Finite Group Databasebeta

← #33004153

Subgroups — #33004153

Order 18688.

446 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618641C211yesmaximal, characteristic
2C2×#17988405C211yesmaximal, characteristic, complemented
3C2×#17988372C211yesmaximal, characteristic, complemented
4C2×#17988371C211yesmaximal, characteristic, complemented
5C2×#17988370C211yesmaximal, characteristic, complemented
6M32×Dic73C211yesmaximal, characteristic, complemented
7C2×#350×C73C211yesmaximal, characteristic, complemented
8C2×#14556597C2211yescharacteristic
9#17989133C411yescharacteristic
10C2×#14556531C2211yescharacteristic
11C22×#11924003C2211yescharacteristic
12#17988663—21no—
13#17988663—21no—
14C8×C22⋊D73—21no—
15C8×C22⋊D73—21no—
16#17988610C411yescharacteristic
17#17988555C411yescharacteristic
18#17988554C411yescharacteristic
19C2×C8×Dic73C2211yescharacteristic
20#17988405—21no—
21#17988405—21no—
22#17988372—22no—
23#17988371—22no—
24#17988370—22no—
25#17988362—21no—
26C16×Dic73—21no—
27C2×#131×C73C2211yescharacteristic
28C2×M32×C73C2211yescharacteristic
29C22×C16×C73C2211yescharacteristic
30#350×C73—22no—
31C2×#11924028C2×C411yescharacteristic
32#14556597—21no—
33#14556597—21no—
34#14556597—21no—
35#14556597—21no—
36C2×#11924012C2×C411yescharacteristic
37C2×#11924011—21no—
38C22×#10596831C2×C411yescharacteristic
39C2×C8×D73—21no—
40#14556589C811yescharacteristic
41#14556587C811yescharacteristic
42#14556580C811yescharacteristic
43#14556578C811yescharacteristic
44#14556563—21no—
45#14556563—21no—
46C4×C22⋊D73—21no—
47C4×C22⋊D73—21no—
48C2×C4×Dic73C2×C411yescharacteristic
49#14556531—21no—
50#14556531D412yescomplemented
51C2×#11924003—21no—
52C2×#11924003—21no—
53C2×#11924003—21no—
54C2×#11924003—21no—
55#14556520—21no—
56#14556520—21no—
57C22⋊#10596831—21no—
58C22⋊#10596831—21no—
59#14556503—21no—
60#14556503—21no—
61C8×Dic73D411yescharacteristic
62C8×Dic73D411yescharacteristic
63C8×Dic73D411yescharacteristic
64C8×Dic73D411yescharacteristic
65C2×#41×C73C2×C411yescharacteristic
66#131×C73—21no—
67#131×C73—21no—
68#131×C73—21no—
69#131×C73—21no—
70C2×M16×C73—21no—
71C2×M16×C73C2×C411yescharacteristic
72C22×C8×C73—21no—
73C22×C8×C73C2311yescharacteristic
74M32×C73—21no—
75M32×C73D412yescomplemented
76C2×C16×C73—21no—
77C2×C16×C73—21no—
78C2×C16×C73—21no—
79C2×C16×C73—21no—
80#11924028—21no—
81#11924028—21no—
82#11924028—21no—
83#11924028—21no—
84C2×Dic146C2×C811yescharacteristic
85C2×D292C2×C811yescharacteristic
86C2×C22⋊D73—21no—
87C2×C22⋊D73—21no—
88C2×C22⋊D73—21no—
89C22×Dic73M1611yescharacteristic
90C22×Dic73M1611yescharacteristic
91C2×C4×D73—21no—
92#11924012—21no—
93#11924012—21no—
94#11924011—41no—
95#11924011—41no—
96C2×#10596831—21no—
97C2×#10596831—21no—
98C2×#10596831—21no—
99C2×#10596831C22⋊C411yescharacteristic
100C2×#10596831C22⋊C411yescharacteristic
101C8×D73—41no—
102C8×D73—41no—
103#11924007—21no—
104#11924007—21no—
105C22⋊Dic73—21no—
106C22⋊Dic73—21no—
107#11924005—21no—
108#11924005—21no—
109C4×Dic73C22⋊C411yescharacteristic
110C4×Dic73C22⋊C411yescharacteristic
111C4×Dic73C2×C811yescharacteristic
112C4×Dic73C2×C811yescharacteristic
113#11924003—22no—
114#11924003—41no—
115#41×C73—21no—
116#41×C73—21no—
117#41×C73—21no—
118#41×C73—21no—
119C2×Q8×C73C2×C811yescharacteristic
120C2×D4×C73—21no—
121C2×D4×C73C2×C811yescharacteristic
122C22×C4×C73—21no—
123C22×C4×C73C22×C411yescharacteristic
124M16×C73—21no—
125M16×C73—21no—
126M16×C73—41no—
127M16×C73—41no—
128C2×C8×C73—21no—
129C2×C8×C73—41no—
130C2×C8×C73—41no—
131C2×C8×C73C2×D411yescharacteristic
132C2×C8×C73C2×D411yescharacteristic
133C2×C8×C73C2×D411yescharacteristic
134C2×C8×C73C2×D411yescharacteristic
135C2×C8×C73#4111yescharacteristic
136C2×C8×C73#4111yescharacteristic
137C16×C73—22no—
138C16×C73—41no—
139C23×C73—21no—
140C23×C73C2×M1611yescharacteristic
141C22×D73—21no—
142Q8×C73—21no—
143Q8×C73—21no—
144D4×C73—21no—
145D4×C73—21no—
146D4×C73—41no—
147D4×C73—41no—
148C2×C4×C73—21no—
149C2×C4×C73—41no—
150C2×C4×C73—41no—
151C2×C4×C73C2×C22⋊C411yescharacteristic
152C2×C4×C73C4×D411yescharacteristic
153C2×C4×C73C4×D411yescharacteristic
154C2×C4×C73C22×C811yescharacteristic
155C2×C4×C73#13111yescharacteristic
156C2×C4×C73#13111yescharacteristic
157C22⋊D73—42no—
158C22⋊D73—41no—
159C22⋊D73—41no—
160C22⋊D73—42no—
161C2×Dic73—22no—
162C2×Dic73—21no—
163C2×Dic73—41no—
164C2×Dic73C22⋊C811yescharacteristic
165C2×Dic73C22⋊C811yescharacteristic
166C2×Dic73C22⋊C811yescharacteristic
167C2×Dic73C22⋊C811yescharacteristic
168D292—21no—
169D292—21no—
170C4×D73—41no—
171C4×D73—41no—
172Dic146—21no—
173Dic146—21no—
174C8×C73—41no—
175C8×C73#12111yescharacteristic
176C8×C73#12111yescharacteristic
177C8×C73#12411yescharacteristic
178C8×C73#12711yescharacteristic
179#10596831—21no—
180#10596831—21no—
181#10596831—41no—
182C22×C73—21no—
183C22×C73—21no—
184C22×C73—41no—
185C22×C73—41no—
186C22×C73—41no—
187C22×C73C2×C22⋊C811yescharacteristic
188C22×C73#43611yescharacteristic
189C22×C73#43611yescharacteristic
190C2×D73—41no—
191C2×D73—41no—
192C2×D73—41no—
193C4×C73—41no—
194C4×C73#39011yescharacteristic
195C4×C73#40811yescharacteristic
196C4×C73C8×D411yescharacteristic
197C4×C73C8×D411yescharacteristic
198Dic73—21no—
199Dic73—21no—
200Dic73—21no—
201Dic73—41no—
202Dic73#35012yescomplemented
203#13193—731nomaximal, Sylow
204C2×C73—21no—
205C2×C73—21no—
206C2×C73—81no—
207C2×C73#195411yescharacteristic
208C2×C73C2×#35011yescharacteristic
209C2×C73#211711yescharacteristic
210D73—81no—
211#2931—731no—
212C2×C4⋊C16—731no—
213C2×#350—731no—
214C2×#350—731no—
215C2×#350—731no—
216C2×#350D7311yescharacteristic, complemented
217C4×M32—731no—
218C73#1319311yescharacteristic, complemented, Sylow
219C2×#131—731no—
220C2×#131C2×D7311yescharacteristic
221#532—731no—
222C2×M32—731no—
223C2×M32C2×D7311yescharacteristic
224C22×C16—731no—
225C22×C16C2×D7311yescharacteristic
226#436—1461no—
227#436—1461no—
228C8×D4—1461no—
229C8×D4—1461no—
230#423—731no—
231#408—731no—
232#408—731no—
233C2×C4×C8—731no—
234C4⋊C16—1461no—
235C4⋊C16—1461no—
236#350—22no—
237#350—1462no—
238#350—1462no—
239#350—1462no—
240#346—1461no—
241C4×C16—1461no—
242C2×#41—731no—
243C2×#41C4×D7311yescharacteristic
244#131—21no—
245#131—21no—
246#131—21no—
247#131—21no—
248#131—1461no—
249#131—1461no—
250#131—1461no—
251#131—1461no—
252C2×M16—21no—
253C2×M16—731no—
254C2×M16—1461no—
255C2×M16C4×D7311yescharacteristic
256C22×C8—21no—
257C22×C8—731no—
258C22×C8—1461no—
259C22×C8C22×D7311yescharacteristic
260C4⋊Q8—731no—
261#127—731no—
262#124—731no—
263#124—731no—
264#121—1461no—
265#121—1461no—
266C4×D4—1461no—
267C4×D4—1461no—
268C2×C42—731no—
269M32—21no—
270M32—732no—
271M32—1461no—
272M32C22⋊D7312yescomplemented
273C2×C16—21no—
274C2×C16—21no—
275C2×C16—21no—
276C2×C16—21no—
277C2×C16—1461no—
278C2×C16—1461no—
279C2×C16—1461no—
280C2×C16—1461no—
281C4⋊C8—1461no—
282C4⋊C8—1461no—
283C22⋊C8—1461no—
284C22⋊C8—1461no—
285C22⋊C8—1461no—
286C22⋊C8—1461no—
287C4×C8—731no—
288C4×C8—731no—
289C4×C8—731no—
290C4×C8—731no—
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295#41—1461no—
296#41—1461no—
297#41—1461no—
298#41—1461no—
299C2×Q8—731no—
300C2×Q8C8×D7311yescharacteristic
301C2×D4—21no—
302C2×D4—731no—
303C2×D4—1461no—
304C2×D4—1461no—
305C2×D4—1461no—
306C2×D4C8×D7311yescharacteristic
307C22×C4—21no—
308C22×C4—731no—
309C22×C4—731no—
310C22×C4—1461no—
311C22×C4C2×C4×D7311yescharacteristic
312M16—21no—
313M16—21no—
314M16—41no—
315M16—41no—
316M16—2921no—
317M16—2921no—
318M16—1461no—
319M16—1461no—
320C2×C8—21no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—2921no—
324C2×C8—2921no—
325C2×C8—731no—
326C2×C8—731no—
327C2×C8—1461no—
328C2×C8—1461no—
329C2×C8—1461no—
330C2×C8D4×D7311yescharacteristic
331C2×C8D4×D7311yescharacteristic
332C2×C8D4×D7311yescharacteristic
333C2×C8C2×C22⋊D7311yescharacteristic
334C2×C8#1192402711yescharacteristic
335C2×C8#1192402811yescharacteristic
336C4⋊C4—1461no—
337C4⋊C4—1461no—
338C22⋊C4—1461no—
339C22⋊C4—1461no—
340C22⋊C4—1461no—
341C22⋊C4—1461no—
342C42—731no—
343C42—731no—
344C42—731no—
345C42—731no—
346C16—22no—
347C16—41no—
348C16—2921no—
349C16—1462no—
350C23—21no—
351C23—1461no—
352C23M16×D7311yescharacteristic
353Q8—21no—
354Q8—21no—
355Q8—1461no—
356Q8—1461no—
357D4—21no—
358D4—21no—
359D4—41no—
360D4—41no—
361D4—2921no—
362D4—2921no—
363D4—2922no—
364D4—2922no—
365D4—1461no—
366D4—1461no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—2921no—
371C2×C4—2921no—
372C2×C4—2921no—
373C2×C4—731no—
374C2×C4—731no—
375C2×C4—731no—
376C2×C4—731no—
377C2×C4—1461no—
378C2×C4—1462no—
379C2×C4C22⋊C4×D7311yescharacteristic
380C2×C4#1455655111yescharacteristic
381C2×C4C4×C22⋊D7311yescharacteristic
382C2×C4C2×C8×D7311yescharacteristic
383C2×C4#1455659711yescharacteristic
384C2×C4#1455659911yescharacteristic
385C8—41no—
386C8—2921no—
387C8—1461no—
388C8—1461no—
389C8#1455656311yescharacteristic
390C8#1455656411yescharacteristic
391C8#1455657711yescharacteristic
392C8#1455658711yescharacteristic
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—2921no—
399C22—2921no—
400C22—2921no—
401C22C22⋊C8×D7311yescharacteristic
402C22#1798866211yescharacteristic
403C22#1798866311yescharacteristic
404C4—41no—
405C4—2921no—
406C4—732no—
407C4—1461no—
408C4—1461no—
409C4—1461no—
410C4#1798848711yescharacteristic
411C4#1798855211yescharacteristic
412C4#1798865011yescharacteristic
413C4C8×C22⋊D7311yescharacteristic
414C2—21no—
415C2—21no—
416C2—81no—
417C2—5841no—
418C2#2261072311yescharacteristic
419C2#350×D7311yescharacteristic
420C2#2261155711yescharacteristic
subgroupG/H
centerC2×C8D4×D73
commutatorC2×C4×C73C22×C8
FrattiniC22×C8C22×D73
FittingC2×#350×C73C2
socleC22×C73C2×C22⋊C8
prime radical#17989133C4
cosocleC22×C8×C73C23
hypercenterC2×#350D73
hypocenterC73#13193
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
2. C2×#17988405C2semidirect
3. C2×#17988372C2semidirect
4. C2×#17988371C2semidirect
5. C2×#17988370C2semidirect
6. M32×Dic73C2semidirect
7. C2×#350×C73C2semidirect
50. #14556531D4semidirect
75. M32×C73D4semidirect
202. Dic73#350semidirect
216. C2×#350D73semidirect
218. C73#13193semidirect
272. M32C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
#226186412
C2×#179884052
C2×#179883722
C2×#179883712
C2×#179883702
M32×Dic732
C2×#350×C732
#1319373