Finite Group Databasebeta

← #34022321

Subgroups — #34022321

Order 18688.

858 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989612C211yesmaximal, characteristic, complemented
2C2×#17989611C211yesmaximal, characteristic, complemented
3#22626054C211yesmaximal, characteristic
4#22626054C211yesmaximal, characteristic
5#22626030C211yesmaximal, characteristic, complemented
6#22626030C211yesmaximal, characteristic, complemented
7#22626003C211yesmaximal, characteristic, complemented
8#22626002C211yesmaximal, characteristic, complemented
9#22626001C211yesmaximal, characteristic, complemented
10#22626000C211yesmaximal, characteristic, complemented
11#22625716C211yesmaximal, characteristic, complemented
12#22625661C211yesmaximal, characteristic, complemented
13#22625660C211yesmaximal, characteristic, complemented
14C42×#10596833C211yesmaximal, characteristic, complemented
15#22612391C211yesmaximal, characteristic
16#17989612—24no—
17#17989611—24no—
18C2×#14556658C2211yescharacteristic
19C2×#14556658C2211yescharacteristic
20C2×#14556658C2211yescharacteristic
21C2×#14556658C2211yescharacteristic
22C2×C4⋊#10596833C2211yescharacteristic
23C2×C4⋊#10596833C2211yescharacteristic
24C2×#14556648C2211yescharacteristic
25C2×#14556648C2211yescharacteristic
26C2×#14556648C2211yescharacteristic
27C2×#14556648C2211yescharacteristic
28C2×C22⋊#10596833C2211yescharacteristic
29C2×C22⋊#10596833C2211yescharacteristic
30C2×C22⋊#10596833C2211yescharacteristic
31C2×C22⋊#10596833C2211yescharacteristic
32C2×#14556646C2211yescharacteristic
33C2×#14556646C2211yescharacteristic
34C2×C4×#10596833C2211yescharacteristic
35C2×C4×#10596833C2211yescharacteristic
36C2×C4×#10596833C2211yescharacteristic
37C2×C4×#10596833C2211yescharacteristic
38C2×C4×#10596833C2211yescharacteristic
39C2×C4×#10596833C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44#17989453C2211yescharacteristic
45#17989453C2211yescharacteristic
46C2×#14556551C2211yescharacteristic
47C2×#14556549C2211yescharacteristic
48C2×#14556547C2211yescharacteristic
49#17988487C411yescharacteristic
50#17988487C411yescharacteristic
51#17988484C411yescharacteristic
52#17988482C411yescharacteristic
53#17988480C411yescharacteristic
54#17988478C411yescharacteristic
55#17988476C411yescharacteristic
56#17988438C2211yescharacteristic
57C22⋊C4×Dic73C2211yescharacteristic
58#17988434C2211yescharacteristic
59C42×Dic73C2211yescharacteristic
60#388×C73C411yescharacteristic
61C22×#10596833C2311yescharacteristic
62C22×#10596833C2311yescharacteristic
63C22×#10596833C2311yescharacteristic
64C22×#10596833C2311yescharacteristic
65C22×#10596833C2311yescharacteristic
66C22×#10596833C2311yescharacteristic
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69#14556658—22no—
70#14556658—22no—
71#14556658—22no—
72#14556658—22no—
73C4⋊#10596833—22no—
74C4⋊#10596833—22no—
75#14556648—22no—
76#14556648—22no—
77#14556648—22no—
78#14556648—22no—
79C22⋊#10596833—22no—
80C22⋊#10596833—22no—
81C22⋊#10596833—22no—
82C22⋊#10596833—22no—
83#14556646—22no—
84#14556646—22no—
85C4×#10596833—22no—
86C4×#10596833—22no—
87C4×#10596833—22no—
88C4×#10596833—22no—
89C4×#10596833—22no—
90C4×#10596833D414yescomplemented
91C22×C22⋊D73C2×C411yescharacteristic
92C23×Dic73C2311yescharacteristic
93C22×C4×D73C2311yescharacteristic
94#14556551—22no—
95#14556551—22no—
96#14556549—22no—
97#14556549—22no—
98#14556547—22no—
99#14556547—22no—
100C2×C4⋊Dic73C2×C411yescharacteristic
101C2×#11924007C2×C411yescharacteristic
102C2×#11924007C2×C411yescharacteristic
103C2×#11924007C2×C411yescharacteristic
104C2×#11924007C2×C411yescharacteristic
105C2×#11924007C2×C411yescharacteristic
106C2×C22⋊Dic73C2×C411yescharacteristic
107C2×C22⋊Dic73C2×C411yescharacteristic
108C2×#11924005C2×C411yescharacteristic
109C2×#11924005C2×C411yescharacteristic
110C2×#11924005C2×C411yescharacteristic
111C2×#11924005C2×C411yescharacteristic
112C2×#11924005C2×C411yescharacteristic
113C2×C4×Dic73C2×C411yescharacteristic
114C2×C4×Dic73C2×C411yescharacteristic
115C2×C4×Dic73C2×C411yescharacteristic
116C2×C4×Dic73C2311yescharacteristic
117C2×C4×Dic73C2311yescharacteristic
118C2×C4×Dic73C2311yescharacteristic
119C2×C4×Dic73C2311yescharacteristic
120C2×C4×Dic73C2311yescharacteristic
121#14556498C2×C411yescharacteristic
122#14556498C2×C411yescharacteristic
123#14556498C2×C411yescharacteristic
124#14556498C2×C411yescharacteristic
125C2×C4⋊C4×C73C2×C411yescharacteristic
126C2×C22⋊C4×C73C2×C411yescharacteristic
127C2×C22⋊C4×C73C2×C411yescharacteristic
128C2×C22⋊C4×C73C2×C411yescharacteristic
129C2×C42×C73C2×C411yescharacteristic
130#95×C73C2×C411yescharacteristic
131#95×C73C2×C411yescharacteristic
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—21no—
152C2×#10596833C2×D412yes—
153C2×#10596833C2×D412yes—
154C2×#10596833#4112yes—
155C2×#10596833#4112yes—
156C23×D73C22×C411yescharacteristic
157C2×C22⋊D73—22no—
158C2×C22⋊D73—22no—
159C2×C22⋊D73—22no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73C22×C411yescharacteristic
167C22×Dic73C22×C411yescharacteristic
168C22×Dic73C22×C411yescharacteristic
169C22×Dic73C22×C411yescharacteristic
170C22×Dic73C22×C411yescharacteristic
171C22×Dic73C22×C411yescharacteristic
172C22×Dic73C2411yescharacteristic
173C2×C4×D73—21no—
174C2×C4×D73—21no—
175C2×C4×D73—21no—
176C2×C4×D73—21no—
177C2×C4×D73—21no—
178C2×C4×D73—21no—
179C4⋊Dic73—22no—
180#11924007—22no—
181#11924007—22no—
182#11924007—22no—
183#11924007—22no—
184#11924007—22no—
185C22⋊Dic73—22no—
186C22⋊Dic73—22no—
187#11924005—22no—
188#11924005—22no—
189#11924005—22no—
190#11924005—22no—
191#11924005—22no—
192C4×Dic73—22no—
193C4×Dic73—22no—
194C4×Dic73—22no—
195C4×Dic73—21no—
196C4×Dic73—21no—
197C4×Dic73—21no—
198C4×Dic73—21no—
199C4×Dic73—21no—
200C4×Dic73—21no—
201C4×Dic73C2×D412yes—
202C4×Dic73#4112yes—
203C4×Dic73#4112yes—
204C4×Dic73#4112yes—
205C24×C73C22×C411yescharacteristic
206C22×C4×C73C22×C411yescharacteristic
207C22×C4×C73C22×C411yescharacteristic
208C22×C4×C73C22×C411yescharacteristic
209C22×C4×C73C22×C411yescharacteristic
210C22×C4×C73C22×C411yescharacteristic
211C22×C4×C73C22×C411yescharacteristic
212C4⋊C4×C73—22no—
213C22⋊C4×C73—22no—
214C22⋊C4×C73—22no—
215C22⋊C4×C73—22no—
216C42×C73—22no—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73—21no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73C23×C411yescharacteristic
225C22×D73—21no—
226C22×D73—21no—
227C22×D73—21no—
228C22×D73—21no—
229C22×D73—21no—
230C22×D73—21no—
231C22×D73—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×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73#11712yes—
248C2×C4×C73C4×D412yes—
249C2×C4×C73#13112yes—
250C22⋊D73—44no—
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—21no—
263C2×Dic73—21no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73—41no—
267C2×Dic73—41no—
268C2×Dic73#11712yes—
269C2×Dic73C4×D412yes—
270C2×Dic73#13112yes—
271C2×Dic73#13112yes—
272C2×Dic73#13112yes—
273C2×Dic73C22×D411yescharacteristic
274C2×Dic73C2×#4111yescharacteristic
275C2×Dic73C2×#4111yescharacteristic
276C2×Dic73C2×#4111yescharacteristic
277C2×Dic73C2×#4111yescharacteristic
278C2×Dic73C2×#4111yescharacteristic
279C4×D73—41no—
280C4×D73—41no—
281C4×D73—41no—
282C4×D73—41no—
283#10596833—22no—
284#10596833—22no—
285#10596833—22no—
286#10596833—22no—
287#10596833—41no—
288#10596833—41no—
289#10596833—41no—
290#10596833—41no—
291C22×C73—41no—
292C22×C73—41no—
293C22×C73—41no—
294C22×C73—41no—
295C22×C73—41no—
296C22×C73—41no—
297C22×C73—41no—
298C22×C73C2×#11711yescharacteristic
299C22×C73C2×C4×D411yescharacteristic
300C22×C73C4×#4111yescharacteristic
301C22×C73C2×#13111yescharacteristic
302C22×C73C2×#13111yescharacteristic
303C22×C73C2×#13111yescharacteristic
304C22×C73C2×#13111yescharacteristic
305C2×D73—41no—
306C2×D73—41no—
307C2×D73—41no—
308C2×D73—41no—
309C2×D73—41no—
310C2×D73—41no—
311C2×D73—41no—
312C4×C73—22no—
313C4×C73—22no—
314C4×C73—22no—
315C4×C73—41no—
316C4×C73—41no—
317C4×C73—41no—
318Dic73—22no—
319Dic73—22no—
320Dic73—41no—
321Dic73—41no—
322Dic73—41no—
323Dic73#43314yescomplemented
324Dic73#52911yescharacteristic
325Dic73#52911yescharacteristic
326Dic73#53211yescharacteristic
327Dic73#53211yescharacteristic
328#21266—731nomaximal, Sylow
329C2×C73—81no—
330C2×C73#229311yescharacteristic
331C2×C73C2×#43311yescharacteristic
332C2×C73#292211yescharacteristic
333C2×C73#293111yescharacteristic
334C2×C73#293111yescharacteristic
335C2×C73#296611yescharacteristic
336C2×C73#296611yescharacteristic
337D73—81no—
338C2×#433—731no—
339C2×#433—731no—
340#2293—731no—
341#1954—731no—
342#1954—731no—
343#1939—731no—
344#1939—731no—
345#1923—731no—
346#1923—731no—
347#1923—731no—
348#1923—731no—
349#1767—731no—
350#1750—731no—
351#1750—731no—
352C42×C8—731no—
353C73#2126611yescharacteristic, complemented, Sylow
354C2×C4×D4—731no—
355C2×#117—731no—
356C2×#117—731no—
357#433—1464no—
358#433—1464no—
359C2×C4⋊C8—731no—
360C2×C4⋊C8—731no—
361C2×C4⋊C8—731no—
362C2×C4⋊C8—731no—
363C2×C4⋊C8—731no—
364C2×C4⋊C8—731no—
365C2×C22⋊C8—731no—
366C2×C22⋊C8—731no—
367C2×C22⋊C8—731no—
368C2×C22⋊C8—731no—
369C2×C22⋊C8—731no—
370C2×C22⋊C8—731no—
371C2×C22⋊C8—731no—
372C2×C22⋊C8—731no—
373C2×#97—731no—
374C2×#97—731no—
375C2×C4×C8—731no—
376C2×C4×C8—731no—
377C2×C4×C8—731no—
378C2×C4×C8—731no—
379C2×C4×C8—731no—
380C2×C4×C8—731no—
381#390—731no—
382#390—731no—
383#389—731no—
384#389—731no—
385#388—731no—
386#388—731no—
387#388—731no—
388#388#6440811yescharacteristic
389C4×C4⋊C4—731no—
390C4×C22⋊C4—731no—
391C4×C22⋊C4—731no—
392C43—731no—
393#336—731no—
394#336—731no—
395#336—731no—
396#336—731no—
397#336—731no—
398#336—731no—
399C22×D4—731no—
400C23×C4—731no—
401C23×C4—731no—
402C22×C8—731no—
403C22×C8—731no—
404C22×C8—731no—
405C22×C8—731no—
406C22×C8—731no—
407C22×C8—731no—
408C22×C8—731no—
409C22×C8—731no—
410C4×D4—1462no—
411C4×D4—1462no—
412#117—1462no—
413#117—1462no—
414#117—1462no—
415#117—1462no—
416C2×C4⋊C4—731no—
417C2×C4⋊C4—731no—
418C2×C4⋊C4—731no—
419C2×C4⋊C4—731no—
420C2×C4⋊C4—731no—
421C2×C4⋊C4—731no—
422C2×C4⋊C4C2×#6440811yescharacteristic
423C2×C22⋊C4—731no—
424C2×C22⋊C4—731no—
425C2×C22⋊C4—731no—
426C2×C22⋊C4—731no—
427C2×C22⋊C4—731no—
428C2×C22⋊C4—731no—
429C2×C22⋊C4—731no—
430C2×C22⋊C4C2×#6440811yescharacteristic
431C2×C22⋊C4C2×#6440811yescharacteristic
432C2×C22⋊C4C2×#6440811yescharacteristic
433C2×C42—731no—
434C2×C42—731no—
435C2×C42—731no—
436C2×C42—731no—
437C2×C42—731no—
438C2×C42—731no—
439C2×C42—731no—
440C2×C42—731no—
441C2×C42C2×#6440811yescharacteristic
442C4⋊C8—1462no—
443C4⋊C8—1462no—
444C4⋊C8—1462no—
445C4⋊C8—1462no—
446C4⋊C8—1462no—
447C4⋊C8—1462no—
448C22⋊C8—1462no—
449C22⋊C8—1462no—
450C22⋊C8—1462no—
451C22⋊C8—1462no—
452C22⋊C8—1462no—
453C22⋊C8—1462no—
454C22⋊C8—1462no—
455C22⋊C8—1462no—
456#97—1462no—
457#97—1462no—
458C4×C8—734no—
459C4×C8—1462no—
460C4×C8—1462no—
461C4×C8—1462no—
462C4×C8—1462no—
463C4×C8—1462no—
464#95—731no—
465#95—731no—
466#95—731no—
467#95—731no—
468#95C2×#6440811yescharacteristic
469#95C2×#6440811yescharacteristic
470C24—731no—
471C24C22×#6440811yescharacteristic
472C2×D4—1462no—
473C2×D4—1462no—
474C2×D4—1462no—
475C22×C4—731no—
476C22×C4—731no—
477C22×C4—731no—
478C22×C4—731no—
479C22×C4—731no—
480C22×C4—731no—
481C22×C4—731no—
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×C4—1461no—
494C22×C4C22×#6440811yescharacteristic
495C22×C4C22×#6440811yescharacteristic
496C22×C4C22×#6440811yescharacteristic
497C22×C4C22×#6440811yescharacteristic
498C22×C4C22×#6440811yescharacteristic
499C22×C4C22×#6440811yescharacteristic
500C2×C8—732no—
501C2×C8—732no—
502C2×C8—732no—
503C2×C8—732no—
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—22no—
525C4⋊C4—1462no—
526C4⋊C4—1462no—
527C4⋊C4—1462no—
528C4⋊C4—1462no—
529C4⋊C4—1462no—
530C4⋊C4—1462no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—1462no—
535C22⋊C4—1462no—
536C22⋊C4—1462no—
537C22⋊C4—1462no—
538C22⋊C4—1462no—
539C22⋊C4—1462no—
540C22⋊C4—1462no—
541C42—22no—
542C42—732no—
543C42—732no—
544C42—732no—
545C42—732no—
546C42—1461no—
547C42—1461no—
548C42—1461no—
549C42—1461no—
550C42—1462no—
551C42—1462no—
552C42—1462no—
553C42—1461no—
554C42—1461no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—1461no—
563C23—1461no—
564C23—1461no—
565C23—1461no—
566C23—1461no—
567C23—1461no—
568C23—1461no—
569C23C23×#6440811yescharacteristic
570D4—2924no—
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—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—2921no—
587C2×C4—2921no—
588C2×C4—2921no—
589C2×C4—2921no—
590C2×C4—2921no—
591C2×C4—2921no—
592C2×C4—2921no—
593C2×C4—2921no—
594C2×C4—732no—
595C2×C4—731no—
596C2×C4—731no—
597C2×C4—731no—
598C2×C4—731no—
599C2×C4—731no—
600C2×C4—731no—
601C2×C4—732no—
602C2×C4—732no—
603C2×C4—732no—
604C2×C4—732no—
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×C4—1461no—
616C2×C4—1461no—
617C2×C4—1461no—
618C2×C4#1455667012yes—
619C2×C4D4×#6440812yes—
620C2×C4#1455667812yes—
621C8—2921no—
622C8—2921no—
623C8—2921no—
624C8—2921no—
625C8—1462no—
626C8—1462no—
627C8—1462no—
628C8—1462no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—2921no—
637C22—2921no—
638C22—2921no—
639C22—2921no—
640C22—2921no—
641C22—2921no—
642C22—2921no—
643C22C2×#1455667011yescharacteristic
644C22C2×D4×#6440811yescharacteristic
645C22#41×#6440811yescharacteristic
646C22C2×#1455667811yescharacteristic
647C22D73⋊#13111yescharacteristic
648C22D73⋊#13111yescharacteristic
649C22D73⋊#13111yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—2921no—
657C4—2921no—
658C4—2921no—
659C4—734no—
660C4—731no—
661C4—731no—
662C4—731no—
663C4—731no—
664C4—1462no—
665C4—1462no—
666C2—81no—
667C2—5841no—
668C2#2262638811yescharacteristic
669C2D73⋊#43311yescharacteristic
670C2#2262661411yescharacteristic
671C2#2262665411yescharacteristic
672C2#2262665511yescharacteristic
673C2#2262674611yescharacteristic
674C2#2262674911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#388×C73C4
prime radicalC22×C22⋊D73C2×C4
cosocleC22×Dic73C24
hypercenter#388#64408
hypocenterC73#21266
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#17989612C2semidirect
2. C2×#17989611C2semidirect
5. #22626030C2semidirect
6. #22626030C2semidirect
7. #22626003C2semidirect
8. #22626002C2semidirect
9. #22626001C2semidirect
10. #22626000C2semidirect
11. #22625716C2semidirect
12. #22625661C2semidirect
13. #22625660C2semidirect
14. C42×#10596833C2semidirect
90. C4×#10596833D4semidirect
323. Dic73#433semidirect
353. C73#21266semidirect

Maximal subgroups

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

subgroupindex
C2×#179896122
C2×#179896112
#226260542
#226260302
#226260032
#226260022
#226260012
#226260002
#226257162
#226256612
#226256602
C42×#105968332
#226123912
#2126673