Finite Group Databasebeta

← #32978884

Subgroups — #32978884

Order 18688.

524 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988659C211yesmaximal, characteristic
2#22609958C211yesmaximal, characteristic, complemented
3#22609954C211yesmaximal, characteristic, complemented
4#22609919C211yesmaximal, characteristic
5#22607798C211yesmaximal, characteristic, complemented
6#22607798C211yesmaximal, characteristic, complemented
7C73×#1799C211yesmaximal, characteristic
8C22×#11924012C411yescharacteristic, complemented
9C23×#10596831C2211yescharacteristic
10#17988659—21no—
11#17988659—21no—
12#17988659—21no—
13#17988659—21no—
14C2×#14556524—21no—
15C2×#14556522—21no—
16C2×C4⋊#10596831C411yescharacteristic, complemented
17C2×#14556506—21no—
18C2×C22⋊#10596831C411yescharacteristic, complemented
19C2×C22⋊#10596831C2211yescharacteristic
20C2×#14556502C411yescharacteristic, complemented
21#17988447C2211yescharacteristic
22#17988447C2211yescharacteristic
23#17988354—21no—
24#17988349—21no—
25#17988349—21no—
26C2×C4×D4×C73C2211yescharacteristic
27C2×#99×C73—21no—
28#380×C73C2211yescharacteristic
29#380×C73C2211yescharacteristic
30#342×C73—21no—
31C2×#11924012—21no—
32C2×#11924012—21no—
33C2×#11924012—42no—
34C22×#10596831—42no—
35C22×#10596831C2×C411yescharacteristic
36C22×#10596831C2×C411yescharacteristic
37C22×#10596831C2×C411yescharacteristic
38C22×#10596831C2×C411yescharacteristic
39C22×#10596831D411yescharacteristic
40C22×#10596831D411yescharacteristic
41C22×#10596831D411yescharacteristic
42C22×#10596831D411yescharacteristic
43C2×C4⋊Dic73—21no—
44C2×C4⋊Dic73—21no—
45C2×C22⋊Dic73—21no—
46C2×C22⋊Dic73—21no—
47#14556524—42no—
48#14556522—42no—
49C4⋊#10596831—21no—
50C4⋊#10596831—21no—
51#14556506—42no—
52C22⋊#10596831—21no—
53C22⋊#10596831—21no—
54C22⋊#10596831—21no—
55C22⋊#10596831—21no—
56#14556502—21no—
57#14556502—21no—
58#14556498—21no—
59#14556498—21no—
60C22×D4×C73D411yescharacteristic
61C23×C4×C73C2×C411yescharacteristic
62C23×C4×C73C2311yescharacteristic
63C4×D4×C73—21no—
64C4×D4×C73—21no—
65C4×D4×C73—21no—
66C4×D4×C73—21no—
67C2×C4⋊C4×C73—21no—
68C2×C4⋊C4×C73—21no—
69C2×C4⋊C4×C73Q811yescharacteristic
70C2×C22⋊C4×C73—21no—
71C2×C22⋊C4×C73—21no—
72C2×C22⋊C4×C73D411yescharacteristic
73C2×C22⋊C4×C73Q811yescharacteristic
74C2×C42×C73C2×C411yescharacteristic
75#99×C73—42no—
76#95×C73—21no—
77#95×C73—21no—
78C22×Dic73—41no—
79C22×Dic73—41no—
80#11924012—42no—
81#11924012—42no—
82C2×#10596831—22no—
83C2×#10596831—22no—
84C2×#10596831—22no—
85C2×#10596831—21no—
86C2×#10596831—21no—
87C2×#10596831—41no—
88C2×#10596831—41no—
89C2×#10596831—41no—
90C2×#10596831—41no—
91C2×#10596831—41no—
92C2×#10596831C22⋊C411yescharacteristic
93C2×#10596831C22⋊C411yescharacteristic
94C2×#10596831C22⋊C411yescharacteristic
95C2×#10596831C22⋊C411yescharacteristic
96C4⋊Dic73—41no—
97C4⋊Dic73—41no—
98C4⋊Dic73—41no—
99C4⋊Dic73—41no—
100C22⋊Dic73—41no—
101C22⋊Dic73—41no—
102C22⋊Dic73—41no—
103C22⋊Dic73—41no—
104C24×C73C4⋊C411yescharacteristic
105C24×C73C2×D411yescharacteristic
106C2×D4×C73—21no—
107C2×D4×C73—21no—
108C2×D4×C73—21no—
109C2×D4×C73—21no—
110C2×D4×C73—21no—
111C2×D4×C73—21no—
112C22×C4×C73—21no—
113C22×C4×C73—21no—
114C22×C4×C73—41no—
115C22×C4×C73—41no—
116C22×C4×C73—41no—
117C22×C4×C73—41no—
118C22×C4×C73—41no—
119C22×C4×C73—41no—
120C22×C4×C73C4⋊C411yescharacteristic
121C22×C4×C73C4⋊C411yescharacteristic
122C22×C4×C73C4⋊C411yescharacteristic
123C22×C4×C73C22×C411yescharacteristic
124C22×C4×C73C2×D411yescharacteristic
125C22×C4×C73C2×D411yescharacteristic
126C22×C4×C73C2×Q811yescharacteristic
127C22×C4×C73#4111yescharacteristic
128C22×C4×C73#4111yescharacteristic
129C4⋊C4×C73—21no—
130C4⋊C4×C73—21no—
131C4⋊C4×C73—41no—
132C4⋊C4×C73—41no—
133C4⋊C4×C73—41no—
134C4⋊C4×C73—41no—
135C22⋊C4×C73—21no—
136C22⋊C4×C73—21no—
137C22⋊C4×C73—21no—
138C22⋊C4×C73—21no—
139C22⋊C4×C73—41no—
140C22⋊C4×C73—41no—
141C22⋊C4×C73—41no—
142C22⋊C4×C73—41no—
143C42×C73—21no—
144C42×C73—21no—
145C23×C73—21no—
146C23×C73—21no—
147C23×C73—21no—
148C23×C73—41no—
149C23×C73—41no—
150C23×C73—41no—
151C23×C73—41no—
152C23×C73C2×C4⋊C411yescharacteristic
153C23×C73#12111yescharacteristic
154C23×C73#12111yescharacteristic
155C23×C73AGL(1,ℤ/8)11yescharacteristic
156C23×C73AGL(1,ℤ/8)11yescharacteristic
157C23×C73#13711yescharacteristic
158C23×C73#13711yescharacteristic
159D4×C73—41no—
160D4×C73—41no—
161D4×C73—41no—
162D4×C73—41no—
163C2×C4×C73—21no—
164C2×C4×C73—21no—
165C2×C4×C73—21no—
166C2×C4×C73—21no—
167C2×C4×C73—21no—
168C2×C4×C73—21no—
169C2×C4×C73—21no—
170C2×C4×C73—21no—
171C2×C4×C73—21no—
172C2×C4×C73—21no—
173C2×C4×C73—21no—
174C2×C4×C73—41no—
175C2×C4×C73—41no—
176C2×C4×C73—41no—
177C2×C4×C73—42no—
178C2×C4×C73—41no—
179C2×C4×C73—41no—
180C2×C4×C73—41no—
181C2×C4×C73—41no—
182C2×C4×C73—81no—
183C2×C4×C73—81no—
184C2×C4×C73—81no—
185C2×C4×C73—81no—
186C2×C4×C73—81no—
187C2×C4×C73—81no—
188C2×C4×C73C2×C22⋊C411yescharacteristic
189C2×C4×C73#11711yescharacteristic
190C2×C4×C73C22⋊Q811yescharacteristic
191C2×C4×C73C22⋊Q811yescharacteristic
192C2×Dic73—81no—
193C2×Dic73—81no—
194C2×Dic73—81no—
195C2×Dic73—81no—
196C2×Dic73—81no—
197C2×Dic73—81no—
198#10596831—21no—
199#10596831—21no—
200#10596831—21no—
201#10596831—41no—
202#10596831—41no—
203#10596831#9912yescomplemented
204C22×C73—21no—
205C22×C73—21no—
206C22×C73—21no—
207C22×C73—21no—
208C22×C73—21no—
209C22×C73—21no—
210C22×C73—41no—
211C22×C73—41no—
212C22×C73—41no—
213C22×C73—41no—
214C22×C73—41no—
215C22×C73—41no—
216C22×C73—41no—
217C22×C73—81no—
218C22×C73—81no—
219C22×C73#38011yescharacteristic
220C22×C73#42811yescharacteristic
221C22×C73#42811yescharacteristic
222C22×C73#46811yescharacteristic
223C22×C73#46811yescharacteristic
224C22×C73#46911yescharacteristic
225C22×C73#47011yescharacteristic
226C4×C73—21no—
227C4×C73—21no—
228C4×C73—21no—
229C4×C73—41no—
230C4×C73—41no—
231C4×C73—41no—
232C4×C73—161no—
233C4×C73—161no—
234C4×C73C2×#9911yescharacteristic
235C4×C73#41011yescharacteristic
236Dic73—161no—
237Dic73—161no—
238#8610—731nomaximal, Sylow
239C2×C73—21no—
240C2×C73—21no—
241C2×C73—21no—
242C2×C73—21no—
243C2×C73—21no—
244C2×C73—21no—
245C2×C73—81no—
246C2×C73#179911yescharacteristic
247C2×C73#180911yescharacteristic
248C2×C73#181211yescharacteristic
249C2×#435—731no—
250#1808—731no—
251#1807—731no—
252#1799—731no—
253#1799D7311yescharacteristic
254#1289—731no—
255#1289—731no—
256C73#861011yescharacteristic, complemented, Sylow
257C22×M16—731no—
258C23×C8—731no—
259C2×C4×D4C2×D7311yescharacteristic
260#435—1461no—
261#435—1461no—
262#435—1461no—
263#435—1461no—
264C2×#107—1461no—
265C2×#106—1461no—
266C2×C4⋊C8—731no—
267C2×#99—21no—
268C2×#99—1461no—
269C2×C22⋊C8—731no—
270C2×C22⋊C8—731no—
271C2×#97—731no—
272#380—731no—
273#380—731no—
274#380C2×D7311yescharacteristic
275#380C2×D7311yescharacteristic
276#342—21no—
277#342—1461no—
278#340—1461no—
279#340—1461no—
280C22×D4C22⋊D7311yescharacteristic
281C23×C4C4×D7311yescharacteristic
282C23×C4C22×D7311yescharacteristic
283C2×M16—2922no—
284C2×M16—1461no—
285C2×M16—1461no—
286C22×C8—2922no—
287C22×C8—731no—
288C22×C8—731no—
289C22×C8—731no—
290C22×C8—731no—
291C22×C8—731no—
292C22×C8—731no—
293C22×C8—731no—
294C22×C8—731no—
295C4×D4—21no—
296C4×D4—21no—
297C4×D4—21no—
298C4×D4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—1461no—
302C2×C4⋊C4—1461no—
303C2×C4⋊C4Dic14611yescharacteristic
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—1461no—
307C2×C22⋊C4—1461no—
308C2×C22⋊C4Dic14611yescharacteristic
309C2×C22⋊C4C22⋊D7311yescharacteristic
310C2×C42C4×D7311yescharacteristic
311#107—2922no—
312#106—2922no—
313C4⋊C8—1461no—
314C4⋊C8—1461no—
315#99—42no—
316#99—2922no—
317C22⋊C8—1461no—
318C22⋊C8—1461no—
319C22⋊C8—1461no—
320C22⋊C8—1461no—
321#97—1461no—
322#97—1461no—
323#95—21no—
324#95—21no—
325#95—1461no—
326#95—1461no—
327C24#1192400711yescharacteristic
328C24C2×C22⋊D7311yescharacteristic
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—2921no—
344C22×C4—2921no—
345C22×C4#1192400711yescharacteristic
346C22×C4#1192400711yescharacteristic
347C22×C4#1192400711yescharacteristic
348C22×C4C2×C4×D7311yescharacteristic
349C22×C4D4×D7311yescharacteristic
350C22×C4D4×D7311yescharacteristic
351C22×C4C2×Dic14611yescharacteristic
352C22×C4#1192402711yescharacteristic
353C22×C4#1192402711yescharacteristic
354M16—2922no—
355M16—2922no—
356C2×C8—2921no—
357C2×C8—2921no—
358C2×C8—2921no—
359C2×C8—2921no—
360C2×C8—2921no—
361C2×C8—731no—
362C2×C8—731no—
363C2×C8—731no—
364C2×C8—731no—
365C2×C8—1461no—
366C2×C8—1461no—
367C2×C8—1462no—
368C2×C8—1462no—
369C2×C8—1462no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—2921no—
377C4⋊C4—2921no—
378C4⋊C4—2921no—
379C4⋊C4—2921no—
380C22⋊C4—21no—
381C22⋊C4—21no—
382C22⋊C4—21no—
383C22⋊C4—21no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—2921no—
389C22⋊C4—2921no—
390C22⋊C4—2921no—
391C22⋊C4—2921no—
392C42—21no—
393C42—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23C2×#1192400711yescharacteristic
402C23#1455656311yescharacteristic
403C23#1455656311yescharacteristic
404C23#1455661611yescharacteristic
405C23#1455661711yescharacteristic
406C23#1455662111yescharacteristic
407C23#1455662211yescharacteristic
408D4—41no—
409D4—41no—
410D4—41no—
411D4—41no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—5841no—
438C2×C4—5841no—
439C2×C4—5841no—
440C2×C4—5841no—
441C2×C4—5841no—
442C2×C4—5841no—
443C2×C4C22⋊C4×D7311yescharacteristic
444C2×C4#1455654711yescharacteristic
445C2×C4#1455656811yescharacteristic
446C2×C4#1455656811yescharacteristic
447C8—2921no—
448C8—2921no—
449C8—732no—
450C8—1461no—
451C8—1461no—
452C8—1461no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—81no—
467C22—81no—
468C22#1798844511yescharacteristic
469C22#1798862711yescharacteristic
470C22#1798863011yescharacteristic
471C22#1798883111yescharacteristic
472C22#1798883511yescharacteristic
473C22#1798883811yescharacteristic
474C22#1798884311yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—41no—
479C4—41no—
480C4—41no—
481C4—161no—
482C4—161no—
483C4—11681no—
484C4—11681no—
485C4#99×D7311yescharacteristic
486C4#1798855911yescharacteristic
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—21no—
492C2—21no—
493C2—81no—
494C2#2260991711yescharacteristic
495C2#2260996211yescharacteristic
496C2#2260997511yescharacteristic
subgroupG/H
centerC22#17988445
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#1799C2
socleC22×C73#380
prime radicalC22×D4×C73D4
cosocleC23×C4×C73C23
hypercenter#1799D73
hypocenterC73#8610
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #22609958C2semidirect
3. #22609954C2semidirect
5. #22607798C2semidirect
6. #22607798C2semidirect
8. C22×#11924012C4semidirect
16. C2×C4⋊#10596831C4semidirect
18. C2×C22⋊#10596831C4semidirect
20. C2×#14556502C4semidirect
203. #10596831#99semidirect
256. C73#8610semidirect

Maximal subgroups

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

subgroupindex
C2×#179886592
#226099582
#226099542
#226099192
#226077982
C73×#17992
#861073