Finite Group Databasebeta

← #33096074

Subgroups — #33096074

Order 18688.

838 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊C4×D73C211yesmaximal, characteristic
2#22610497C211yesmaximal, characteristic, complemented
3#22610495C211yesmaximal, characteristic, complemented
4#22610493C211yesmaximal, characteristic, complemented
5#22610491C211yesmaximal, characteristic, complemented
6#22610489C211yesmaximal, characteristic, complemented
7#22610487C211yesmaximal, characteristic, complemented
8#22610485C211yesmaximal, characteristic, complemented
9#22609998C211yesmaximal, characteristic
10#22609998C211yesmaximal, characteristic
11#22609910C211yesmaximal, characteristic
12#22609908C211yesmaximal, characteristic
13#22609694C211yesmaximal, characteristic
14#22609688C211yesmaximal, characteristic
15C73×#1917C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D73C411yescharacteristic
17C2×C4⋊C4×D73C411yescharacteristic
18C2×C42×D73C2211yescharacteristic
19C2×C42×D73C2211yescharacteristic
20C2×C42×D73C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×#14556520C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×#14556503C2211yescharacteristic
25C2×#14556503C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556502C2211yescharacteristic
29C2×C8×Dic73C2211yescharacteristic
30C2×C8×Dic73C2211yescharacteristic
31C4⋊C4×Dic73C411yescharacteristic
32C4⋊C4×Dic73C411yescharacteristic
33C4×#11924007C2211yescharacteristic
34C4×#11924007C2211yescharacteristic
35C4×C4⋊Dic73C2211yescharacteristic
36#17988438C411yescharacteristic
37#17988438C411yescharacteristic
38#95×D73C411yescharacteristic
39#95×D73C411yescharacteristic
40#17988342C2211yescharacteristic
41#17988342C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44#17988341C2211yescharacteristic
45#17988341C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C2×C4⋊C8×C73C2211yescharacteristic
53C2×#97×C73C2211yescharacteristic
54C4×C4⋊C4×C73C2211yescharacteristic
55#336×C73C2211yescharacteristic
56#336×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×C4×D73C2×C411yescharacteristic
60C22×C4×D73C2×C411yescharacteristic
61C22×C4×D73C2×C411yescharacteristic
62C22×C4×D73C2×C411yescharacteristic
63C22×C4×D73C2×C411yescharacteristic
64C22×C4×D73C2×C411yescharacteristic
65C22×C4×D73C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C2×C4⋊Dic73C2×C411yescharacteristic
71C2×C4⋊Dic73C2×C411yescharacteristic
72C2×#11924007C2×C411yescharacteristic
73C2×#11924007C2×C411yescharacteristic
74C2×#11924007C2×C411yescharacteristic
75C2×#11924007C2×C411yescharacteristic
76C4⋊C4×D73—24no—
77C4⋊C4×D73—24no—
78C2×C4×Dic73C2×C411yescharacteristic
79C2×C4×Dic73C2×C411yescharacteristic
80C2×C4×Dic73C2×C411yescharacteristic
81C2×C4×Dic73C2×C411yescharacteristic
82C2×C4×Dic73C2×C411yescharacteristic
83C2×C4×Dic73C2×C411yescharacteristic
84C2×C4×Dic73C2311yescharacteristic
85C2×C4×Dic73C2311yescharacteristic
86C2×C4×Dic73C2311yescharacteristic
87C42×D73—22no—
88C42×D73—22no—
89C42×D73—41no—
90C42×D73—41no—
91C42×D73—41no—
92C42×D73—41no—
93C4⋊#10596831—41no—
94#14556520—41no—
95#14556520—41no—
96#14556503—22no—
97#14556503—22no—
98#14556503—22no—
99#14556503—22no—
100#14556502—41no—
101C8×Dic73—41no—
102C8×Dic73—41no—
103#14556498C2×C411yescharacteristic
104#14556498C2×C411yescharacteristic
105#14556498C2×C411yescharacteristic
106#14556498C2×C411yescharacteristic
107#14556498C2×C411yescharacteristic
108#14556498C2×C411yescharacteristic
109C22×C8×C73C2311yescharacteristic
110C22×C8×C73C2311yescharacteristic
111C22×C8×C73C2311yescharacteristic
112C22×C8×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2×C411yescharacteristic
114C2×C4⋊C4×C73C2×C411yescharacteristic
115C2×C42×C73C2311yescharacteristic
116C2×C42×C73C2311yescharacteristic
117C2×C42×C73C2311yescharacteristic
118C4⋊C8×C73—41no—
119#97×C73—41no—
120#95×C73C2×C411yescharacteristic
121#95×C73C2×C411yescharacteristic
122C23×D73C22×C411yescharacteristic
123C22×Dic73C22×C411yescharacteristic
124C22×Dic73C22×C411yescharacteristic
125C22×Dic73C22×C411yescharacteristic
126C22×Dic73C22×C411yescharacteristic
127C22×Dic73C22×C411yescharacteristic
128C22×Dic73C22×C411yescharacteristic
129C22×Dic73C22×C411yescharacteristic
130C2×C4×D73—22no—
131C2×C4×D73—22no—
132C2×C4×D73—21no—
133C2×C4×D73—21no—
134C2×C4×D73—21no—
135C2×C4×D73—21no—
136C2×C4×D73—22no—
137C2×C4×D73—22no—
138C2×C4×D73—22no—
139C2×C4×D73—22no—
140C2×C4×D73—22no—
141C2×C4×D73—22no—
142C2×C4×D73—22no—
143C2×C4×D73—22no—
144C2×C4×D73—22no—
145C2×C4×D73—22no—
146C2×C4×D73—22no—
147C2×C4×D73—22no—
148C2×C4×D73—41no—
149C2×C4×D73—41no—
150C2×C4×D73—41no—
151C2×C4×D73—41no—
152C2×C4×D73#4112yes—
153C2×C4×D73#4112yes—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C4⋊Dic73—22no—
167C4⋊Dic73M1614yes—
168#11924007—22no—
169#11924007—22no—
170#11924007—22no—
171#11924007M1614yes—
172C4×Dic73—21no—
173C4×Dic73—21no—
174C4×Dic73—21no—
175C4×Dic73—21no—
176C4×Dic73—21no—
177C4×Dic73—21no—
178C4×Dic73—22no—
179C4×Dic73—22no—
180C4×Dic73—41no—
181C4×Dic73—41no—
182C4×Dic73—41no—
183C4×Dic73—41no—
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—22no—
205C42×C73—21no—
206C42×C73—21no—
207C42×C73—21no—
208C42×C73—21no—
209C42×C73—21no—
210C42×C73—21no—
211C23×C73C23×C411yescharacteristic
212C22×D73—21no—
213C22×D73—21no—
214C22×D73—21no—
215C22×D73—21no—
216C22×D73#11712yes—
217C22×D73#13112yes—
218C22×D73#13112yes—
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×C73—21no—
235C2×C4×C73C2×M1612yes—
236C2×C4×C73C2×M1612yes—
237C2×C4×C73C2×#4111yescharacteristic
238C2×C4×C73C2×#4111yescharacteristic
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#11712yes—
260C2×Dic73C2×M1612yes—
261C2×Dic73C2×M1612yes—
262C2×Dic73C2×M1612yes—
263C2×Dic73C2×M1612yes—
264C4×D73—28no—
265C4×D73—22no—
266C4×D73—22no—
267C4×D73—22no—
268C4×D73—22no—
269C4×D73—44no—
270C4×D73—44no—
271C4×D73—44no—
272C4×D73—44no—
273C4×D73—44no—
274C8×C73—41no—
275C8×C73—41no—
276C8×C73—41no—
277C8×C73—41no—
278#10596831—41no—
279#10596831—41no—
280#10596831—41no—
281#10596831—41no—
282C22×C73C2×#11711yescharacteristic
283C22×C73#51811yescharacteristic
284C22×C73#51911yescharacteristic
285C22×C73C22×M1611yescharacteristic
286C22×C73C22×M1611yescharacteristic
287C22×C73C2×#13111yescharacteristic
288C22×C73C2×#13111yescharacteristic
289C2×D73—22no—
290C2×D73—22no—
291C2×D73—22no—
292C2×D73—22no—
293C2×D73—22no—
294C2×D73—22no—
295C2×D73#43314yes—
296C4×C73—22no—
297C4×C73—22no—
298C4×C73—41no—
299C4×C73—41no—
300C4×C73—41no—
301C4×C73—41no—
302C4×C73#53911yescharacteristic
303C4×C73#53911yescharacteristic
304C4×C73#53911yescharacteristic
305C4×C73#53911yescharacteristic
306Dic73—22no—
307Dic73—22no—
308Dic73—22no—
309Dic73—22no—
310Dic73—22no—
311Dic73—41no—
312Dic73—41no—
313#21914—731nomaximal, Sylow
314C2×C73#231311yescharacteristic
315C2×C73C2×#43311yescharacteristic
316C2×C73#292011yescharacteristic
317C2×C73#297411yescharacteristic
318C2×C73#297411yescharacteristic
319C2×C73#298411yescharacteristic
320C2×C73#298411yescharacteristic
321D73—24no—
322C2×C4×C4⋊C4—731no—
323#1917—731no—
324#1917—731no—
325#1917—731no—
326#1917D7311yescharacteristic, complemented
327#1916—731no—
328#1916—731no—
329#1916—731no—
330#1916—731no—
331#1817—731no—
332#1817—731no—
333#1797—731no—
334#1797—731no—
335#1749—731no—
336C4×C22⋊C8—731no—
337C73#2191411yescharacteristic, complemented, Sylow
338C22×C4⋊C4—731no—
339C22×C4⋊C4—731no—
340C22×C42—731no—
341C22×C42—731no—
342C22×C42—731no—
343C2×C4⋊C8—731no—
344C2×C4⋊C8—731no—
345C2×C4⋊C8—731no—
346C2×C4⋊C8C2×D7311yescharacteristic
347C2×C22⋊C8—731no—
348C2×C22⋊C8—731no—
349C2×C22⋊C8—731no—
350C2×C22⋊C8—731no—
351C2×#97—731no—
352C2×#97C2×D7311yescharacteristic
353C2×C4×C8—731no—
354C2×C4×C8—731no—
355C4×C4⋊C4—731no—
356C4×C4⋊C4—731no—
357C4×C4⋊C4—731no—
358C4×C4⋊C4—731no—
359C4×C4⋊C4—731no—
360C4×C4⋊C4—731no—
361C4×C4⋊C4—731no—
362C4×C4⋊C4C2×D7311yescharacteristic
363C2×#95—731no—
364C2×#95—731no—
365#336—731no—
366#336—731no—
367#336—731no—
368#336—731no—
369#336—731no—
370#336—731no—
371#336—731no—
372#336—731no—
373#336—731no—
374#336—731no—
375#336—731no—
376#336—731no—
377#336C2×D7311yescharacteristic
378#336C2×D7311yescharacteristic
379#336C2×D7311yescharacteristic
380#336C2×D7311yescharacteristic
381C23×C4—731no—
382C23×C4—731no—
383C23×C4—731no—
384C23×C4—731no—
385C23×C4—731no—
386C23×C4—731no—
387C23×C4—731no—
388C22×C8—731no—
389C22×C8—731no—
390C22×C8—731no—
391C22×C8—731no—
392C22×C8C22×D7311yescharacteristic
393C22×C8C22×D7311yescharacteristic
394C22×C8C22×D7311yescharacteristic
395C22×C8C22×D7311yescharacteristic
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—1464no—
403C2×C4⋊C4—1464no—
404C2×C4⋊C4C4×D7311yescharacteristic
405C2×C4⋊C4C4×D7311yescharacteristic
406C2×C42—2921no—
407C2×C42—2921no—
408C2×C42—2921no—
409C2×C42—2921no—
410C2×C42—731no—
411C2×C42—731no—
412C2×C42—731no—
413C2×C42—731no—
414C2×C42—731no—
415C2×C42—731no—
416C2×C42—731no—
417C2×C42—731no—
418C2×C42—731no—
419C2×C42—1462no—
420C2×C42—1462no—
421C2×C42C22×D7311yescharacteristic
422C2×C42C22×D7311yescharacteristic
423C2×C42C22×D7311yescharacteristic
424C4⋊C8—41no—
425C4⋊C8—2921no—
426C4⋊C8—2921no—
427C4⋊C8—2921no—
428C22⋊C8—1462no—
429C22⋊C8—1462no—
430C22⋊C8—1462no—
431C22⋊C8—1462no—
432#97—41no—
433#97—2921no—
434C4×C8—2921no—
435C4×C8—2921no—
436#95—731no—
437#95—731no—
438#95—731no—
439#95—731no—
440#95—731no—
441#95—731no—
442#95C4×D7311yescharacteristic
443#95C4×D7311yescharacteristic
444C24—731no—
445C22×C4—2921no—
446C22×C4—2921no—
447C22×C4—2921no—
448C22×C4—2921no—
449C22×C4—731no—
450C22×C4—731no—
451C22×C4—731no—
452C22×C4—731no—
453C22×C4—731no—
454C22×C4—732no—
455C22×C4—732no—
456C22×C4—731no—
457C22×C4—731no—
458C22×C4—1462no—
459C22×C4—1462no—
460C22×C4—1462no—
461C22×C4—1462no—
462C22×C4—1462no—
463C22×C4—1462no—
464C22×C4—1462no—
465C22×C4—1462no—
466C22×C4—1462no—
467C22×C4—1462no—
468C22×C4—1462no—
469C22×C4—1462no—
470C22×C4—1462no—
471C22×C4—1462no—
472C22×C4—1461no—
473C22×C4—1461no—
474C22×C4—1461no—
475C22×C4—1461no—
476C22×C4C2×C4×D7311yescharacteristic
477C22×C4C2×C4×D7311yescharacteristic
478C22×C4C2×C4×D7311yescharacteristic
479C22×C4C2×C4×D7311yescharacteristic
480C22×C4C2×C4×D7311yescharacteristic
481C22×C4C2×C4×D7311yescharacteristic
482C22×C4C23×D7311yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—1461no—
496C2×C8—1461no—
497C2×C8—1461no—
498C2×C8—1461no—
499C2×C8—1461no—
500C2×C8—1461no—
501C2×C8—1461no—
502C2×C8—1461no—
503C2×C8—1461no—
504C2×C8—1461no—
505C2×C8—1461no—
506C2×C8—1461no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—734no—
510C4⋊C4—734no—
511C4⋊C4—1462no—
512C4⋊C4—1462no—
513C4⋊C4—1462no—
514C4⋊C4—1462no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—2921no—
522C42—2921no—
523C42—2921no—
524C42—2921no—
525C42—1462no—
526C42—1462no—
527C42—1461no—
528C42—1461no—
529C42—1461no—
530C42—1461no—
531C42—1461no—
532C42—1461no—
533C23—732no—
534C23—732no—
535C23—732no—
536C23—1461no—
537C23—1461no—
538C23—1461no—
539C23—1461no—
540C23C22×C4×D7311yescharacteristic
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—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—2924no—
558C2×C4—2924no—
559C2×C4—2924no—
560C2×C4—2924no—
561C2×C4—2924no—
562C2×C4—732no—
563C2×C4—732no—
564C2×C4—732no—
565C2×C4—732no—
566C2×C4—732no—
567C2×C4—1468no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4—1461no—
571C2×C4—1461no—
572C2×C4—1461no—
573C2×C4—1461no—
574C2×C4—1461no—
575C2×C4—1461no—
576C2×C4—1461no—
577C2×C4—1461no—
578C2×C4—1461no—
579C2×C4—1461no—
580C2×C4—1461no—
581C2×C4—1461no—
582C2×C4—1461no—
583C2×C4—1461no—
584C2×C4—1462no—
585C2×C4—1462no—
586C2×C4—1462no—
587C2×C4—1462no—
588C2×C4M16×D7312yes—
589C2×C4M16×D7312yes—
590C2×C4#41×D7311yescharacteristic
591C2×C4#41×D7311yescharacteristic
592C2×C4#1455663611yescharacteristic
593C2×C4#1455663711yescharacteristic
594C2×C4#1455663811yescharacteristic
595C2×C4#1455663911yescharacteristic
596C8—41no—
597C8—41no—
598C8—41no—
599C8—41no—
600C8—2921no—
601C8—2921no—
602C8—2921no—
603C8—2921no—
604C22—734no—
605C22—1462no—
606C22—1462no—
607C22—1462no—
608C22—1462no—
609C22—1462no—
610C22—1462no—
611C22#117×D7311yescharacteristic
612C22#1798905911yescharacteristic
613C22#1798906311yescharacteristic
614C22C2×M16×D7311yescharacteristic
615C22C2×M16×D7311yescharacteristic
616C22#131×D7311yescharacteristic
617C22#131×D7311yescharacteristic
618C4—22no—
619C4—22no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—2921no—
625C4—2921no—
626C4—1462no—
627C4—1462no—
628C4—1462no—
629C4—1462no—
630C4—1462no—
631C4#1798917811yescharacteristic
632C4#1798918011yescharacteristic
633C4#1798918311yescharacteristic
634C4#1798918511yescharacteristic
635C2—1464no—
636C2#2261253011yescharacteristic
637C2#433×D7311yescharacteristic
638C2#2261856111yescharacteristic
639C2#2261896111yescharacteristic
640C2#2261896311yescharacteristic
641C2#2261901711yescharacteristic
642C2#2261901711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1917C2
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenter#1917D73
hypocenterC73#21914
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
2. #22610497C2semidirect
3. #22610495C2semidirect
4. #22610493C2semidirect
5. #22610491C2semidirect
6. #22610489C2semidirect
7. #22610487C2semidirect
8. #22610485C2semidirect
15. C73×#1917C2semidirect
326. #1917D73semidirect
337. C73#21914semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊C4×D732
#226104972
#226104952
#226104932
#226104912
#226104892
#226104872
#226104852
#226099982
#226099102
#226099082
#226096942
#226096882
C73×#19172
#2191473