic, complemented
11#22608157C211yesmaximal, characteristic, complemented
12#22608153C211yesmaximal, characteristic
13#22608153C211yesmaximal, characteristic
14C4×#14556498C211yesmaximal, characteristic, complemented
15C2×#388×C73C211yesmaximal, characteristic
16C24×Dic73C2211yescharacteristic
17C22×C4⋊Dic73C2211yescharacteristic
18C22×#11924007C2211yescharacteristic
19C22×#11924007C2211yescharacteristic
20C22×C22⋊Dic73C2211yescharacteristic
21C22×C22⋊Dic73C2211yescharacteristic
22C22×C22⋊Dic73C2211yescharacteristic
23C22×C4×Dic73C2211yescharacteristic
24C22×C4×Dic73C2211yescharacteristic
25C22×C4×Dic73C2211yescharacteristic
26#17988480—24no—
27C22⋊C4×Dic73C418yescomplemented
28C2×#14556498C2211yescharacteristic
29C2×#14556498C2211yescharacteristic
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
46C22×C4⋊C4×C73C2211yescharacteristic
47C22×C22⋊C4×C73C2211yescharacteristic
48C22×C22⋊C4×C73C2211yescharacteristic
49C22×C22⋊C4×C73C2211yescharacteristic
50C22×C42×C73C2211yescharacteristic
51#388×C73—24no—
52C2×#95×C73C2211yescharacteristic
53C2×#95×C73C2211yescharacteristic
54C23×Dic73—22no—
55C23×Dic73—22no—
56C23×Dic73—41no—
57C23×Dic73—41no—
58C23×Dic73—41no—
59C23×Dic73—41no—
60C23×Dic73C2×C414yes—
61C23×Dic73C2311yescharacteristic
62C23×Dic73C2311yescharacteristic
63C23×Dic73C2311yescharacteristic
64C23×Dic73C2311yescharacteristic
65C23×Dic73C2311yescharacteristic
66C23×Dic73C2311yescharacteristic
67C23×Dic73C2311yescharacteristic
68C23×Dic73C2311yescharacteristic
69C2×C4⋊Dic73—22no—
70C2×C4⋊Dic73—22no—
71C2×C4⋊Dic73—41no—
72C2×#11924007—22no—
73C2×#11924007—22no—
74C2×#11924007—22no—
75C2×#11924007—22no—
76C2×#11924007—41no—
77C2×#11924007—41no—
78C2×C22⋊Dic73—22no—
79C2×C22⋊Dic73—22no—
80C2×C22⋊Dic73—22no—
81C2×C22⋊Dic73—22no—
82C2×C22⋊Dic73—22no—
83C2×C22⋊Dic73—22no—
84C2×C22⋊Dic73—41no—
85C2×C22⋊Dic73—41no—
86C2×C22⋊Dic73C2×C414yes—
87C2×C4×Dic73—22no—
88C2×C4×Dic73—22no—
89C2×C4×Dic73—41no—
90C2×C4×Dic73—41no—
91C2×C4×Dic73—41no—
92C2×C4×Dic73—41no—
93C2×C4×Dic73—41no—
94C2×C4×Dic73C2×C414yes—
95C2×C4×Dic73C2×C414yes—
96#14556498—22no—
97#14556498—22no—
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—41no—
107#14556498—41no—
108#14556498—41no—
109#14556498—41no—
110#14556498—41no—
111#14556498—41no—
112#14556498C2×C414yes—
113#14556498C2×C414yes—
114C25×C73C2311yescharacteristic
115C23×C4×C73C2311yescharacteristic
116C23×C4×C73C2311yescharacteristic
117C23×C4×C73C2311yescharacteristic
118C23×C4×C73C2311yescharacteristic
119C23×C4×C73C2311yescharacteristic
120C23×C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73—22no—
122C2×C4⋊C4×C73—22no—
123C2×C4⋊C4×C73—41no—
124C2×C22⋊C4×C73—22no—
125C2×C22⋊C4×C73—22no—
126C2×C22⋊C4×C73—22no—
127C2×C22⋊C4×C73—22no—
128C2×C22⋊C4×C73—41no—
129C2×C22⋊C4×C73—41no—
130C2×C22⋊C4×C73C2×C414yes—
131C2×C22⋊C4×C73D414yes—
132C2×C22⋊C4×C73Q814yes—
133C2×C42×C73—22no—
134C2×C42×C73—22no—
135C2×C42×C73—41no—
136#95×C73—22no—
137#95×C73—22no—
138C22×Dic73—21no—
139C22×Dic73—21no—
140C22×Dic73—21no—
141C22×Dic73—21no—
142C22×Dic73—21no—
143C22×Dic73—21no—
144C22×Dic73—21no—
145C22×Dic73—21no—
146C22×Dic73—21no—
147C22×Dic73—21no—
148C22×Dic73—21no—
149C22×Dic73—21no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73—21no—
154C22×Dic73—21no—
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—28no—
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—44no—
186C22×Dic73—44no—
187C22×Dic73—44no—
188C22×Dic73—44no—
189C22×Dic73—44no—
190C22×Dic73—44no—
191C22×Dic73C22×C412yes—
192C22×Dic73C22×C412yes—
193C22×Dic73C22×C412yes—
194C22×Dic73C22×C412yes—
195C22×Dic73#4112yes—
196C22×Dic73#4112yes—
197C22×Dic73#4112yes—
198C22×Dic73#4112yes—
199C22×Dic73#4112yes—
200C22×Dic73#4112yes—
201C4⋊Dic73—44no—
202#11924007—44no—
203#11924007—44no—
204C22⋊Dic73—28no—
205C22⋊Dic73—44no—
206C22⋊Dic73—44no—
207C4×Dic73—44no—
208C4×Dic73—44no—
209C4×Dic73—44no—
210C24×C73—21no—
211C24×C73—21no—
212C24×C73—21no—
213C24×C73—21no—
214C24×C73—21no—
215C24×C73—21no—
216C24×C73—21no—
217C24×C73—21no—
218C24×C73—21no—
219C24×C73—21no—
220C24×C73—21no—
221C24×C73—21no—
222C24×C73C22×C412yes—
223C24×C73C2×D412yes—
224C24×C73C2×Q812yes—
225C24×C73C2411yescharacteristic
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×C73C2×D412yes—
263C22×C4×C73C2×D412yes—
264C22×C4×C73C2×Q812yes—
265C22×C4×C73C2×Q812yes—
266C22×C4×C73#4112yes—
267C22×C4×C73#4112yes—
268C4⋊C4×C73—44no—
269C22⋊C4×C73—44no—
270C22⋊C4×C73—44no—
271C22⋊C4×C73C4⋊C4116yescomplemented
272C42×C73—44no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73—22no—
277C23×C73—22no—
278C23×C73—22no—
279C23×C73—22no—
280C23×C73—22no—
281C23×C73—22no—
282C23×C73—22no—
283C23×C73—22no—
284C23×C73—22no—
285C23×C73—22no—
286C23×C73—22no—
287C23×C73—22no—
288C23×C73—22no—
289C23×C73—22no—
290C23×C73—22no—
291C23×C73—41no—
292C23×C73—41no—
293C23×C73—41no—
294C23×C73—41no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—41no—
298C23×C73—41no—
299C23×C73—41no—
300C23×C73—41no—
301C23×C73—41no—
302C23×C73—41no—
303C23×C73—41no—
304C23×C73—41no—
305C23×C73—41no—
306C23×C73—41no—
307C23×C73C2×C4⋊C414yes—
308C23×C73C23×C411yescharacteristic
309C23×C73C22×D411yescharacteristic
310C23×C73C22×Q811yescharacteristic
311C23×C73C2×#4111yescharacteristic
312C23×C73C2×#4111yescharacteristic
313C23×C73C2×#4111yescharacteristic
314C23×C73C2×#4111yescharacteristic
315C23×C73C2×#4111yescharacteristic
316C23×C73C2×#4111yescharacteristic
317C23×C73C2×#4111yescharacteristic
318C23×C73C2×#4111yescharacteristic
319C23×C73H(5,𝔽2)11yescharacteristic
320C23×C73H(5,𝔽2)11yescharacteristic
321C23×C73H(5,𝔽2)11yescharacteristic
322C23×C73H(5,𝔽2)11yescharacteristic
323C2×C4×C73—22no—
324C2×C4×C73—22no—
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—41no—
342C2×C4×C73—41no—
343C2×C4×C73—41no—
344C2×C4×C73—41no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
347C2×C4×C73—41no—
348C2×C4×C73—41no—
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×C73C2×C4⋊C414yes—
364C2×C4×C73C2×C4⋊C414yes—
365C2×Dic73—22no—
366C2×Dic73—22no—
367C2×Dic73—22no—
368C2×Dic73—22no—
369C2×Dic73—22no—
370C2×Dic73—22no—
371C2×Dic73—22no—
372C2×Dic73—22no—
373C2×Dic73—22no—
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—22no—
387C2×Dic73—22no—
388C2×Dic73—22no—
389C2×Dic73—416no—
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#11714yes—
421C2×Dic73#11714yes—
422C22×C73—24no—
423C22×C73—24no—
424C22×C73—24no—
425C22×C73—42no—
426C22×C73—42no—
427C22×C73—42no—
428C22×C73—42no—
429C22×C73—42no—
430C22×C73—42no—
431C22×C73—42no—
432C22×C73—42no—
433C22×C73—42no—
434C22×C73—42no—
435C22×C73—42no—
436C22×C73—42no—
437C22×C73C22×C4⋊C411yescharacteristic
438C22×C73C2×#11711yescharacteristic
439C22×C73C2×#11711yescharacteristic
440C22×C73C4×#4111yescharacteristic
441C22×C73C4×#4111yescharacteristic
442C22×C73#51811yescharacteristic
443C22×C73#51811yescharacteristic
444C22×C73#52911yescharacteristic
445C22×C73#52911yescharacteristic
446C22×C73#52911yescharacteristic
447C22×C73#52911yescharacteristic
448C22×C73#53211yescharacteristic
449C22×C73#53211yescharacteristic
450C22×C73#53311yescharacteristic
451C22×C73#53311yescharacteristic
452C22×C73#53811yescharacteristic
453C22×C73#53811yescharacteristic
454C22×C73#53811yescharacteristic
455C22×C73#53811yescharacteristic
456C22×C73#54611yescharacteristic
457C22×C73#54611yescharacteristic
458C22×C73#54611yescharacteristic
459C22×C73#54611yescharacteristic
460C22×C73#55111yescharacteristic
461C22×C73#55111yescharacteristic
462C22×C73#55311yescharacteristic
463C22×C73#55311yescharacteristic
464C22×C73#55311yescharacteristic
465C22×C73#55311yescharacteristic
466C22×C73#55411yescharacteristic
467C22×C73#55411yescharacteristic
468C22×C73#55411yescharacteristic
469C22×C73#55411yescharacteristic
470C22×C73#55911yescharacteristic
471C22×C73#55911yescharacteristic
472C4×C73—24no—
473C4×C73—24no—
474C4×C73—42no—
475C4×C73—42no—
476C4×C73—81no—
477C4×C73—81no—
478Dic73—24no—
479Dic73—24no—
480Dic73—42no—
481Dic73—42no—
482Dic73—42no—
483Dic73—42no—
484Dic73—81no—
485Dic73—81no—
486#13948—731nomaximal, Sylow
487C2×C73—44no—
488C2×C73#228511yescharacteristic
489C2×C73#229811yescharacteristic
490C2×C73#231211yescharacteristic
491C2×C73#234911yescharacteristic
492C2×C73#234911yescharacteristic
493C2×C73#235311yescharacteristic
494C2×C73#235711yescharacteristic
495C2×C73#255711yescharacteristic
496C2×C73#255711yescharacteristic
497C2×C73#255911yescharacteristic
498C2×C73#255911yescharacteristic
499C2×C73#258711yescharacteristic
500C2×C73#258711yescharacteristic
501C2×C73#258911yescharacteristic
502C2×C73#258911yescharacteristic
503C2×#388—731no—
504C2×#388D7311yescharacteristic
505C2×C4×C22⋊C4—731no—
506#1442—731no—
507#1442—731no—
508#1439—731no—
509#1439—731no—
510#1436—731no—
511#1436—731no—
512C4⋊#95—731no—
513C4⋊#95—731no—
514#1434—731no—
515C22⋊#95—731no—
516C22⋊#95—731no—
517C4×#95—731no—
518C73#1394811yescharacteristic, complemented, Sylow
519C24×C4—731no—
520C22×C4⋊C4—731no—
521C22×C4⋊C4—731no—
522C22×C4⋊C4—731no—
523C22×C4⋊C4C2×D7311yescharacteristic
524C22×C22⋊C4—731no—
525C22×C22⋊C4—731no—
526C22×C22⋊C4—731no—
527C22×C22⋊C4C2×D7311yescharacteristic
528C22×C22⋊C4C2×D7311yescharacteristic
529C22×C22⋊C4C2×D7311yescharacteristic
530C22×C42—731no—
531C22×C42—731no—
532C22×C42—731no—
533C22×C42C2×D7311yescharacteristic
534#388—24no—
535#388—1464no—
536C4×C22⋊C4—738no—
537C2×#95—731no—
538C2×#95—731no—
539C2×#95—731no—
540C2×#95—731no—
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×#95C2×D7311yescharacteristic
556C2×#95C2×D7311yescharacteristic
557C25C22×D7311yescharacteristic
558C23×C4—2921no—
559C23×C4—2921no—
560C23×C4—2921no—
561C23×C4—2921no—
562C23×C4—734no—
563C23×C4—731no—
564C23×C4—731no—
565C23×C4—731no—
566C23×C4—731no—
567C23×C4—731no—
568C23×C4—731no—
569C23×C4—731no—
570C23×C4—731no—
571C23×C4—1462no—
572C23×C4—1462no—
573C23×C4C22×D7311yescharacteristic
574C23×C4C22×D7311yescharacteristic
575C23×C4C22×D7311yescharacteristic
576C23×C4C22×D7311yescharacteristic
577C23×C4C22×D7311yescharacteristic
578C23×C4C22×D7311yescharacteristic
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—2921no—
583C2×C4⋊C4—2921no—
584C2×C4⋊C4—2921no—
585C2×C4⋊C4—1462no—
586C2×C4⋊C4—1462no—
587C2×C4⋊C4—1462no—
588C2×C4⋊C4—1462no—
589C2×C4⋊C4—1462no—
590C2×C4⋊C4—1462no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—41no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—2921no—
598C2×C22⋊C4—2921no—
599C2×C22⋊C4—734no—
600C2×C22⋊C4—1462no—
601C2×C22⋊C4—1462no—
602C2×C22⋊C4—1462no—
603C2×C22⋊C4—1462no—
604C2×C22⋊C4—1462no—
605C2×C22⋊C4—1462no—
606C2×C22⋊C4Dic14614yes—
607C2×C22⋊C4C4×D7314yes—
608C2×C22⋊C4C22⋊D7314yes—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—41no—
612C2×C42—2921no—
613C2×C42—2921no—
614C2×C42—2921no—
615C2×C42—2921no—
616C2×C42—2921no—
617C2×C42—734no—
618C2×C42—734no—
619C2×C42—1462no—
620C2×C42—1462no—
621#95—22no—
622#95—22no—
623#95—2921no—
624#95—2921no—
625#95—2921no—
626#95—2921no—
627#95—2921no—
628#95—2921no—
629#95—734no—
630#95—734no—
631#95—1462no—
632#95—1462no—
633#95—1462no—
634#95—1462no—
635#95—1462no—
636#95—1462no—
637#95—1462no—
638#95—1462no—
639#95—1462no—
640#95—1462no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×C4×D7312yes—
654C24C2×C22⋊D7312yes—
655C24C2×Dic14612yes—
656C24C23×D7311yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
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—2924no—
692C22×C4—2924no—
693C22×C4—2924no—
694C22×C4—2924no—
695C22×C4—2924no—
696C22×C4—2924no—
697C22×C4—732no—
698C22×C4—732no—
699C22×C4—732no—
700C22×C4—732no—
701C22×C4—732no—
702C22×C4—732no—
703C22×C4—732no—
704C22×C4—732no—
705C22×C4—732no—
706C22×C4—732no—
707C22×C4—1461no—
708C22×C4—1461no—
709C22×C4—1461no—
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—1468no—
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×C4C2×C4×D7312yes—
755C22×C4C2×C4×D7312yes—
756C22×C4C2×C22⋊D7312yes—
757C22×C4C2×C22⋊D7312yes—
758C22×C4C2×Dic14612yes—
759C22×C4C2×Dic14612yes—
760C22×C4#1192402712yes—
761C22×C4#1192402712yes—
762C4⋊C4—44no—
763C4⋊C4—2924no—
764C4⋊C4—2924no—
765C4⋊C4—2924no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—2924no—
769C22⋊C4—2924no—
770C22⋊C4—1468no—
771C22⋊C4#11924007116yescomplemented
772C42—44no—
773C42—2924no—
774C42—2924no—
775C42—2924no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×#1192400714yes—
811C23C22×C4×D7311yescharacteristic
812C23C22×C22⋊D7311yescharacteristic
813C23C22×Dic14611yescharacteristic
814C23#41×D7311yescharacteristic
815C23#41×D7311yescharacteristic
816C23#41×D7311yescharacteristic
817C23#41×D7311yescharacteristic
818C23#41×D7311yescharacteristic
819C23#41×D7311yescharacteristic
820C23C2×#1192402711yescharacteristic
821C23C2×#1192402711yescharacteristic
822C23#1455663611yescharacteristic
823C23#1455663611yescharacteristic
824C23#1455663711yescharacteristic
825C23#1455663711yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
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—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
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—2921no—
867C2×C4—2921no—
868C2×C4—2921no—
869C2×C4—2921no—
870C2×C4—2921no—
871C2×C4—2921no—
872C2×C4—2921no—
873C2×C4—2921no—
874C2×C4—2921no—
875C2×C4—2921no—
876C2×C4—2921no—
877C2×C4—2921no—
878C2×C4—2921no—
879C2×C4—2921no—
880C2×C4—2921no—
881C2×C4—2921no—
882C2×C4—29216no—
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—734no—
898C2×C4—734no—
899C2×C4—1462no—
900C2×C4—1462no—
901C2×C4—1462no—
902C2×C4—1462no—
903C2×C4—1462no—
904C2×C4—1462no—
905C2×C4—1462no—
906C2×C4—1462no—
907C2×C4—1462no—
908C2×C4—1462no—
909C2×C4—1462no—
910C2×C4—1462no—
911C2×C4—1462no—
912C2×C4—1462no—
913C2×C4—1462no—
914C2×C4—1462no—
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×C4C2×#1192400714yes—
924C2×C4C2×#1192400714yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×#1192400711yescharacteristic
941C22#117×D7311yescharacteristic
942C22#117×D7311yescharacteristic
943C22C4×#1192402711yescharacteristic
944C22C4×#1192402711yescharacteristic
945C22#1798905911yescharacteristic
946C22#1798905911yescharacteristic
947C22#1798911411yescharacteristic
948C22#1798911611yescharacteristic
949C22#1798911811yescharacteristic
950C22#1798912011yescharacteristic
951C22#1798913311yescharacteristic
952C22#1798913311yescharacteristic
953C22#1798914011yescharacteristic
954C22#1798914011yescharacteristic
955C22#1798916911yescharacteristic
956C22#1798917111yescharacteristic
957C22#1798917311yescharacteristic
958C22#1798917611yescharacteristic
959C22#1798922511yescharacteristic
960C22#1798922511yescharacteristic
961C22#1798923111yescharacteristic
962C22#1798923111yescharacteristic
963C22#1798926011yescharacteristic
964C22#1798926711yescharacteristic
965C22#1798928011yescharacteristic
966C22#1798928411yescharacteristic
967C22#1798928811yescharacteristic
968C22#1798928811yescharacteristic
969C22#1798929411yescharacteristic
970C22#1798929411yescharacteristic
971C22#1798929611yescharacteristic
972C22#1798929611yescharacteristic
973C22#1798931911yescharacteristic
974C22#1798932111yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—81no—
980C4—81no—
981C4—2922no—
982C4—2922no—
983C4—2922no—
984C4—2922no—
985C4—5841no—
986C4—5841no—
987C4—1464no—
988C4—1464no—
989C2—44no—
990C2#2261233411yescharacteristic
991C2#2261242511yescharacteristic
992C2#2261252511yescharacteristic
993C2#2261283611yescharacteristic
994C2#2261283611yescharacteristic
995C2#2261286611yescharacteristic
996C2#2261290111yescharacteristic
997C2#2261502611yescharacteristic
998C2#2261502811yescharacteristic
999C2#2261505611yescharacteristic
1000C2#2261505811yescharacteristic
1001C2#2261534811yescharacteristic
1002C2#2261535011yescharacteristic
1003C2#2261537811yescharacteristic
1004C2#2261538011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×#388×C73C2
socle, cosocleC24×C73C24
prime radicalC25×C73C23
hypercenterC2×#388D73
hypocenterC73#13948
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. #22608190C2semidirect
4. #22608187C2semidirect
7. #22608164C2semidirect
8. #22608162C2semidirect
9. #22608160C2semidirect
10. #22608159C2semidirect
11. #22608157C2semidirect
14. C4×#14556498C2semidirect
27. C22⋊C4×Dic73C4semidirect
271. C22⋊C4×C73C4⋊C4semidirect
518. C73#13948semidirect
771. C22⋊C4#11924007semidirect

Maximal subgroups

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

subgroupindex
C2×#179884802
C2×C22⋊C4×Dic732
#226081902
#226081872
#226081742
#226081642
#226081622
#226081602
#226081592
#226081572
#226081532
C4×#145564982
C2×#388×C732
#1394873