Finite Group Databasebeta

← #34029353

Subgroups — #34029353

Order 18688.

792 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626054C211yesmaximal, characteristic
2#22626030C211yesmaximal, characteristic, complemented
3#22626029C211yesmaximal, characteristic, complemented
4#22626003C211yesmaximal, characteristic, complemented
5#22626002C211yesmaximal, characteristic, complemented
6#22626001C211yesmaximal, characteristic, complemented
7#22626000C211yesmaximal, characteristic, complemented
8#22625987C211yesmaximal, characteristic, complemented
9#22625985C211yesmaximal, characteristic, complemented
10#22625906C211yesmaximal, characteristic
11#22625875C211yesmaximal, characteristic, complemented
12#22625874C211yesmaximal, characteristic, complemented
13#22625788C211yesmaximal, characteristic, complemented
14#22625786C211yesmaximal, characteristic, complemented
15#22612458C211yesmaximal, characteristic
16C23×#10596833C2211yescharacteristic
17C2×#14556658C2211yescharacteristic
18C2×#14556658C2211yescharacteristic
19C2×#14556658C2211yescharacteristic
20C2×#14556658C2211yescharacteristic
21C2×C4⋊#10596833C2211yescharacteristic
22C2×C4⋊#10596833C2211yescharacteristic
23C2×C4⋊#10596833C2211yescharacteristic
24C2×#14556648C2211yescharacteristic
25C2×#14556648C2211yescharacteristic
26C2×#14556648C2211yescharacteristic
27C2×#14556648C2211yescharacteristic
28C2×C22⋊#10596833C2211yescharacteristic
29C2×C22⋊#10596833C2211yescharacteristic
30C2×C22⋊#10596833C2211yescharacteristic
31C2×C4×#10596833C2211yescharacteristic
32C2×C4×#10596833C2211yescharacteristic
33C2×C4×#10596833C2211yescharacteristic
34#17989453C2211yescharacteristic
35#17989453C2211yescharacteristic
36#17989453C2211yescharacteristic
37#17989453C2211yescharacteristic
38#17989453C2211yescharacteristic
39#17989453C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44C2×#14556573C411yescharacteristic
45C2×#14556551C2211yescharacteristic
46C2×C42×D73C2211yescharacteristic
47#17988475C411yescharacteristic
48#17988472C411yescharacteristic
49#17988471C411yescharacteristic
50#17988463C411yescharacteristic
51#17988458C411yescharacteristic
52#17988449C411yescharacteristic
53C4⋊C4×Dic73C2211yescharacteristic
54#17988438C2211yescharacteristic
55C22⋊C4×Dic73C2211yescharacteristic
56C22⋊C4×Dic73C2211yescharacteristic
57#17988434C2211yescharacteristic
58#388×C73C411yescharacteristic
59C22×#10596833—41no—
60C22×#10596833—41no—
61C22×#10596833—41no—
62C22×#10596833C2311yescharacteristic
63C22×#10596833C2311yescharacteristic
64C22×#10596833C2311yescharacteristic
65C22×#10596833C2311yescharacteristic
66C22×#10596833C2311yescharacteristic
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69C22×#10596833C2311yescharacteristic
70#14556658—41no—
71#14556658—41no—
72#14556658—41no—
73#14556658—41no—
74C4⋊#10596833—41no—
75C4⋊#10596833—41no—
76C4⋊#10596833—41no—
77#14556648—41no—
78#14556648—41no—
79#14556648—41no—
80#14556648—41no—
81C22⋊#10596833—41no—
82C22⋊#10596833—41no—
83C22⋊#10596833—41no—
84C4×#10596833—41no—
85C4×#10596833—41no—
86C4×#10596833—41no—
87C22×C22⋊D73C2×C411yescharacteristic
88C23×Dic73C2311yescharacteristic
89C22×C4×D73C2×C411yescharacteristic
90C22×C4×D73C2×C411yescharacteristic
91C22×C4×D73C2311yescharacteristic
92#14556573C818yescomplemented
93#14556551—41no—
94#14556551—41no—
95C2×C4⋊Dic73C2×C411yescharacteristic
96C2×#11924007C2×C411yescharacteristic
97C2×#11924007C2×C411yescharacteristic
98C2×#11924007C2×C411yescharacteristic
99C2×C22⋊Dic73C2×C411yescharacteristic
100C2×C22⋊Dic73C2×C411yescharacteristic
101C2×#11924005C2×C411yescharacteristic
102C2×#11924005C2×C411yescharacteristic
103C2×#11924005C2×C411yescharacteristic
104C2×C4×Dic73C2×C411yescharacteristic
105C2×C4×Dic73C2311yescharacteristic
106C2×C4×Dic73C2311yescharacteristic
107C2×C4×Dic73C2311yescharacteristic
108C2×C4×Dic73C2311yescharacteristic
109C2×C4×Dic73C2311yescharacteristic
110C42×D73—41no—
111C42×D73—41no—
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120C2×C4⋊C4×C73C2×C411yescharacteristic
121C2×C22⋊C4×C73C2×C411yescharacteristic
122C2×C22⋊C4×C73C2×C411yescharacteristic
123C2×C22⋊C4×C73C2×C411yescharacteristic
124C2×C42×C73C2×C411yescharacteristic
125#95×C73C2×C411yescharacteristic
126#95×C73C2×C411yescharacteristic
127C2×#10596833—21no—
128C2×#10596833—21no—
129C2×#10596833—21no—
130C2×#10596833—21no—
131C2×#10596833—21no—
132C2×#10596833—21no—
133C2×#10596833—21no—
134C2×#10596833—21no—
135C2×#10596833—21no—
136C2×#10596833—21no—
137C2×#10596833—21no—
138C2×#10596833—21no—
139C2×#10596833—21no—
140C2×#10596833—21no—
141C2×#10596833—21no—
142C2×#10596833—21no—
143C2×#10596833—21no—
144C2×#10596833—21no—
145C2×#10596833—21no—
146C2×#10596833—21no—
147C2×#10596833—21no—
148C2×#10596833—21no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—44no—
152C23×D73C22×C411yescharacteristic
153C2×C22⋊D73—41no—
154C2×C22⋊D73—41no—
155C2×C22⋊D73C2×C814yes—
156C22×Dic73—21no—
157C22×Dic73—21no—
158C22×Dic73—21no—
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73C22×C411yescharacteristic
163C22×Dic73C22×C411yescharacteristic
164C22×Dic73C22×C411yescharacteristic
165C22×Dic73C22×C411yescharacteristic
166C22×Dic73C22×C411yescharacteristic
167C22×Dic73C22×C411yescharacteristic
168C22×Dic73C2411yescharacteristic
169C2×C4×D73—21no—
170C2×C4×D73—21no—
171C2×C4×D73—21no—
172C2×C4×D73—21no—
173C2×C4×D73—21no—
174C2×C4×D73—21no—
175C2×C4×D73—41no—
176C2×C4×D73—41no—
177C2×C4×D73—41no—
178C2×C4×D73—41no—
179C2×C4×D73—41no—
180C2×C4×D73C2×C814yescomplemented
181C4⋊Dic73C2×C814yescomplemented
182#11924007—41no—
183#11924007—41no—
184#11924007C2×C814yescomplemented
185C22⋊Dic73—41no—
186C22⋊Dic73C2×C814yes—
187#11924005—41no—
188#11924005—41no—
189#11924005C2×C814yescomplemented
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C4×Dic73—21no—
196C4×Dic73—21no—
197C4×Dic73—21no—
198C4×Dic73—21no—
199C4×Dic73—21no—
200C4×Dic73—41no—
201C24×C73C22×C411yescharacteristic
202C22×C4×C73C22×C411yescharacteristic
203C22×C4×C73C22×C411yescharacteristic
204C22×C4×C73C22×C411yescharacteristic
205C22×C4×C73C22×C411yescharacteristic
206C22×C4×C73C22×C411yescharacteristic
207C22×C4×C73C22×C411yescharacteristic
208C4⋊C4×C73—41no—
209C22⋊C4×C73—41no—
210C22⋊C4×C73—41no—
211C22⋊C4×C73C2×C814yes—
212C42×C73—41no—
213C23×C73—21no—
214C23×C73—21no—
215C23×C73—21no—
216C23×C73—21no—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73C22×C812yes—
220C23×C73C23×C411yescharacteristic
221C22×D73—21no—
222C22×D73—21no—
223C22×D73—21no—
224C22×D73—21no—
225C22×D73—21no—
226C22×D73—21no—
227C22×D73C22×C812yes—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73C22×C812yes—
245C2×C4×C73C22×C812yes—
246C22⋊D73—44no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—21no—
252C2×Dic73—21no—
253C2×Dic73—21no—
254C2×Dic73—21no—
255C2×Dic73—21no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—21no—
261C2×Dic73—21no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73C22×C812yes—
267C2×Dic73C22×C812yes—
268C2×Dic73C22×C812yes—
269C2×Dic73H(5,𝔽2)11yescharacteristic
270C2×Dic73H(5,𝔽2)11yescharacteristic
271C2×Dic73H(5,𝔽2)11yescharacteristic
272C2×Dic73H(5,𝔽2)11yescharacteristic
273C2×Dic732−1+411yescharacteristic
274C2×Dic732−1+411yescharacteristic
275C4×D73—44no—
276C4×D73—44no—
277C4×D73—41no—
278C4×D73—41no—
279C4×D73—41no—
280C4×D73—41no—
281#10596833—41no—
282#10596833—41no—
283#10596833—41no—
284#10596833—41no—
285#10596833—41no—
286#10596833—41no—
287#10596833—41no—
288#10596833—41no—
289C22×C73—22no—
290C22×C73—22no—
291C22×C73—22no—
292C22×C73—41no—
293C22×C73—41no—
294C22×C73—41no—
295C22×C73—41no—
296C22×C73#51811yescharacteristic
297C22×C73#52011yescharacteristic
298C22×C73#52011yescharacteristic
299C22×C73C23×C811yescharacteristic
300C22×C73#56811yescharacteristic
301C22×C73#56811yescharacteristic
302C22×C73#56811yescharacteristic
303C2×D73—22no—
304C2×D73—22no—
305C2×D73—22no—
306C2×D73—41no—
307C2×D73—41no—
308C2×D73—41no—
309C2×D73—41no—
310C4×C73—22no—
311C4×C73—22no—
312C4×C73—41no—
313C4×C73—41no—
314C4×C73—41no—
315C4×C73—41no—
316Dic73—22no—
317Dic73—22no—
318Dic73—22no—
319Dic73—41no—
320Dic73—41no—
321Dic73—41no—
322Dic73#56011yescharacteristic
323Dic73#56211yescharacteristic
324Dic73#56211yescharacteristic
325Dic73#56311yescharacteristic
326#23314—731nomaximal, Sylow
327C2×C73—42no—
328C2×C73#237611yescharacteristic
329C2×C73#297211yescharacteristic
330C2×C73#297811yescharacteristic
331C2×C73#298811yescharacteristic
332C2×C73#298811yescharacteristic
333C2×C73#299511yescharacteristic
334C2×C73#299511yescharacteristic
335D73—42no—
336C4×#123—731no—
337#1954—731no—
338#1939—731no—
339#1939—731no—
340#1923—731no—
341#1923—731no—
342#1923—731no—
343#1923—731no—
344#1916—731no—
345#1916—731no—
346#1869—731no—
347#1850—731no—
348#1850—731no—
349#1797—731no—
350#1797—731no—
351C73#2331411yescharacteristic, complemented, Sylow
352C23×C8—731no—
353C2×#123—731no—
354C2×C4×D4—731no—
355C22×C42—731no—
356C2×C4⋊C8—731no—
357C2×C4⋊C8—731no—
358C2×C4⋊C8—731no—
359C2×C4⋊C8—731no—
360C2×C4⋊C8—731no—
361C2×C4⋊C8—731no—
362C2×C4⋊C8—731no—
363C2×C22⋊C8—731no—
364C2×C22⋊C8—731no—
365C2×C22⋊C8—731no—
366C2×C22⋊C8—731no—
367C2×C22⋊C8—731no—
368C2×C22⋊C8—731no—
369C2×C22⋊C8—731no—
370C2×C4×C8—731no—
371C2×C4×C8—731no—
372C2×C4×C8—731no—
373#388—731no—
374#388#6440811yescharacteristic
375#387—731no—
376#387—731no—
377#386—731no—
378#385—731no—
379#381—731no—
380C4×C4⋊C4—731no—
381C4×C4⋊C4—731no—
382C4×C22⋊C4—731no—
383C4×C22⋊C4—731no—
384C4×C22⋊C4—731no—
385#336—731no—
386#336—731no—
387#336—731no—
388#336—731no—
389#336—731no—
390#336—731no—
391#336—731no—
392#336—731no—
393#336—731no—
394#336—731no—
395C22×D4—731no—
396C23×C4—731no—
397C23×C4—731no—
398C23×C4—731no—
399C23×C4—731no—
400C22×C8—2921no—
401C22×C8—2921no—
402C22×C8—2921no—
403C22×C8—731no—
404C22×C8—731no—
405C22×C8—731no—
406C22×C8—731no—
407C22×C8—731no—
408C22×C8—731no—
409C22×C8—731no—
410C22×C8—731no—
411#123—738no—
412C4×D4—2921no—
413C4×D4—2921no—
414C2×C4⋊C4—731no—
415C2×C4⋊C4—731no—
416C2×C4⋊C4—731no—
417C2×C4⋊C4—731no—
418C2×C4⋊C4C2×#6440811yescharacteristic
419C2×C22⋊C4—731no—
420C2×C22⋊C4—731no—
421C2×C22⋊C4—731no—
422C2×C22⋊C4—731no—
423C2×C22⋊C4—731no—
424C2×C22⋊C4C2×#6440811yescharacteristic
425C2×C22⋊C4C2×#6440811yescharacteristic
426C2×C22⋊C4C2×#6440811yescharacteristic
427C2×C42—2921no—
428C2×C42—2921no—
429C2×C42—731no—
430C2×C42—731no—
431C2×C42—731no—
432C2×C42—731no—
433C2×C42—731no—
434C2×C42—731no—
435C2×C42C2×#6440811yescharacteristic
436C4⋊C8—2921no—
437C4⋊C8—2921no—
438C4⋊C8—2921no—
439C4⋊C8—2921no—
440C4⋊C8—2921no—
441C4⋊C8—2921no—
442C4⋊C8—2921no—
443C22⋊C8—2921no—
444C22⋊C8—2921no—
445C22⋊C8—2921no—
446C22⋊C8—2921no—
447C22⋊C8—2921no—
448C22⋊C8—2921no—
449C22⋊C8—2921no—
450C4×C8—2921no—
451C4×C8—2921no—
452C4×C8—2921no—
453#95—731no—
454#95—731no—
455#95—731no—
456#95—731no—
457#95—731no—
458#95—731no—
459#95—731no—
460#95—731no—
461#95C2×#6440811yescharacteristic
462#95C2×#6440811yescharacteristic
463C24—731no—
464C24C22×#6440811yescharacteristic
465C2×D4—2921no—
466C2×D4—2921no—
467C2×D4—734no—
468C22×C4—2921no—
469C22×C4—2921no—
470C22×C4—2921no—
471C22×C4—2921no—
472C22×C4—2921no—
473C22×C4—734no—
474C22×C4—731no—
475C22×C4—731no—
476C22×C4—731no—
477C22×C4—731no—
478C22×C4—731no—
479C22×C4—731no—
480C22×C4—731no—
481C22×C4—1461no—
482C22×C4—1461no—
483C22×C4—1461no—
484C22×C4—1461no—
485C22×C4—1461no—
486C22×C4—1461no—
487C22×C4—1461no—
488C22×C4—1461no—
489C22×C4—1461no—
490C22×C4—1461no—
491C22×C4—1461no—
492C22×C4—1461no—
493C22×C4C22×#6440811yescharacteristic
494C22×C4C22×#6440811yescharacteristic
495C22×C4C22×#6440811yescharacteristic
496C22×C4C22×#6440811yescharacteristic
497C22×C4C22×#6440811yescharacteristic
498C22×C4C22×#6440811yescharacteristic
499C2×C8—2924no—
500C2×C8—1461no—
501C2×C8—1461no—
502C2×C8—1461no—
503C2×C8—1461no—
504C2×C8—1461no—
505C2×C8—1461no—
506C2×C8—1461no—
507C2×C8—1461no—
508C2×C8—1461no—
509C2×C8—1461no—
510C2×C8—1461no—
511C2×C8—1461no—
512C2×C8—1461no—
513C2×C8—1461no—
514C2×C8—1461no—
515C2×C8—1461no—
516C2×C8—1461no—
517C2×C8—1461no—
518C2×C8—1461no—
519C2×C8—1461no—
520C2×C8—1461no—
521C2×C8—1461no—
522C2×C8—1461no—
523C2×C8—1461no—
524C4⋊C4—41no—
525C4⋊C4—2921no—
526C4⋊C4—2921no—
527C4⋊C4—734no—
528C4⋊C4—734no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—2921no—
532C22⋊C4—2921no—
533C22⋊C4—2921no—
534C22⋊C4—734no—
535C22⋊C4—734no—
536C22⋊C4#1192403614yes—
537C42—41no—
538C42—2921no—
539C42—1461no—
540C42—1461no—
541C42—1461no—
542C42—1461no—
543C42—1461no—
544C42—1461no—
545C42—1461no—
546C42—1461no—
547C42—1461no—
548C42—1461no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—732no—
556C23—1461no—
557C23—1461no—
558C23—1461no—
559C23—1461no—
560C23—1461no—
561C23—1461no—
562C23C2×#1192403612yes—
563C23C23×#6440811yescharacteristic
564D4—2924no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—2924no—
582C2×C4—2924no—
583C2×C4—2921no—
584C2×C4—2921no—
585C2×C4—2921no—
586C2×C4—2921no—
587C2×C4—2921no—
588C2×C4—2921no—
589C2×C4—2921no—
590C2×C4—2921no—
591C2×C4—731no—
592C2×C4—731no—
593C2×C4—731no—
594C2×C4—731no—
595C2×C4—731no—
596C2×C4—731no—
597C2×C4—732no—
598C2×C4—732no—
599C2×C4—732no—
600C2×C4—1461no—
601C2×C4—1461no—
602C2×C4—1461no—
603C2×C4—1461no—
604C2×C4—1461no—
605C2×C4—1461no—
606C2×C4—1461no—
607C2×C4—1461no—
608C2×C4—1461no—
609C2×C4—1461no—
610C2×C4—1461no—
611C2×C4—1461no—
612C2×C4—1461no—
613C2×C4—1461no—
614C2×C4—1461no—
615C2×C4C2×#1192403612yes—
616C2×C4C2×#1192403612yes—
617C8—2921no—
618C8—2921no—
619C8—2921no—
620C8—2921no—
621C8—2921no—
622C8—2921no—
623C8—2921no—
624C8—2921no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—2921no—
633C22—2921no—
634C22—2921no—
635C22—2921no—
636C22—1462no—
637C22—1462no—
638C22—1462no—
639C22#1798965411yescharacteristic
640C22#1798965611yescharacteristic
641C22#1798965611yescharacteristic
642C22C22×#1192403611yescharacteristic
643C22#1798966511yescharacteristic
644C22#1798966611yescharacteristic
645C22#1798966611yescharacteristic
646C4—22no—
647C4—22no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—2921no—
653C4—2921no—
654C4—2921no—
655C4—731no—
656C4—731no—
657C4—731no—
658C4—731no—
659C4—1462no—
660C4—1462no—
661C4—1462no—
662C2—42no—
663C2—2922no—
664C2#2262647111yescharacteristic
665C2#2262677911yescharacteristic
666C2#2262680811yescharacteristic
667C2#2262684711yescharacteristic
668C2#2262684811yescharacteristic
669C2#2262688611yescharacteristic
670C2#2262688711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutatorC22×C73C23×C8
Fitting#388×C73C4
socleC23×C73C23×C4
prime radicalC22×C22⋊D73C2×C4
cosocleC22×Dic73C24
hypercenter#388#64408
hypocenterC73#23314
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #22626030C2semidirect
3. #22626029C2semidirect
4. #22626003C2semidirect
5. #22626002C2semidirect
6. #22626001C2semidirect
7. #22626000C2semidirect
8. #22625987C2semidirect
9. #22625985C2semidirect
11. #22625875C2semidirect
12. #22625874C2semidirect
13. #22625788C2semidirect
14. #22625786C2semidirect
92. #14556573C8semidirect
180. C2×C4×D73C2×C8semidirect
181. C4⋊Dic73C2×C8semidirect
184. #11924007C2×C8semidirect
189. #11924005C2×C8semidirect
351. C73#23314semidirect

Maximal subgroups

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

subgroupindex
#226260542
#226260302
#226260292
#226260032
#226260022
#226260012
#226260002
#226259872
#226259852
#226259062
#226258752
#226258742
#226257882
#226257862
#226124582
#2331473