Finite Group Databasebeta

← #33002860

Subgroups — #33002860

Order 18688.

470 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989003C211yesmaximal, characteristic, complemented
2C2×#17988705C211yesmaximal, characteristic
3C2×#17988370C211yesmaximal, characteristic, complemented
4C2×#17988370C211yesmaximal, characteristic, complemented
5#22611544C211yesmaximal, characteristic, complemented
6#22608013C211yesmaximal, characteristic, complemented
7C73×#1374C211yesmaximal, characteristic, complemented
8C2×#14556613C411yescharacteristic
9C2×#14556597C2211yescharacteristic
10C2×#14556597C2211yescharacteristic
11#17989003—22no—
12#17989003—22no—
13C2×#14556531C2211yescharacteristic
14C2×#14556531C2211yescharacteristic
15C2×#14556530—21no—
16C2×C16×D73—21no—
17#17988705—22no—
18#17988705—22no—
19C2×#14556527C411yescharacteristic
20C2×#14556519C411yescharacteristic
21C2×#14556519C411yescharacteristic
22#17988370—22no—
23#17988370—22no—
24#17988366—21no—
25#17988366—21no—
26C22×C16×C73C2211yescharacteristic
27C22×C16×C73C2211yescharacteristic
28C2×C4×C8×C73C2211yescharacteristic
29C2×#11924028C2×C411yescharacteristic
30C2×#11924028C2×C411yescharacteristic
31#14556613—22no—
32#14556613—22no—
33C2×Dic292C811yescharacteristic
34C2×#11924017C811yescharacteristic
35C2×#11924017C811yescharacteristic
36C2×D584C811yescharacteristic
37#14556597—21no—
38#14556597—21no—
39#14556597—21no—
40#14556597—21no—
41#14556597—21no—
42#14556597—21no—
43#14556597D412yes—
44#14556597D412yes—
45C2×#11924012C2×C411yescharacteristic
46C2×#11924012C2×C411yescharacteristic
47C2×#11924011—21no—
48C2×#11924011—21no—
49C2×C8×D73—21no—
50C2×C8×D73—21no—
51#14556531—21no—
52#14556531—21no—
53#14556531—21no—
54#14556531D412yes—
55#14556530—24no—
56C2×#11924003—21no—
57C2×#11924003—21no—
58C16×D73—24no—
59#14556527—22no—
60#14556519—22no—
61#14556519—22no—
62C22×C8×C73C2×C411yescharacteristic
63C22×C8×C73C2311yescharacteristic
64C2×C42×C73C2×C411yescharacteristic
65C2×C16×C73—21no—
66C2×C16×C73—21no—
67C2×C16×C73—21no—
68C2×C16×C73—21no—
69C2×C16×C73—21no—
70C2×C16×C73D411yescharacteristic
71C2×C16×C73D411yescharacteristic
72C4×C8×C73—21no—
73C4×C8×C73—21no—
74#11924028—21no—
75#11924028—21no—
76#11924028—21no—
77#11924028—21no—
78#11924028—21no—
79#11924028—21no—
80#11924028C22⋊C412yes—
81#11924028M1612yes—
82C2×Dic146C2×C811yescharacteristic
83C2×Dic146C2×C811yescharacteristic
84C2×D292C2×C811yescharacteristic
85C2×D292C2×C811yescharacteristic
86C2×C22⋊D73—21no—
87C2×C22⋊D73—21no—
88C2×C4×D73—21no—
89C2×C4×D73—21no—
90Dic292—22no—
91#11924017—22no—
92#11924017—22no—
93D584—22no—
94#11924012—21no—
95#11924012—21no—
96#11924012—21no—
97#11924012C22⋊C412yes—
98#11924011—22no—
99#11924011—22no—
100#11924011—41no—
101#11924011—41no—
102C2×#10596831—21no—
103C2×#10596831—21no—
104C8×D73—22no—
105C8×D73—22no—
106C8×D73—41no—
107C8×D73—41no—
108#11924003—22no—
109#11924003—41no—
110C22×C4×C73—21no—
111C22×C4×C73C22×C411yescharacteristic
112C2×C8×C73—21no—
113C2×C8×C73—21no—
114C2×C8×C73C2×C811yescharacteristic
115C2×C8×C73C2×C811yescharacteristic
116C2×C8×C73C2×D411yescharacteristic
117C2×C8×C73C2×D411yescharacteristic
118C2×C8×C73C2×D411yescharacteristic
119C2×C8×C73C2×D411yescharacteristic
120C2×C8×C73#4111yescharacteristic
121C2×C8×C73#4111yescharacteristic
122C42×C73—21no—
123C42×C73—21no—
124C16×C73—21no—
125C16×C73—21no—
126C16×C73—41no—
127C23×C73#13111yescharacteristic
128C22×D73—21no—
129C22×D73—21no—
130C2×C4×C73—22no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73C2×C22⋊C411yescharacteristic
134C2×C4×C73C4×D411yescharacteristic
135C2×C4×C73C4×D411yescharacteristic
136C2×C4×C73C22×C811yescharacteristic
137C2×C4×C73C2×M1611yescharacteristic
138C2×C4×C73#13111yescharacteristic
139C22⋊D73—22no—
140C22⋊D73—22no—
141C22⋊D73—41no—
142C22⋊D73—41no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145D292—21no—
146D292—21no—
147D292—21no—
148D292C22⋊C812yes—
149C4×D73—22no—
150C4×D73—22no—
151C4×D73—41no—
152C4×D73—41no—
153Dic146—21no—
154Dic146—21no—
155Dic146—21no—
156Dic146C22⋊C812yes—
157C8×C73—21no—
158C8×C73—21no—
159C8×C73#12011yescharacteristic
160C8×C73#12111yescharacteristic
161C8×C73#12111yescharacteristic
162C8×C73#12311yescharacteristic
163#10596831—22no—
164#10596831—41no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73#40811yescharacteristic
168C22×C73C8×D411yescharacteristic
169C22×C73#43511yescharacteristic
170C2×D73—22no—
171C2×D73—41no—
172C2×D73—41no—
173C2×D73—41no—
174C2×D73—41no—
175C2×D73—41no—
176C4×C73—42no—
177C4×C73#38611yescharacteristic
178C4×C73C2×C22⋊C811yescharacteristic
179C4×C73C8×D411yescharacteristic
180C4×C73#43511yescharacteristic
181Dic73—22no—
182Dic73—41no—
183#12980—731nomaximal, Sylow
184C2×C73—21no—
185C2×C73—21no—
186C2×C73#186911yescharacteristic
187C2×C73#217011yescharacteristic
188C2×C73#217111yescharacteristic
189D73—42no—
190D73—81no—
191C2×#504—731no—
192C2×#443—731no—
193C2×#350—731no—
194C2×#350—731no—
195#2113—731no—
196#1376—731no—
197#1374D7311yescharacteristic, complemented
198C73#1298011yescharacteristic, complemented, Sylow
199C2×#135—731no—
200C2×#131—731no—
201C2×#131—731no—
202#504—1462no—
203#504—1462no—
204C2×M32—731no—
205C2×M32—731no—
206C2×M32—1461no—
207C22×C16—1461no—
208C22×C16C2×D7311yescharacteristic
209C22×C16C2×D7311yescharacteristic
210#443—1462no—
211#443—1462no—
212C2×#108—731no—
213C2×#104—731no—
214C2×#104—731no—
215C2×C4×C8C2×D7311yescharacteristic
216#350—1462no—
217#350—1462no—
218C22⋊C16—1461no—
219C22⋊C16—1461no—
220C2×#41—731no—
221C2×#41—731no—
222#135—1462no—
223#135—1462no—
224C2×Q16—731no—
225C2×SD16—731no—
226C2×SD16—731no—
227C2×D8—731no—
228#131—732no—
229#131—732no—
230#131—1461no—
231#131—1461no—
232#131—1461no—
233#131—1461no—
234#131—1461no—
235#131—1461no—
236C2×M16—731no—
237C2×M16—731no—
238C2×M16—1461no—
239C2×M16—1461no—
240C22×C8—1461no—
241C22×C8—1461no—
242C22×C8C4×D7311yescharacteristic
243C22×C8C22×D7311yescharacteristic
244C2×C42C4×D7311yescharacteristic
245M32—732no—
246M32—1464no—
247M32—1461no—
248M32—1461no—
249M32—1461no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16—21no—
253C2×C16—21no—
254C2×C16—21no—
255C2×C16—1464no—
256C2×C16—1461no—
257C2×C16—1461no—
258C2×C16D29211yescharacteristic
259C2×C16D29211yescharacteristic
260#108—1462no—
261#104—1462no—
262#104—1462no—
263C4×C8—21no—
264C4×C8—21no—
265#41—732no—
266#41—732no—
267#41—1461no—
268#41—1461no—
269#41—1461no—
270#41—1461no—
271#41—1461no—
272#41—1461no—
273C2×Q8—731no—
274C2×Q8—731no—
275C2×D4—731no—
276C2×D4—731no—
277C2×D4—1461no—
278C2×D4—1461no—
279C22×C4—21no—
280C22×C4—1461no—
281C22×C4—1461no—
282C22×C4C2×C4×D7311yescharacteristic
283Q16—1462no—
284SD16—1462no—
285SD16—1462no—
286D8—1462no—
287M16—2921no—
288M16—2921no—
289M16—732no—
290M16—1461no—
291M16—1461no—
292M16—1461no—
293M16—1462no—
294M16—1462no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—2921no—
298C2×C8—2921no—
299C2×C8—1461no—
300C2×C8—1461no—
301C2×C8—1462no—
302C2×C8—1462no—
303C2×C8C8×D7311yescharacteristic
304C2×C8C8×D7311yescharacteristic
305C2×C8D4×D7311yescharacteristic
306C2×C8D4×D7311yescharacteristic
307C2×C8D4×D7311yescharacteristic
308C2×C8C2×D29211yescharacteristic
309C2×C8#1192402811yescharacteristic
310C2×C8#1192402911yescharacteristic
311C42—21no—
312C42—21no—
313C16—21no—
314C16—21no—
315C16—41no—
316C16—2921no—
317C16—1462no—
318C23—1461no—
319C23—1461no—
320C23#1455659711yescharacteristic
321Q8—732no—
322Q8—1461no—
323Q8—1461no—
324Q8—1461no—
325D4—2921no—
326D4—2921no—
327D4—732no—
328D4—1462no—
329D4—1462no—
330D4—1461no—
331D4—1461no—
332D4—1461no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—2921no—
337C2×C4—2921no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1462no—
341C2×C4—1462no—
342C2×C4C22⋊C4×D7311yescharacteristic
343C2×C4#1455655311yescharacteristic
344C2×C4C4×D29211yescharacteristic
345C2×C4C2×C8×D7311yescharacteristic
346C2×C4M16×D7311yescharacteristic
347C2×C4#1455659911yescharacteristic
348C8—21no—
349C8—21no—
350C8—2921no—
351C8—1462no—
352C8#1455656111yescharacteristic
353C8#1455656411yescharacteristic
354C8#1455656611yescharacteristic
355C8#1455657611yescharacteristic
356C22—21no—
357C22—21no—
358C22—2921no—
359C22—2921no—
360C22—2921no—
361C22—2921no—
362C22—2921no—
363C22—1462no—
364C22#1798855211yescharacteristic
365C22C8×D29211yescharacteristic
366C22#1798865711yescharacteristic
367C4—42no—
368C4—2921no—
369C4—1462no—
370C4#1798846511yescharacteristic
371C4C22⋊C8×D7311yescharacteristic
372C4#1798865211yescharacteristic
373C4#1798866011yescharacteristic
374C2—21no—
375C2—21no—
376C2—2922no—
377C2—5841no—
378C2#2261022211yescharacteristic
379C2#2261176911yescharacteristic
380C2#2261177411yescharacteristic
subgroupG/H
centerC2×C8C2×D292
commutatorC2×C4×C73C22×C8
FrattiniC22×C8C22×D73
FittingC73×#1374C2
socleC22×C73C8×D4
prime radicalC2×#14556613C4
cosocleC22×C8×C73C23
hypercenter#1374D73
hypocenterC73#12980
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ #1374

Complements

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

NH ≅ G/Ntype
1. C2×#17989003C2semidirect
3. C2×#17988370C2semidirect
4. C2×#17988370C2semidirect
5. #22611544C2semidirect
6. #22608013C2semidirect
7. C73×#1374C2semidirect
197. #1374D73semidirect
198. C73#12980semidirect

Maximal subgroups

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

subgroupindex
C2×#179890032
C2×#179887052
C2×#179883702
#226115442
#226080132
C73×#13742
#1298073