Finite Group Databasebeta

← #33002846

Subgroups — #33002846

Order 18688.

494 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D73C211yesmaximal, characteristic, complemented
2#22618623C211yesmaximal, characteristic
3C2×#17988371C211yesmaximal, characteristic, complemented
4C2×#17988366C211yesmaximal, characteristic, complemented
5#22608021C211yesmaximal, characteristic, complemented
6#22608019C211yesmaximal, characteristic, complemented
7C2×#350×C73C211yesmaximal, characteristic, complemented
8C22×C8×D73C2211yescharacteristic
9#17989094C411yescharacteristic
10C2×#14556531C2211yescharacteristic
11C2×#14556530—21no—
12M32×D73—22no—
13M32×D73—22no—
14C22×#11924003C2211yescharacteristic
15C2×C16×D73—21no—
16#17988656—21no—
17#17988656—21no—
18C8×C22⋊D73—21no—
19C8×C22⋊D73—21no—
20#17988615C411yescharacteristic
21#17988554C411yescharacteristic
22#17988550C411yescharacteristic
23#17988542C2211yescharacteristic
24#17988371—22no—
25#17988366—21no—
26#17988366—21no—
27C2×#131×C73C2211yescharacteristic
28C2×M32×C73C2211yescharacteristic
29C22×C16×C73C2211yescharacteristic
30#350×C73—22no—
31C22×C4×D73C2×C411yescharacteristic
32C2×#11924012C2×C411yescharacteristic
33C22×#10596831C2×C411yescharacteristic
34C2×C8×D73—21no—
35C2×C8×D73—21no—
36C2×C8×D73—21no—
37C2×C8×D73—21no—
38C2×C8×D73D411yescharacteristic
39C2×C8×D73D411yescharacteristic
40C2×C8×D73D411yescharacteristic
41C2×C8×D73D411yescharacteristic
42#14556572—21no—
43#14556567C811yescharacteristic
44#14556567C811yescharacteristic
45#14556562C811yescharacteristic
46#14556562C811yescharacteristic
47#14556559—21no—
48C4×C22⋊D73—21no—
49C4×C22⋊D73—21no—
50#14556550C2×C411yescharacteristic
51#14556531—21no—
52#14556531D412yescomplemented
53#14556530—24no—
54C2×#11924003—21no—
55C2×#11924003—21no—
56C2×#11924003—21no—
57C2×#11924003—21no—
58C16×D73—24no—
59#14556520—21no—
60#14556520—21no—
61C22⋊#10596831—21no—
62C22⋊#10596831—21no—
63#14556503—21no—
64#14556503—21no—
65#14556501—21no—
66C8×Dic73—21no—
67C2×#41×C73C2×C411yescharacteristic
68#131×C73—21no—
69#131×C73—21no—
70#131×C73—21no—
71#131×C73—21no—
72C2×M16×C73—21no—
73C2×M16×C73C2×C411yescharacteristic
74C22×C8×C73—21no—
75C22×C8×C73C2311yescharacteristic
76M32×C73—21no—
77M32×C73D412yescomplemented
78C2×C16×C73—21no—
79C2×C16×C73—21no—
80C2×C16×C73—21no—
81C2×C16×C73—21no—
82C23×D73M1611yescharacteristic
83C2×C22⋊D73—21no—
84C2×C22⋊D73—21no—
85C22×Dic73M1611yescharacteristic
86C2×C4×D73—21no—
87C2×C4×D73—21no—
88C2×C4×D73—21no—
89C2×C4×D73—21no—
90C2×C4×D73C22⋊C411yescharacteristic
91C2×C4×D73C22⋊C411yescharacteristic
92C2×C4×D73C2×C811yescharacteristic
93C2×C4×D73C2×C811yescharacteristic
94#11924012—21no—
95#11924012—21no—
96C2×#10596831—21no—
97C2×#10596831—21no—
98C2×#10596831—21no—
99C2×#10596831C22⋊C411yescharacteristic
100C2×#10596831C22⋊C411yescharacteristic
101C8×D73—21no—
102C8×D73—21no—
103C8×D73—21no—
104C8×D73—21no—
105C8×D73—21no—
106C8×D73—21no—
107C8×D73—21no—
108C8×D73—21no—
109C4⋊Dic73C2×C811yescharacteristic
110C4⋊Dic73C2×C811yescharacteristic
111#11924007—21no—
112#11924007—21no—
113C22⋊Dic73—21no—
114C22⋊Dic73—21no—
115C22⋊Dic73—21no—
116#11924005—21no—
117#11924005—21no—
118C4×Dic73—21no—
119#11924003—22no—
120#11924003—41no—
121#41×C73—21no—
122#41×C73—21no—
123#41×C73—21no—
124#41×C73—21no—
125C2×Q8×C73C2×C811yescharacteristic
126C2×D4×C73—21no—
127C2×D4×C73C2×C811yescharacteristic
128C22×C4×C73—21no—
129C22×C4×C73C22×C411yescharacteristic
130M16×C73—21no—
131M16×C73—21no—
132M16×C73—41no—
133M16×C73—41no—
134C2×C8×C73—21no—
135C2×C8×C73—41no—
136C2×C8×C73—41no—
137C2×C8×C73C2×D411yescharacteristic
138C2×C8×C73C2×D411yescharacteristic
139C2×C8×C73C2×D411yescharacteristic
140C2×C8×C73C2×D411yescharacteristic
141C2×C8×C73#4111yescharacteristic
142C2×C8×C73#4111yescharacteristic
143C16×C73—22no—
144C16×C73—41no—
145C23×C73—21no—
146C23×C73C2×M1611yescharacteristic
147C22×D73—21no—
148C22×D73—21no—
149C22×D73—22no—
150C22×D73—41no—
151C22×D73C22⋊C811yescharacteristic
152C22×D73C22⋊C811yescharacteristic
153Q8×C73—21no—
154Q8×C73—21no—
155D4×C73—21no—
156D4×C73—21no—
157D4×C73—41no—
158D4×C73—41no—
159C2×C4×C73—21no—
160C2×C4×C73—41no—
161C2×C4×C73—41no—
162C2×C4×C73C2×C22⋊C411yescharacteristic
163C2×C4×C73C4×D411yescharacteristic
164C2×C4×C73C4×D411yescharacteristic
165C2×C4×C73C22×C811yescharacteristic
166C2×C4×C73#13111yescharacteristic
167C2×C4×C73#13111yescharacteristic
168C22⋊D73—42no—
169C22⋊D73—42no—
170C2×Dic73—21no—
171C2×Dic73—21no—
172C2×Dic73—21no—
173C2×Dic73—21no—
174C2×Dic73C22⋊C811yescharacteristic
175C2×Dic73C22⋊C811yescharacteristic
176C4×D73—21no—
177C4×D73—21no—
178C4×D73—21no—
179C4×D73—21no—
180C4×D73—21no—
181C4×D73—21no—
182C4×D73—21no—
183C4×D73—21no—
184C8×C73—41no—
185C8×C73#12011yescharacteristic
186C8×C73#12111yescharacteristic
187C8×C73#12111yescharacteristic
188C8×C73#12311yescharacteristic
189#10596831—21no—
190#10596831—21no—
191#10596831—41no—
192C22×C73—21no—
193C22×C73—21no—
194C22×C73—41no—
195C22×C73—41no—
196C22×C73—41no—
197C22×C73C2×C22⋊C811yescharacteristic
198C22×C73#43511yescharacteristic
199C22×C73#43511yescharacteristic
200C2×D73—21no—
201C2×D73—21no—
202C2×D73—21no—
203C2×D73—21no—
204C2×D73—21no—
205C2×D73—42no—
206C2×D73—42no—
207C2×D73#35012yescomplemented
208C4×C73—41no—
209C4×C73#38611yescharacteristic
210C4×C73#40811yescharacteristic
211C4×C73C8×D411yescharacteristic
212C4×C73C8×D411yescharacteristic
213Dic73—21no—
214Dic73—21no—
215Dic73—41no—
216Dic73—41no—
217#12978—731nomaximal, Sylow
218C2×C73—21no—
219C2×C73—21no—
220C2×C73—81no—
221C2×C73#186911yescharacteristic
222C2×C73C2×#35011yescharacteristic
223C2×C73#211711yescharacteristic
224D73—22no—
225D73—41no—
226C22×M32—731no—
227#2929—731no—
228C2×#350—731no—
229C2×#350D7311yescharacteristic, complemented
230C2×C22⋊C16—731no—
231#1379—731no—
232#1379—731no—
233C73#1297811yescharacteristic, complemented, Sylow
234C2×#131C2×D7311yescharacteristic
235C23×C8—731no—
236#525—731no—
237C2×M32—731no—
238C2×M32—1461no—
239C2×M32—1462no—
240C2×M32—1462no—
241C2×M32C2×D7311yescharacteristic
242C22×C16—731no—
243C22×C16—1461no—
244C22×C16C2×D7311yescharacteristic
245#435—1461no—
246#435—1461no—
247C8×D4—1461no—
248C8×D4—1461no—
249#424—731no—
250#408—731no—
251#407—731no—
252#405—731no—
253#350—22no—
254#350—1462no—
255C22⋊C16—1461no—
256C22⋊C16—1461no—
257C2×#41C4×D7311yescharacteristic
258C23×C4—731no—
259#131—21no—
260#131—21no—
261#131—21no—
262#131—21no—
263C2×M16—21no—
264C2×M16—731no—
265C2×M16C4×D7311yescharacteristic
266C22×C8—21no—
267C22×C8—731no—
268C22×C8—731no—
269C22×C8—731no—
270C22×C8—731no—
271C22×C8—731no—
272C22×C8—1461no—
273C22×C8—1461no—
274C22×C8—1461no—
275C22×C8—1461no—
276C22×C8C22×D7311yescharacteristic
277#123—1461no—
278C22⋊Q8—731no—
279C22⋊Q8—731no—
280#121—731no—
281#121—731no—
282#120—1461no—
283C4×D4—1461no—
284C4×D4—1461no—
285#117—731no—
286M32—21no—
287M32—732no—
288M32—1464no—
289M32—1461no—
290M32C22⋊D7312yescomplemented
291C2×C16—21no—
292C2×C16—21no—
293C2×C16—21no—
294C2×C16—21no—
295C2×C16—1464no—
296C2×C16—1461no—
297C2×C16—1461no—
298C2×C16—1461no—
299C2×C16—1461no—
300C4⋊C8—1461no—
301C4⋊C8—1461no—
302C22⋊C8—1461no—
303C22⋊C8—1461no—
304C22⋊C8—1461no—
305C22⋊C8—1461no—
306#97—1461no—
307C4×C8—1461no—
308C24—731no—
309#41—21no—
310#41—21no—
311#41—21no—
312#41—21no—
313C2×Q8C8×D7311yescharacteristic
314C2×D4—21no—
315C2×D4—1461no—
316C2×D4—1461no—
317C2×D4C8×D7311yescharacteristic
318C22×C4—21no—
319C22×C4—731no—
320C22×C4—731no—
321C22×C4—731no—
322C22×C4—731no—
323C22×C4—731no—
324C22×C4—1461no—
325C22×C4—1461no—
326C22×C4—1461no—
327C22×C4—1461no—
328C22×C4C2×C4×D7311yescharacteristic
329M16—21no—
330M16—21no—
331M16—41no—
332M16—41no—
333M16—1461no—
334M16—1461no—
335C2×C8—21no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—731no—
339C2×C8—731no—
340C2×C8—1461no—
341C2×C8—1461no—
342C2×C8—1461no—
343C2×C8—1461no—
344C2×C8—1461no—
345C2×C8—1461no—
346C2×C8—1461no—
347C2×C8—1461no—
348C2×C8—1461no—
349C2×C8—1461no—
350C2×C8—1461no—
351C2×C8D4×D7311yescharacteristic
352C2×C8D4×D7311yescharacteristic
353C2×C8D4×D7311yescharacteristic
354C2×C8C2×C22⋊D7311yescharacteristic
355C2×C8#1192402711yescharacteristic
356C2×C8#1192402811yescharacteristic
357C4⋊C4—731no—
358C4⋊C4—731no—
359C4⋊C4—1461no—
360C4⋊C4—1461no—
361C22⋊C4—1461no—
362C22⋊C4—1461no—
363C22⋊C4—1461no—
364C22⋊C4—1461no—
365C22⋊C4—1461no—
366C42—1461no—
367C16—22no—
368C16—41no—
369C16—2921no—
370C16—1462no—
371C23—21no—
372C23—2921no—
373C23—731no—
374C23—731no—
375C23—1462no—
376C23—1461no—
377C23—1461no—
378C23M16×D7311yescharacteristic
379Q8—21no—
380Q8—21no—
381D4—21no—
382D4—21no—
383D4—41no—
384D4—41no—
385D4—2922no—
386D4—2922no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—731no—
391C2×C4—731no—
392C2×C4—1461no—
393C2×C4—1461no—
394C2×C4—1461no—
395C2×C4—1461no—
396C2×C4—1461no—
397C2×C4—1461no—
398C2×C4—1461no—
399C2×C4—1461no—
400C2×C4—1461no—
401C2×C4—1461no—
402C2×C4—1461no—
403C2×C4—1461no—
404C2×C4C22⋊C4×D7311yescharacteristic
405C2×C4#1455655111yescharacteristic
406C2×C4C4×C22⋊D7311yescharacteristic
407C2×C4C2×C8×D7311yescharacteristic
408C2×C4#1455659711yescharacteristic
409C2×C4#1455659911yescharacteristic
410C8—41no—
411C8—2921no—
412C8—1461no—
413C8—1461no—
414C8#1455655911yescharacteristic
415C8#1455656211yescharacteristic
416C8#1455656411yescharacteristic
417C8#1455657311yescharacteristic
418C22—21no—
419C22—21no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—2922no—
424C22—2922no—
425C22—732no—
426C22—1461no—
427C22—1461no—
428C22—1461no—
429C22—1461no—
430C22—1461no—
431C22C22⋊C8×D7311yescharacteristic
432C22#1798865611yescharacteristic
433C22#1798866111yescharacteristic
434C4—41no—
435C4—2921no—
436C4—2921no—
437C4—1461no—
438C4—1461no—
439C4#1798846311yescharacteristic
440C4#1798855211yescharacteristic
441C4#1798865011yescharacteristic
442C4C8×C22⋊D7311yescharacteristic
443C2—21no—
444C2—21no—
445C2—81no—
446C2—2921no—
447C2—1462no—
448C2#2261022011yescharacteristic
449C2#350×D7311yescharacteristic
450C2#2261155711yescharacteristic
subgroupG/H
centerC2×C8D4×D73
commutatorC2×C4×C73C22×C8
FrattiniC22×C8C22×D73
FittingC2×#350×C73C2
socleC22×C73C2×C22⋊C8
prime radical#17989094C4
cosocleC22×C8×C73C23
hypercenterC2×#350D73
hypocenterC73#12978
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
1. C2×M32×D73C2semidirect
3. C2×#17988371C2semidirect
4. C2×#17988366C2semidirect
5. #22608021C2semidirect
6. #22608019C2semidirect
7. C2×#350×C73C2semidirect
52. #14556531D4semidirect
77. M32×C73D4semidirect
207. C2×D73#350semidirect
229. C2×#350D73semidirect
233. C73#12978semidirect
290. M32C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D732
#226186232
C2×#179883712
C2×#179883662
#226080212
#226080192
C2×#350×C732
#1297873