Finite Group Databasebeta

← #33102136

Subgroups — #33102136

Order 18688.

1132 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989277C211yesmaximal, characteristic
2#22612798C212yesmaximal, complemented
3#22610916C212yesmaximal, complemented
4#22610386C214yesmaximal
5#22610007C212yesmaximal, complemented
6#22609919C211yesmaximal, characteristic
7#22609662C212yesmaximal, complemented
8C4×#99×C73C211yesmaximal, characteristic
9#17989277—22no—
10#17989277—24no—
11#17989277—22no—
12C2×#14556584C412yescomplemented
13C2×#14556583C411yescharacteristic, complemented
14C2×#14556581C412yescomplemented
15C2×#14556572C2212yes—
16C2×#14556570C411yescharacteristic, complemented
17C2×#14556570C2211yescharacteristic
18C2×C4×Dic146C411yescharacteristic, complemented
19C2×#14556550C411yescharacteristic, complemented
20C2×#14556547C2214yes—
21C2×#14556547C2212yes—
22C22×C4⋊Dic73C2211yescharacteristic
23C2×#14556506C2212yes—
24#17988485—22no—
25#17988472—24no—
26#17988448C2214yes—
27#17988447C2212yes—
28C4×C4⋊Dic73—22no—
29#17988354C2212yes—
30#17988353C2214yes—
31#17988353C2214yes—
32C2×C4×D4×C73C2211yescharacteristic
33C2×#99×C73C2212yes—
34C4×C22⋊C4×C73C2212yes—
35#342×C73C2211yescharacteristic
36#342×C73C2211yescharacteristic
37C22×Dic146C2×C411yescharacteristic
38C23×Dic73C2312yes—
39#14556584—24no—
40#14556584—24no—
41#14556583—22no—
42#14556583—22no—
43#14556581—24no—
44#14556581—24no—
45#14556572—24no—
46#14556572—24no—
47#14556570—22no—
48#14556570—22no—
49#14556570—22no—
50#14556570—22no—
51C4×Dic146—22no—
52C4×Dic146—21no—
53C4×Dic146—21no—
54#14556550—22no—
55#14556550—21no—
56#14556550—21no—
57#14556547—24no—
58#14556547—24no—
59#14556547—28no—
60#14556547—44no—
61C2×C4⋊Dic73—22no—
62C2×C4⋊Dic73C2×C411yescharacteristic
63C2×C4⋊Dic73C2×C411yescharacteristic
64C2×C4⋊Dic73C2×C411yescharacteristic
65C2×C4⋊Dic73C2×C412yes—
66C2×C4⋊Dic73D412yes—
67C2×C4⋊Dic73D414yes—
68C2×C4⋊Dic73D412yes—
69C2×#11924007—24no—
70C2×#11924007C2×C412yes—
71C2×#11924007C2×C412yes—
72C2×#11924007C2×C412yes—
73C2×#11924007C2×C412yes—
74C2×#11924007C2×C412yes—
75C2×C22⋊Dic73C2×C412yes—
76C2×C22⋊Dic73C2×C412yes—
77C2×C22⋊Dic73C2314yes—
78C2×C22⋊Dic73C2312yes—
79C2×C4×Dic73—24no—
80C2×C4×Dic73C2×C412yes—
81C2×C4×Dic73C2×C412yes—
82#14556506—42no—
83#14556498—24no—
84#14556498—24no—
85#14556498—22no—
86C22×D4×C73C2311yescharacteristic
87C23×C4×C73C2×C411yescharacteristic
88C23×C4×C73C2311yescharacteristic
89C4×D4×C73—22no—
90C4×D4×C73—22no—
91C2×C4⋊C4×C73C2×C411yescharacteristic
92C2×C22⋊C4×C73C2×C411yescharacteristic
93C2×C22⋊C4×C73C2312yes—
94C2×C22⋊C4×C73C2311yescharacteristic
95C2×C22⋊C4×C73C2312yes—
96C2×C42×C73—22no—
97C2×C42×C73C2×C411yescharacteristic
98#99×C73—24no—
99#95×C73—22no—
100C2×Dic146—21no—
101C2×Dic146—21no—
102C2×Dic146—42no—
103C22×Dic73—24no—
104C22×Dic73—22no—
105C22×Dic73—22no—
106C22×Dic73—24no—
107C22×Dic73C22×C412yes—
108C22×Dic73C22×C412yes—
109C22×Dic73C22×C412yes—
110C22×Dic73C22×C412yes—
111C22×Dic73C2×D414yes—
112C22×Dic73C2×D414yes—
113C4⋊Dic73—21no—
114C4⋊Dic73—21no—
115C4⋊Dic73—44no—
116C4⋊Dic73C22⋊C412yes—
117C4⋊Dic73C22⋊C411yescharacteristic
118C4⋊Dic73C22⋊C411yescharacteristic
119C4⋊Dic73C22⋊C412yes—
120C4⋊Dic73C22⋊C412yes—
121C4⋊Dic73C22⋊C414yes—
122C4⋊Dic73C22⋊C414yes—
123#11924007—24no—
124#11924007—24no—
125#11924007—24no—
126#11924007—22no—
127#11924007—22no—
128#11924007—24no—
129#11924007—48no—
130C22⋊Dic73—24no—
131C22⋊Dic73—22no—
132C22⋊Dic73—22no—
133C22⋊Dic73—24no—
134C22⋊Dic73—24no—
135C22⋊Dic73—24no—
136C4×Dic73—22no—
137C4×Dic73—22no—
138C4×Dic73—22no—
139C4×Dic73—22no—
140C4×Dic73—48no—
141C24×C73C22×C411yescharacteristic
142C24×C73C2411yescharacteristic
143C2×D4×C73—22no—
144C2×D4×C73—22no—
145C2×D4×C73—21no—
146C2×D4×C73—21no—
147C22×C4×C73—22no—
148C22×C4×C73—21no—
149C22×C4×C73—21no—
150C22×C4×C73—22no—
151C22×C4×C73—42no—
152C22×C4×C73—42no—
153C22×C4×C73C22×C411yescharacteristic
154C22×C4×C73C22×C411yescharacteristic
155C22×C4×C73C22×C411yescharacteristic
156C22×C4×C73C22×C411yescharacteristic
157C22×C4×C73C22×C411yescharacteristic
158C22×C4×C73C2×D412yes—
159C22×C4×C73C2×D412yes—
160C4⋊C4×C73—22no—
161C22⋊C4×C73—22no—
162C22⋊C4×C73—22no—
163C22⋊C4×C73—22no—
164C22⋊C4×C73—22no—
165C22⋊C4×C73—22no—
166C22⋊C4×C73#4114yes—
167C42×C73—21no—
168C42×C73—21no—
169C42×C73—44no—
170C23×C73—21no—
171C23×C73—21no—
172C23×C73—21no—
173C23×C73—41no—
174C23×C73—41no—
175C23×C73—41no—
176C23×C73—41no—
177C23×C73C23×C411yescharacteristic
178C23×C73C22×D412yes—
179C23×C73C2×#4112yes—
180C23×C73H(5,𝔽2)11yescharacteristic
181C23×C732−1+411yescharacteristic
182D4×C73—42no—
183D4×C73—42no—
184C2×C4×C73—24no—
185C2×C4×C73—22no—
186C2×C4×C73—21no—
187C2×C4×C73—21no—
188C2×C4×C73—21no—
189C2×C4×C73—21no—
190C2×C4×C73—21no—
191C2×C4×C73—24no—
192C2×C4×C73—41no—
193C2×C4×C73—42no—
194C2×C4×C73—42no—
195C2×C4×C73—42no—
196C2×C4×C73—42no—
197C2×C4×C73—42no—
198C2×C4×C73—41no—
199C2×C4×C73—41no—
200C2×C4×C73—42no—
201C2×C4×C73—42no—
202C2×C4×C73—42no—
203C2×C4×C73C2×C22⋊C411yescharacteristic
204C2×C4×C73C2×C22⋊C412yes—
205C2×C4×C73C2×C22⋊C411yescharacteristic
206C2×Dic73—22no—
207C2×Dic73—22no—
208C2×Dic73—22no—
209C2×Dic73—22no—
210C2×Dic73—24no—
211C2×Dic73—24no—
212C2×Dic73—24no—
213C2×Dic73—24no—
214C2×Dic73—22no—
215C2×Dic73—22no—
216C2×Dic73—42no—
217C2×Dic73—42no—
218C2×Dic73—44no—
219C2×Dic73—44no—
220C2×Dic73—44no—
221C2×Dic73C2×C22⋊C412yes—
222C2×Dic73C2×C22⋊C412yes—
223C2×Dic73C2×C22⋊C414yes—
224Dic146—42no—
225Dic146—42no—
226C22×C73—22no—
227C22×C73—21no—
228C22×C73—22no—
229C22×C73—21no—
230C22×C73—42no—
231C22×C73—41no—
232C22×C73—41no—
233C22×C73—41no—
234C22×C73—41no—
235C22×C73—41no—
236C22×C73—81no—
237C22×C73—81no—
238C22×C73C22×C22⋊C411yescharacteristic
239C22×C73C4×#4111yescharacteristic
240C22×C73#52011yescharacteristic
241C22×C73#54612yes—
242C22×C73#54712yes—
243C4×C73—21no—
244C4×C73—22no—
245C4×C73—44no—
246C4×C73—41no—
247C4×C73—41no—
248C4×C73—41no—
249C4×C73—82no—
250C4×C73#41012yes—
251Dic73—22no—
252Dic73—24no—
253Dic73—22no—
254Dic73—42no—
255Dic73—42no—
256Dic73—84no—
257#22478—731nomaximal, Sylow
258C2×C73—22no—
259C2×C73—22no—
260C2×C73—21no—
261C2×C73—21no—
262C2×C73—81no—
263C2×C73#233911yescharacteristic
264C2×C73C2×#41011yescharacteristic
265C2×C73#288411yescharacteristic
266C2×#552—731no—
267#2344—732no—
268#1996—732no—
269#1899—734no—
270#1820—732no—
271#1799—731no—
272C4×#99D7311yescharacteristic
273#1740—732no—
274C73#2247811yescharacteristic, complemented, Sylow
275#552—1462no—
276#552—1464no—
277#552—1462no—
278C2×#126—732no—
279C2×#125—732no—
280C2×#125—731no—
281C2×#123—732no—
282C2×C22⋊Q8—731no—
283C2×C22⋊Q8—731no—
284C2×C4×Q8—731no—
285C2×C4×D4C2×D7311yescharacteristic
286C2×#117—731no—
287C2×#117—732no—
288C2×#117—734no—
289C22×C4⋊C4—731no—
290C2×#99—732no—
291C2×#99C2×D7312yes—
292#389—1462no—
293#387—1464no—
294#381—734no—
295#380—732no—
296C4×C4⋊C4—1462no—
297C4×C22⋊C4C2×D7312yes—
298#342—734no—
299#342—734no—
300#342—732no—
301#342C2×D7311yescharacteristic
302#342C2×D7311yescharacteristic
303C22×Q8—731no—
304C22×D4C22×D7311yescharacteristic
305C23×C4—732no—
306C23×C4C4×D7311yescharacteristic
307C23×C4C22×D7311yescharacteristic
308#126—1464no—
309#126—1464no—
310#125—1462no—
311#125—1462no—
312#125—1464no—
313#125—1464no—
314#123—1464no—
315#123—1464no—
316C22⋊Q8—1462no—
317C22⋊Q8—1462no—
318C22⋊Q8—1462no—
319C22⋊Q8—1462no—
320C4×Q8—1462no—
321C4×Q8—1461no—
322C4×Q8—1461no—
323C4×D4—22no—
324C4×D4—22no—
325#117—2924no—
326#117—1468no—
327#117—1464no—
328#117—1464no—
329#117—1462no—
330#117—1461no—
331#117—1461no—
332C2×C4⋊C4—731no—
333C2×C4⋊C4—731no—
334C2×C4⋊C4—732no—
335C2×C4⋊C4—732no—
336C2×C4⋊C4—734no—
337C2×C4⋊C4—732no—
338C2×C4⋊C4—732no—
339C2×C4⋊C4—731no—
340C2×C4⋊C4—732no—
341C2×C4⋊C4—732no—
342C2×C4⋊C4—732no—
343C2×C4⋊C4—732no—
344C2×C4⋊C4—1464no—
345C2×C4⋊C4—1462no—
346C2×C4⋊C4C4×D7311yescharacteristic
347C2×C22⋊C4—732no—
348C2×C22⋊C4—732no—
349C2×C22⋊C4—732no—
350C2×C22⋊C4—734no—
351C2×C22⋊C4C4×D7311yescharacteristic
352C2×C22⋊C4C22×D7312yes—
353C2×C22⋊C4C22×D7311yescharacteristic
354C2×C22⋊C4C22×D7312yes—
355C2×C42—22no—
356C2×C42—732no—
357C2×C42—732no—
358C2×C42—1464no—
359C2×C42C4×D7311yescharacteristic
360#99—24no—
361#99—2922no—
362#95—22no—
363#95—1464no—
364#95—1464no—
365#95—1462no—
366C24C2×C4×D7311yescharacteristic
367C24C23×D7311yescharacteristic
368C2×Q8—2922no—
369C2×Q8—1461no—
370C2×Q8—1461no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—21no—
374C2×D4—21no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—732no—
382C22×C4—732no—
383C22×C4—732no—
384C22×C4—732no—
385C22×C4—734no—
386C22×C4—734no—
387C22×C4—1464no—
388C22×C4—1464no—
389C22×C4—1462no—
390C22×C4—1462no—
391C22×C4C2×C4×D7311yescharacteristic
392C22×C4C2×C4×D7311yescharacteristic
393C22×C4C2×C4×D7311yescharacteristic
394C22×C4C2×C4×D7311yescharacteristic
395C22×C4C2×C4×D7311yescharacteristic
396C22×C4D4×D7312yes—
397C22×C4D4×D7312yes—
398C4⋊C4—22no—
399C4⋊C4—2924no—
400C4⋊C4—2928no—
401C4⋊C4—732no—
402C4⋊C4—731no—
403C4⋊C4—731no—
404C4⋊C4—732no—
405C4⋊C4—732no—
406C4⋊C4—734no—
407C4⋊C4—734no—
408C4⋊C4—1464no—
409C4⋊C4—1464no—
410C4⋊C4—1462no—
411C4⋊C4—1462no—
412C4⋊C4—1464no—
413C4⋊C4—1464no—
414C4⋊C4—1461no—
415C4⋊C4—1461no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—1464no—
422C22⋊C4—1464no—
423C22⋊C4—1462no—
424C22⋊C4—1462no—
425C22⋊C4—1464no—
426C22⋊C4—1464no—
427C22⋊C4#1192402814yes—
428C42—21no—
429C42—21no—
430C42—44no—
431C42—2928no—
432C42—1462no—
433C42—1462no—
434C42—1462no—
435C42—1462no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23C22×C4×D7311yescharacteristic
444C23C2×D4×D7312yes—
445C23C2×#1192402812yes—
446C23#1455663711yescharacteristic
447C23#1455663811yescharacteristic
448Q8—2922no—
449Q8—2922no—
450D4—42no—
451D4—42no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—2922no—
472C2×C4—2922no—
473C2×C4—2924no—
474C2×C4—2924no—
475C2×C4—2924no—
476C2×C4—732no—
477C2×C4—732no—
478C2×C4—734no—
479C2×C4—1462no—
480C2×C4—1462no—
481C2×C4—1464no—
482C2×C4—1464no—
483C2×C4—1464no—
484C2×C4—1464no—
485C2×C4—1462no—
486C2×C4—1462no—
487C2×C4—1462no—
488C2×C4—1462no—
489C2×C4C22⋊C4×D7311yescharacteristic
490C2×C4C22⋊C4×D7312yes—
491C2×C4C22⋊C4×D7311yescharacteristic
492C22—22no—
493C22—21no—
494C22—22no—
495C22—21no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—81no—
503C22—81no—
504C22C2×C22⋊C4×D7311yescharacteristic
505C22C4×#1192402811yescharacteristic
506C22#1798906711yescharacteristic
507C22#1798923312yes—
508C22#1798924212yes—
509C4—21no—
510C4—22no—
511C4—44no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—82no—
516C4—2922no—
517C4—2922no—
518C4—5844no—
519C4—1462no—
520C4—1462no—
521C4—1464no—
522C4#1798855912yes—
523C2—22no—
524C2—22no—
525C2—21no—
526C2—21no—
527C2—81no—
528C2#2261276211yescharacteristic
529C2C2×#1798855911yescharacteristic
530C2#2261839311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D73
commutatorC23×C73C23×C4
FrattiniC24C23×D73
FittingC4×#99×C73C2
socleC22×C73C22×C22⋊C4
prime radicalC22×D4×C73C23
cosocleC24×C73C24
hypercenterC4×#99D73
hypocenterC73#22478
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #22612798C2semidirect
3. #22610916C2semidirect
5. #22610007C2semidirect
7. #22609662C2semidirect
12. C2×#14556584C4semidirect
13. C2×#14556583C4semidirect
14. C2×#14556581C4semidirect
16. C2×#14556570C4semidirect
18. C2×C4×Dic146C4semidirect
19. C2×#14556550C4semidirect
274. C73#22478semidirect

Maximal subgroups

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

subgroupindex
C2×#179892772
#226127982
#226109162
#226103862
#226100072
#226099192
#226096622
C4×#99×C732
#2247873