Finite Group Databasebeta

← #34035020

Subgroups — #34035020

Order 18688.

484 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22627158C211yesmaximal, characteristic, complemented
2#22627156C211yesmaximal, characteristic, complemented
3#22627147C211yesmaximal, characteristic, complemented
4#22627145C211yesmaximal, characteristic, complemented
5#22627144C211yesmaximal, characteristic, complemented
6#22627144C211yesmaximal, characteristic, complemented
7#22627143C211yesmaximal, characteristic, complemented
8#22627141C211yesmaximal, characteristic, complemented
9#22627137C211yesmaximal, characteristic, complemented
10#22627136C211yesmaximal, characteristic, complemented
11#22627133C211yesmaximal, characteristic, complemented
12#22627123C211yesmaximal, characteristic, complemented
13#22627122C211yesmaximal, characteristic, complemented
14#22627119C211yesmaximal, characteristic, complemented
15#22626746C211yesmaximal, characteristic
16C2×#14556688C2211yescharacteristic
17C2×#14556687C2211yescharacteristic
18C2×#14556687C2211yescharacteristic
19C2×#14556687C2211yescharacteristic
20C2×#14556686C2211yescharacteristic
21C22×#11924040C2211yescharacteristic
22#17989690C2211yescharacteristic
23#17989690C2211yescharacteristic
24#17989690C2211yescharacteristic
25#17989690C2211yescharacteristic
26C4⋊#11924040C2211yescharacteristic
27C4⋊#11924040C2211yescharacteristic
28C4⋊#11924040C2211yescharacteristic
29C4⋊#11924040C2211yescharacteristic
30C4⋊#11924040C2211yescharacteristic
31C4⋊#11924040C2211yescharacteristic
32#17989684C2211yescharacteristic
33#17989684C2211yescharacteristic
34C22⋊#11924040C2211yescharacteristic
35C22⋊#11924040C2211yescharacteristic
36C22⋊#11924040C2211yescharacteristic
37C22⋊#11924040C2211yescharacteristic
38#17989681C2211yescharacteristic
39#17989681C2211yescharacteristic
40#17989681C2211yescharacteristic
41#17989681C2211yescharacteristic
42C4×#11924040C2211yescharacteristic
43C4×#11924040C2211yescharacteristic
44#17989639C411yescharacteristic
45#17989636C2211yescharacteristic
46#17989620C411yescharacteristic
47#17989618C411yescharacteristic
48#17989616C411yescharacteristic
49#17989614C2211yescharacteristic
50#17989614C2211yescharacteristic
51D4×#10596833C2211yescharacteristic
52#17989612C411yescharacteristic
53#17989611C411yescharacteristic
54#17989607C411yescharacteristic
55#17989552C2211yescharacteristic
56#17989551C2211yescharacteristic
57C2×C4×#10596833C2211yescharacteristic
58#17989114C411yescharacteristic
59#14556688—41no—
60#14556687—41no—
61#14556687—41no—
62#14556687—41no—
63#14556686—41no—
64C2×#11924040—41no—
65C2×#11924040C2311yescharacteristic
66C2×#11924040C2311yescharacteristic
67C2×#11924040C2311yescharacteristic
68C2×#11924040C2311yescharacteristic
69C2×#11924040C2311yescharacteristic
70C2×#11924040C2311yescharacteristic
71C2×#11924040C2311yescharacteristic
72C2×#11924040C2311yescharacteristic
73C2×#11924038C2×C411yescharacteristic
74C2×#11924037C2×C411yescharacteristic
75C2×#11924036C2311yescharacteristic
76C22×#10596833C2×C411yescharacteristic
77C22×#10596833C2311yescharacteristic
78C22×#10596833C2311yescharacteristic
79#14556658C2×C411yescharacteristic
80#14556658C2×C411yescharacteristic
81#14556658C2×C411yescharacteristic
82#14556658C2×C411yescharacteristic
83C4⋊#10596833C2×C411yescharacteristic
84C4⋊#10596833C2×C411yescharacteristic
85#14556648C2×C411yescharacteristic
86#14556648C2×C411yescharacteristic
87C22⋊#10596833C2×C411yescharacteristic
88C22⋊#10596833C2×C411yescharacteristic
89C22⋊#10596833C2×C411yescharacteristic
90C22⋊#10596833C2×C411yescharacteristic
91#14556646C2×C411yescharacteristic
92#14556646C2×C411yescharacteristic
93#14556646C2×C411yescharacteristic
94#14556646C2×C411yescharacteristic
95C4×#10596833C2×C411yescharacteristic
96C4×#10596833C2×C411yescharacteristic
97C4×#10596833C2311yescharacteristic
98C4×#10596833C2311yescharacteristic
99C4×#10596833C2311yescharacteristic
100C4×#10596833C2311yescharacteristic
101#14556586C811yescharacteristic
102#14556584C811yescharacteristic
103#14556581C811yescharacteristic
104#14556577C811yescharacteristic
105#14556574C811yescharacteristic
106#14556568C811yescharacteristic
107#14556563C811yescharacteristic
108#14556556C2×C411yescharacteristic
109D4×Dic73C2×C411yescharacteristic
110#14556551C2×C411yescharacteristic
111#14556551C2×C411yescharacteristic
112#14556549C2×C411yescharacteristic
113#14556547C2×C411yescharacteristic
114C2×C4×Dic73C2×C411yescharacteristic
115#123×C73C811yescharacteristic
116#11924040—21no—
117#11924040—21no—
118#11924040—21no—
119#11924040—21no—
120#11924040—21no—
121#11924040—21no—
122#11924040—21no—
123#11924040—21no—
124#11924038—41no—
125#11924037—41no—
126#11924036—21no—
127#11924036—21no—
128C2×#10596833—21no—
129C2×#10596833—21no—
130C2×#10596833—21no—
131C2×#10596833—21no—
132C2×#10596833—41no—
133C2×#10596833C22×C411yescharacteristic
134C2×#10596833C22×C411yescharacteristic
135C2×#10596833C22×C411yescharacteristic
136C2×#10596833C22×C411yescharacteristic
137C2×#10596833C22×C411yescharacteristic
138C2×#10596833C22×C411yescharacteristic
139C2×#10596833C22×C411yescharacteristic
140C2×#10596833C2411yescharacteristic
141C2×Dic146C2×C811yescharacteristic
142C2×C22⋊D73C2×C811yescharacteristic
143C2×C22⋊D73C2×C811yescharacteristic
144C22×Dic73C2×C811yescharacteristic
145C22×Dic73C22×C411yescharacteristic
146C22×Dic73C22×C411yescharacteristic
147C2×C4×D73C22×C411yescharacteristic
148C4⋊Dic73C2×C811yescharacteristic
149C4⋊Dic73C2×C811yescharacteristic
150#11924007C2×C811yescharacteristic
151#11924007C2×C811yescharacteristic
152#11924007C2×C811yescharacteristic
153#11924007C2×C811yescharacteristic
154#11924007C2×C811yescharacteristic
155#11924007C2×C811yescharacteristic
156C22⋊Dic73C2×C811yescharacteristic
157C22⋊Dic73C2×C811yescharacteristic
158C22⋊Dic73C2×C811yescharacteristic
159#11924005C2×C811yescharacteristic
160#11924005C2×C811yescharacteristic
161#11924005C2×C811yescharacteristic
162#11924005C2×C811yescharacteristic
163C4×Dic73C2×C811yescharacteristic
164C4×Dic73C2×C811yescharacteristic
165C4×Dic73C22×C411yescharacteristic
166C4×Dic73C22×C411yescharacteristic
167C4×Dic73C22×C411yescharacteristic
168C4×Dic73C22×C411yescharacteristic
169C2×D4×C73C2×C811yescharacteristic
170C22×C4×C73C2×C811yescharacteristic
171C4⋊C4×C73C2×C811yescharacteristic
172C4⋊C4×C73C2×C811yescharacteristic
173C22⋊C4×C73C2×C811yescharacteristic
174C22⋊C4×C73C2×C811yescharacteristic
175C22⋊C4×C73C2×C811yescharacteristic
176C23×C73C22×C811yescharacteristic
177C23×C73C22×C811yescharacteristic
178C22×D73C22×C811yescharacteristic
179D4×C73—41no—
180C2×C4×C73—41no—
181C2×C4×C73C22×C811yescharacteristic
182C2×C4×C73C22×C811yescharacteristic
183C2×C4×C73C22×C811yescharacteristic
184C2×C4×C73C22×C811yescharacteristic
185C2×C4×C73C22×C811yescharacteristic
186C22⋊D73—41no—
187C22⋊D73—41no—
188C2×Dic73—21no—
189C2×Dic73—21no—
190C2×Dic73—21no—
191C2×Dic73—21no—
192C2×Dic73—41no—
193C2×Dic73C22×C811yescharacteristic
194C2×Dic73C22×C811yescharacteristic
195C2×Dic73C22×C811yescharacteristic
196C2×Dic73C22×C811yescharacteristic
197C2×Dic73C22×C811yescharacteristic
198C2×Dic73C22×C811yescharacteristic
199C2×Dic73C23×C411yescharacteristic
200C4×D73—21no—
201C4×D73—21no—
202Dic146—41no—
203#10596833—21no—
204#10596833—21no—
205#10596833—21no—
206#10596833—21no—
207#10596833—21no—
208#10596833—21no—
209#10596833—21no—
210#10596833H(5,𝔽2)11yescharacteristic
211#105968332−1+411yescharacteristic
212C22×C73—21no—
213C22×C73—21no—
214C22×C73—21no—
215C22×C73—21no—
216C22×C73—21no—
217C22×C73—21no—
218C22×C73C23×C811yescharacteristic
219C2×D73—21no—
220C2×D73—21no—
221C2×D73—21no—
222C4×C73—21no—
223C4×C73—21no—
224C4×C73—21no—
225C4×C73—21no—
226C4×C73—21no—
227Dic73—21no—
228Dic73—21no—
229Dic73—21no—
230Dic73—21no—
231Dic73—21no—
232Dic73—21no—
233Dic73#52011yescharacteristic
234Dic73#56811yescharacteristic
235#33509—731nomaximal, Sylow
236C2×C73—41no—
237C2×C73—41no—
238C2×C73#298811yescharacteristic
239C2×C73#340711yescharacteristic
240C2×C73#340711yescharacteristic
241D73—41no—
242#2966—731no—
243#2183—731no—
244#2183—731no—
245#2169—731no—
246#2169—731no—
247#2168—731no—
248#2168—731no—
249#2168—731no—
250#2168—731no—
251#2164—731no—
252#2164—731no—
253#2163—731no—
254#2151—731no—
255#2151—731no—
256#2150—731no—
257C73#3350911yescharacteristic, complemented, Sylow
258#529—731no—
259C2×M32—731no—
260C2×M32—731no—
261C2×M32—731no—
262C2×M32—731no—
263C22×C16—731no—
264C22×C16—731no—
265#446—731no—
266C8×Q8—731no—
267#436—731no—
268#435—731no—
269#435—731no—
270C8×D4—731no—
271C8×D4—731no—
272C8×D4—731no—
273#433—731no—
274#433—731no—
275#432—731no—
276#405—731no—
277#405—731no—
278C2×C4×C8—731no—
279C4⋊C16—731no—
280C4⋊C16—731no—
281C4⋊C16—731no—
282C4⋊C16—731no—
283C4⋊C16—731no—
284C4⋊C16—731no—
285C4⋊C16—731no—
286C4⋊C16—731no—
287C4⋊C16—731no—
288C4⋊C16—731no—
289C22⋊C16—731no—
290C22⋊C16—731no—
291C22⋊C16—731no—
292C22⋊C16—731no—
293C22⋊C16—731no—
294C22⋊C16—731no—
295#346—731no—
296#346—731no—
297#346—731no—
298#346—731no—
299C4×C16—731no—
300C4×C16—731no—
301C2×M16—731no—
302C2×M16—731no—
303C22×C8—731no—
304C22×C8—731no—
305C22×C8—731no—
306C22×C8—731no—
307#126—731no—
308#126—731no—
309#125—731no—
310#124—731no—
311#123—731no—
312#123#1059684211yescharacteristic
313C22⋊Q8—731no—
314#121—731no—
315C4×Q8—731no—
316C4×D4—731no—
317C4×D4—731no—
318C4×D4—731no—
319#117—731no—
320#117—731no—
321C2×C42—731no—
322M32—2921no—
323M32—2921no—
324M32—2921no—
325M32—2921no—
326C2×C16—2921no—
327C2×C16—2921no—
328C2×C16—731no—
329C2×C16—731no—
330C2×C16—731no—
331C2×C16—731no—
332C2×C16—731no—
333C2×C16—731no—
334C2×C16—731no—
335C2×C16—731no—
336C4⋊C8—731no—
337C4⋊C8—731no—
338C4⋊C8—731no—
339C4⋊C8—731no—
340C4⋊C8—731no—
341C4⋊C8—731no—
342C22⋊C8—731no—
343C22⋊C8—731no—
344C22⋊C8—731no—
345C22⋊C8—731no—
346C22⋊C8—731no—
347C22⋊C8—731no—
348#97—731no—
349#97—731no—
350#97—731no—
351#97—731no—
352C4×C8—731no—
353C4×C8—731no—
354C4×C8—731no—
355C4×C8—731no—
356C4×C8—731no—
357C4×C8—731no—
358C2×Q8—731no—
359C2×D4—731no—
360C2×D4—731no—
361C2×D4C2×#1059684211yescharacteristic
362C22×C4—731no—
363C22×C4—731no—
364C22×C4—731no—
365C22×C4—731no—
366C22×C4C2×#1059684211yescharacteristic
367M16—2921no—
368M16—2921no—
369C2×C8—2921no—
370C2×C8—731no—
371C2×C8—731no—
372C2×C8—731no—
373C2×C8—731no—
374C2×C8—731no—
375C2×C8—731no—
376C2×C8—731no—
377C2×C8—731no—
378C2×C8—1461no—
379C2×C8—1461no—
380C2×C8—1461no—
381C2×C8—1461no—
382C2×C8—1461no—
383C2×C8—1461no—
384C4⋊C4—731no—
385C4⋊C4—731no—
386C4⋊C4—731no—
387C4⋊C4—731no—
388C4⋊C4—731no—
389C4⋊C4—731no—
390C4⋊C4—731no—
391C4⋊C4—731no—
392C4⋊C4C2×#1059684211yescharacteristic
393C4⋊C4C2×#1059684211yescharacteristic
394C22⋊C4—731no—
395C22⋊C4—731no—
396C22⋊C4—731no—
397C22⋊C4—731no—
398C22⋊C4—731no—
399C22⋊C4—731no—
400C22⋊C4—731no—
401C22⋊C4C2×#1059684211yescharacteristic
402C22⋊C4C2×#1059684211yescharacteristic
403C22⋊C4C2×#1059684211yescharacteristic
404C42—731no—
405C42—731no—
406C42—731no—
407C42—731no—
408C42—731no—
409C42—731no—
410C16—1461no—
411C16—1461no—
412C16—1461no—
413C16—1461no—
414C16—1461no—
415C16—1461no—
416C16—1461no—
417C16—1461no—
418C23—731no—
419C23C22×#1059684211yescharacteristic
420C23C22×#1059684211yescharacteristic
421Q8—2921no—
422D4—41no—
423D4—2921no—
424D4—2921no—
425C2×C4—41no—
426C2×C4—2921no—
427C2×C4—731no—
428C2×C4—731no—
429C2×C4—731no—
430C2×C4—731no—
431C2×C4—731no—
432C2×C4—731no—
433C2×C4—731no—
434C2×C4—1461no—
435C2×C4—1461no—
436C2×C4—1461no—
437C2×C4—1461no—
438C2×C4—1461no—
439C2×C4—1461no—
440C2×C4C22×#1059684211yescharacteristic
441C2×C4C22×#1059684211yescharacteristic
442C2×C4C22×#1059684211yescharacteristic
443C2×C4C22×#1059684211yescharacteristic
444C2×C4C22×#1059684211yescharacteristic
445C8—731no—
446C8—731no—
447C8—1461no—
448C8—1461no—
449C8—1461no—
450C8—1461no—
451C8—1461no—
452C8—1461no—
453C8—1461no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—1461no—
461C22—1461no—
462C22—1461no—
463C22C23×#1059684211yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—731no—
470C4—731no—
471C4—1461no—
472C4—1461no—
473C4—1461no—
474C4—1461no—
475C4—1461no—
476C4—1461no—
477C2—41no—
478C2—41no—
479C2—2921no—
480C2#2262717511yescharacteristic
481C2#2262718411yescharacteristic
482C2#2262718511yescharacteristic
subgroupG/H
center, FrattiniC22C23×#10596842
commutator, socleC22×C73C23×C8
Fitting#123×C73C8
prime radical#14556563C8
cosocleC2×#10596833C24
hypercenter#123#10596842
hypocenterC73#33509
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #22627158C2semidirect
2. #22627156C2semidirect
3. #22627147C2semidirect
4. #22627145C2semidirect
5. #22627144C2semidirect
6. #22627144C2semidirect
7. #22627143C2semidirect
8. #22627141C2semidirect
9. #22627137C2semidirect
10. #22627136C2semidirect
11. #22627133C2semidirect
12. #22627123C2semidirect
13. #22627122C2semidirect
14. #22627119C2semidirect
257. C73#33509semidirect

Maximal subgroups

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

subgroupindex
#226271582
#226271562
#226271472
#226271452
#226271442
#226271432
#226271412
#226271372
#226271362
#226271332
#226271232
#226271222
#226271192
#226267462
#3350973