Finite Group Databasebeta

← #33096347

Subgroups — #33096347

Order 18688.

790 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988647C211yesmaximal, characteristic
2C2×#17988646C211yesmaximal, characteristic
3#22612411C211yesmaximal, characteristic
4#22610655C211yesmaximal, characteristic, complemented
5#22610653C211yesmaximal, characteristic, complemented
6#22610652C211yesmaximal, characteristic, complemented
7#22610651C211yesmaximal, characteristic, complemented
8#22610649C211yesmaximal, characteristic, complemented
9#22610648C211yesmaximal, characteristic, complemented
10#22610646C211yesmaximal, characteristic, complemented
11#22609914C211yesmaximal, characteristic
12#22609912C211yesmaximal, characteristic
13#22609910C211yesmaximal, characteristic
14#22609908C211yesmaximal, characteristic
15C73×#1939C211yesmaximal, characteristic, complemented
16C2×#14556548C2211yescharacteristic
17C2×#14556548C2211yescharacteristic
18C2×C42×D73C2211yescharacteristic
19#17988647—24no—
20#17988646—24no—
21C2×C4⋊#10596831C2211yescharacteristic
22C2×C4⋊#10596831C2211yescharacteristic
23C2×C4⋊#10596831C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×#14556520C2211yescharacteristic
26C2×#14556520C2211yescharacteristic
27C2×#14556520C2211yescharacteristic
28C2×#14556520C2211yescharacteristic
29C2×#14556520C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556502C2211yescharacteristic
35C2×#14556501C2211yescharacteristic
36C2×C8×Dic73C2211yescharacteristic
37#17988484C411yescharacteristic
38#17988484C411yescharacteristic
39#17988482C411yescharacteristic
40#17988482C411yescharacteristic
41#17988461C411yescharacteristic
42#17988461C411yescharacteristic
43#17988458C411yescharacteristic
44#17988458C411yescharacteristic
45C4×#11924007C2211yescharacteristic
46C4×#11924007C2211yescharacteristic
47C4×C4⋊Dic73C2211yescharacteristic
48#17988342C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C2×C4⋊C8×C73C2211yescharacteristic
55C2×C4⋊C8×C73C2211yescharacteristic
56C2×C4⋊C8×C73C2211yescharacteristic
57C2×C4×C8×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×C4×D73C2×C411yescharacteristic
62C22×C4×D73C2×C411yescharacteristic
63C22×C4×D73C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68#14556548—41no—
69#14556548—41no—
70#14556548D414yes—
71#14556548Q814yes—
72C2×C4⋊Dic73C2×C411yescharacteristic
73C2×C4⋊Dic73C2×C411yescharacteristic
74C2×#11924007C2×C411yescharacteristic
75C2×#11924007C2×C411yescharacteristic
76C2×#11924007C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C2×#11924007C2×C411yescharacteristic
80C2×#11924007C2×C411yescharacteristic
81C2×#11924007C2×C411yescharacteristic
82C2×#11924005C2×C411yescharacteristic
83C2×#11924005C2×C411yescharacteristic
84C2×#11924005C2×C411yescharacteristic
85C2×#11924005C2×C411yescharacteristic
86C2×C4×Dic73C2×C411yescharacteristic
87C2×C4×Dic73C2×C411yescharacteristic
88C2×C4×Dic73C2311yescharacteristic
89C2×C4×Dic73C2311yescharacteristic
90C2×C4×Dic73C2311yescharacteristic
91C42×D73—41no—
92C42×D73—41no—
93C4⋊#10596831—22no—
94C4⋊#10596831—41no—
95C4⋊#10596831—41no—
96#14556520—22no—
97#14556520—22no—
98#14556520—41no—
99#14556520—41no—
100#14556520—41no—
101#14556520—41no—
102#14556503—22no—
103#14556503—22no—
104#14556503—22no—
105#14556503—22no—
106#14556502—22no—
107#14556501—22no—
108C8×Dic73—22no—
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115C22×C8×C73C2311yescharacteristic
116C22×C8×C73C2311yescharacteristic
117C22×C8×C73C2311yescharacteristic
118C22×C8×C73C2311yescharacteristic
119C2×C4⋊C4×C73C2×C411yescharacteristic
120C2×C4⋊C4×C73C2×C411yescharacteristic
121C2×C42×C73C2311yescharacteristic
122C2×C42×C73C2311yescharacteristic
123C2×C42×C73C2311yescharacteristic
124C4⋊C8×C73—22no—
125C4⋊C8×C73—41no—
126C4⋊C8×C73—41no—
127C4×C8×C73—22no—
128#95×C73C2×C411yescharacteristic
129#95×C73C2×C411yescharacteristic
130C23×D73C22×C411yescharacteristic
131C22×Dic73C22×C411yescharacteristic
132C22×Dic73C22×C411yescharacteristic
133C22×Dic73C22×C411yescharacteristic
134C22×Dic73C22×C411yescharacteristic
135C22×Dic73C22×C411yescharacteristic
136C22×Dic73C22×C411yescharacteristic
137C22×Dic73C22×C411yescharacteristic
138C2×C4×D73—21no—
139C2×C4×D73—21no—
140C2×C4×D73—21no—
141C2×C4×D73—21no—
142C2×C4×D73—22no—
143C2×C4×D73—22no—
144C2×C4×D73—41no—
145C2×C4×D73—41no—
146C2×C4×D73—41no—
147C2×C4×D73—41no—
148C2×C4×D73C2×D412yes—
149C2×C4×D73C2×Q812yes—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C4⋊Dic73—22no—
163C4⋊Dic73—41no—
164#11924007—22no—
165#11924007—22no—
166#11924007—41no—
167#11924007—41no—
168#11924007—41no—
169#11924007—41no—
170#11924007C4⋊C414yes—
171#11924007C4⋊C414yes—
172#11924005—41no—
173#11924005—41no—
174#11924005C4⋊C414yes—
175#11924005C4⋊C414yes—
176C4×Dic73—21no—
177C4×Dic73—21no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—41no—
181C4×Dic73—41no—
182C4×Dic73C2×D412yes—
183C4×Dic73C2×Q812yes—
184C22×C4×C73C22×C411yescharacteristic
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C22×C411yescharacteristic
188C22×C4×C73C22×C411yescharacteristic
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C2411yescharacteristic
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C4⋊C4×C73—22no—
204C4⋊C4×C73—41no—
205C42×C73—21no—
206C42×C73—21no—
207C42×C73—21no—
208C42×C73—21no—
209C42×C73C2×D412yes—
210C42×C73C2×Q812yes—
211C23×C73C23×C411yescharacteristic
212C22×D73—21no—
213C22×D73—21no—
214C22×D73—21no—
215C22×D73—21no—
216C22×D73—21no—
217C22×D73—21no—
218C22×D73C2×C4⋊C412yes—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
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×C73C2×C4⋊C412yes—
235C2×C4×C73C2×C4⋊C412yes—
236C2×C4×C73#13112yes—
237C2×C4×C73C22×D411yescharacteristic
238C2×C4×C73C22×Q811yescharacteristic
239C2×C4×C73H(5,𝔽2)11yescharacteristic
240C2×C4×C73H(5,𝔽2)11yescharacteristic
241C2×C4×C732−1+411yescharacteristic
242C2×C4×C732−1+411yescharacteristic
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
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×Dic73C2×C4⋊C412yes—
261C2×Dic73C2×C4⋊C412yes—
262C2×Dic73C2×C4⋊C412yes—
263C2×Dic73#13112yes—
264C4×D73—22no—
265C4×D73—22no—
266C4×D73—22no—
267C4×D73—22no—
268C4×D73—44no—
269C4×D73—44no—
270C8×C73—41no—
271C8×C73—41no—
272C8×C73—41no—
273C8×C73—41no—
274#10596831—41no—
275#10596831—41no—
276#10596831—41no—
277#10596831—41no—
278C22×C73C22×C4⋊C411yescharacteristic
279C22×C73#51811yescharacteristic
280C22×C73#51911yescharacteristic
281C22×C73C2×#13111yescharacteristic
282C22×C73C2×#13111yescharacteristic
283C22×C73#56811yescharacteristic
284C22×C73#56811yescharacteristic
285C2×D73—22no—
286C2×D73—22no—
287C2×D73—22no—
288C2×D73—41no—
289C2×D73—41no—
290C2×D73—41no—
291C2×D73—41no—
292C4×C73—22no—
293C4×C73—22no—
294C4×C73—22no—
295C4×C73—41no—
296C4×C73—41no—
297C4×C73—41no—
298C4×C73#53711yescharacteristic
299C4×C73#53711yescharacteristic
300C4×C73#54411yescharacteristic
301C4×C73#54411yescharacteristic
302Dic73—22no—
303Dic73—22no—
304Dic73—22no—
305Dic73—22no—
306Dic73—41no—
307Dic73—41no—
308Dic73—41no—
309#21958—731nomaximal, Sylow
310C2×C73#231611yescharacteristic
311C2×C73#290611yescharacteristic
312C2×C73#290611yescharacteristic
313C2×C73#297711yescharacteristic
314C2×C73#297811yescharacteristic
315C2×C73#298511yescharacteristic
316C2×C73#298511yescharacteristic
317D73—42no—
318C2×#433—731no—
319C2×#433—731no—
320#2296—731no—
321#1940—731no—
322#1940—731no—
323#1940—731no—
324#1940—731no—
325#1939—731no—
326#1939—731no—
327#1939—731no—
328#1939D7311yescharacteristic, complemented
329#1798—731no—
330#1798—731no—
331#1797—731no—
332#1797—731no—
333C73#2195811yescharacteristic, complemented, Sylow
334C2×#117—731no—
335C2×#117—731no—
336C22×C42—731no—
337#433—1464no—
338#433—1464no—
339C2×C4⋊C8—731no—
340C2×C4⋊C8—731no—
341C2×C4⋊C8—731no—
342C2×C4⋊C8—731no—
343C2×C4⋊C8—731no—
344C2×C4⋊C8—731no—
345C2×C4⋊C8—731no—
346C2×C4⋊C8—731no—
347C2×C4⋊C8—731no—
348C2×C4⋊C8C2×D7311yescharacteristic
349C2×C4⋊C8C2×D7311yescharacteristic
350C2×C4⋊C8C2×D7311yescharacteristic
351C2×C22⋊C8—731no—
352C2×C22⋊C8—731no—
353C2×C22⋊C8—731no—
354C2×C22⋊C8—731no—
355C2×#97—731no—
356C2×#97—731no—
357C2×C4×C8—731no—
358C2×C4×C8C2×D7311yescharacteristic
359#389—731no—
360#389—731no—
361#389—731no—
362#389—731no—
363#385—731no—
364#385—731no—
365#385—731no—
366#385—731no—
367C4×C4⋊C4—731no—
368C4×C4⋊C4—731no—
369C4×C4⋊C4—731no—
370C4×C4⋊C4C2×D7311yescharacteristic
371#336—731no—
372#336—731no—
373#336—731no—
374#336—731no—
375#336—731no—
376#336—731no—
377#336C2×D7311yescharacteristic
378#336C2×D7311yescharacteristic
379C23×C4—731no—
380C23×C4—731no—
381C23×C4—731no—
382C22×C8—731no—
383C22×C8—731no—
384C22×C8—731no—
385C22×C8—731no—
386C22×C8C22×D7311yescharacteristic
387C22×C8C22×D7311yescharacteristic
388C22×C8C22×D7311yescharacteristic
389C22×C8C22×D7311yescharacteristic
390#117—2921no—
391#117—2921no—
392#117—734no—
393#117—734no—
394C2×C4⋊C4—731no—
395C2×C4⋊C4—731no—
396C2×C4⋊C4—731no—
397C2×C4⋊C4—731no—
398C2×C4⋊C4—731no—
399C2×C4⋊C4—731no—
400C2×C4⋊C4—731no—
401C2×C4⋊C4—731no—
402C2×C4⋊C4—731no—
403C2×C4⋊C4—731no—
404C2×C4⋊C4C4×D7311yescharacteristic
405C2×C4⋊C4C4×D7311yescharacteristic
406C2×C22⋊C4—731no—
407C2×C22⋊C4—731no—
408C2×C22⋊C4—731no—
409C2×C22⋊C4—731no—
410C2×C42—2921no—
411C2×C42—2921no—
412C2×C42—731no—
413C2×C42—731no—
414C2×C42—731no—
415C2×C42—731no—
416C2×C42—731no—
417C2×C42C22×D7311yescharacteristic
418C2×C42C22×D7311yescharacteristic
419C2×C42C22×D7311yescharacteristic
420C4⋊C8—22no—
421C4⋊C8—41no—
422C4⋊C8—41no—
423C4⋊C8—2921no—
424C4⋊C8—2921no—
425C4⋊C8—2921no—
426C4⋊C8—2921no—
427C4⋊C8—2921no—
428C4⋊C8—2921no—
429C4⋊C8—1462no—
430C4⋊C8—1462no—
431C4⋊C8—1462no—
432C22⋊C8—1462no—
433C22⋊C8—1462no—
434C22⋊C8—1462no—
435C22⋊C8—1462no—
436#97—1462no—
437#97—1462no—
438C4×C8—22no—
439C4×C8—1462no—
440#95—731no—
441#95—731no—
442#95—731no—
443#95—731no—
444#95—731no—
445#95—731no—
446#95C4×D7311yescharacteristic
447#95C4×D7311yescharacteristic
448C24—731no—
449C22×C4—2921no—
450C22×C4—2921no—
451C22×C4—2921no—
452C22×C4—2921no—
453C22×C4—731no—
454C22×C4—731no—
455C22×C4—731no—
456C22×C4—731no—
457C22×C4—732no—
458C22×C4—732no—
459C22×C4—731no—
460C22×C4—731no—
461C22×C4—731no—
462C22×C4—1462no—
463C22×C4—1462no—
464C22×C4—1461no—
465C22×C4—1461no—
466C22×C4—1461no—
467C22×C4—1461no—
468C22×C4C2×C4×D7311yescharacteristic
469C22×C4C2×C4×D7311yescharacteristic
470C22×C4C2×C4×D7311yescharacteristic
471C22×C4C2×C4×D7311yescharacteristic
472C22×C4C2×C4×D7311yescharacteristic
473C22×C4C2×C4×D7311yescharacteristic
474C22×C4C23×D7311yescharacteristic
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8—1461no—
492C2×C8—1461no—
493C2×C8—1461no—
494C2×C8—1461no—
495C2×C8—1461no—
496C2×C8—1461no—
497C2×C8—1461no—
498C2×C8—1461no—
499C4⋊C4—22no—
500C4⋊C4—41no—
501C4⋊C4—2921no—
502C4⋊C4—2921no—
503C4⋊C4—2921no—
504C4⋊C4—2921no—
505C4⋊C4—2921no—
506C4⋊C4—734no—
507C4⋊C4—734no—
508C4⋊C4—1462no—
509C4⋊C4—1462no—
510C4⋊C4—1462no—
511C22⋊C4—2921no—
512C22⋊C4—2921no—
513C22⋊C4—734no—
514C22⋊C4—734no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—2921no—
520C42—2921no—
521C42—732no—
522C42—732no—
523C42—1461no—
524C42—1461no—
525C42—1461no—
526C42—1461no—
527C42D4×D7312yes—
528C42Q8×D7312yes—
529C23—732no—
530C23—1461no—
531C23—1461no—
532C23—1461no—
533C23—1461no—
534C23—1461no—
535C23—1461no—
536C23C22×C4×D7311yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—2924no—
553C2×C4—2924no—
554C2×C4—732no—
555C2×C4—732no—
556C2×C4—732no—
557C2×C4—732no—
558C2×C4—1461no—
559C2×C4—1461no—
560C2×C4—1461no—
561C2×C4—1461no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4—1461no—
571C2×C4—1461no—
572C2×C4—1461no—
573C2×C4—1461no—
574C2×C4—1461no—
575C2×C4—1462no—
576C2×C4—1462no—
577C2×C4—1462no—
578C2×C4—1462no—
579C2×C4C4⋊C4×D7312yes—
580C2×C4C4⋊C4×D7312yes—
581C2×C4#1455659712yes—
582C2×C4C2×D4×D7311yescharacteristic
583C2×C4C2×Q8×D7311yescharacteristic
584C2×C4#1455663611yescharacteristic
585C2×C4#1455663711yescharacteristic
586C2×C4#1455663811yescharacteristic
587C2×C4#1455663911yescharacteristic
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—2921no—
593C8—2921no—
594C8—2921no—
595C8—2921no—
596C22—2921no—
597C22—2921no—
598C22—2921no—
599C22—2921no—
600C22—1462no—
601C22—1462no—
602C22—1462no—
603C22C2×C4⋊C4×D7311yescharacteristic
604C22#1798905911yescharacteristic
605C22#1798906311yescharacteristic
606C22#131×D7311yescharacteristic
607C22C2×#1455659711yescharacteristic
608C22#1798935211yescharacteristic
609C22#1798935311yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—2921no—
617C4—2921no—
618C4—2921no—
619C4—1462no—
620C4—1462no—
621C4—1462no—
622C4—1462no—
623C4#1798916611yescharacteristic
624C4#1798916711yescharacteristic
625C4#1798921411yescharacteristic
626C4#1798921711yescharacteristic
627C2—2922no—
628C2#2261254611yescharacteristic
629C2#2261849611yescharacteristic
630C2#2261849811yescharacteristic
631C2#2261898411yescharacteristic
632C2#2261898811yescharacteristic
633C2#2261902211yescharacteristic
634C2#2261902411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1939C2
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenter#1939D73
hypocenterC73#21958
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
4. #22610655C2semidirect
5. #22610653C2semidirect
6. #22610652C2semidirect
7. #22610651C2semidirect
8. #22610649C2semidirect
9. #22610648C2semidirect
10. #22610646C2semidirect
15. C73×#1939C2semidirect
328. #1939D73semidirect
333. C73#21958semidirect

Maximal subgroups

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

subgroupindex
C2×#179886472
C2×#179886462
#226124112
#226106552
#226106532
#226106522
#226106512
#226106492
#226106482
#226106462
#226099142
#226099122
#226099102
#226099082
C73×#19392
#2195873