Finite Group Databasebeta

← #13061691

Subgroups — #13061691

Order 1344.

480 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×#121C211yesmaximal, characteristic, complemented
2#10621423C211yesmaximal, characteristic, complemented
3#10621422C211yesmaximal, characteristic, complemented
4#10621422C211yesmaximal, characteristic, complemented
5#10621422C211yesmaximal, characteristic, complemented
6#10621421C211yesmaximal, characteristic, complemented
7#10621418C211yesmaximal, characteristic, complemented
8#10621412C211yesmaximal, characteristic, complemented
9C4×#4268C211yesmaximal, characteristic, complemented
10#10621377C211yesmaximal, characteristic, complemented
11#10621372C211yesmaximal, characteristic, complemented
12#10621367C211yesmaximal, characteristic, complemented
13#10621366C211yesmaximal, characteristic, complemented
14#10621364C211yesmaximal, characteristic, complemented
15#10621360C211yesmaximal, characteristic, complemented
16#90306—31nomaximal, Hall
17C2×C3×C7×D4C2211yescharacteristic
18C2×C3×C7×D4C2211yescharacteristic
19C2×C3×C7×D4C2211yescharacteristic
20C22×C3×C4×C7C2211yescharacteristic
21C2×#4268C2211yescharacteristic
22C2×#4268C2211yescharacteristic
23C2×#4268C2211yescharacteristic
24C2×#4268C2211yescharacteristic
25C2×#4268C2211yescharacteristic
26C2×#4268C2211yescharacteristic
27C22×Dic21C2211yescharacteristic
28C22×Dic21C2211yescharacteristic
29C2×D84C2211yescharacteristic
30C2×C4×D21C2211yescharacteristic
31C2×C4×D21C2211yescharacteristic
32C3×C7×C4⋊C4C2211yescharacteristic
33C3×C7×C22⋊C4C2211yescharacteristic
34C3×C7×C22⋊C4C2211yescharacteristic
35#66636C2211yescharacteristic
36#66636C2211yescharacteristic
37#66636C2211yescharacteristic
38#66636C2211yescharacteristic
39#66631C2211yescharacteristic
40#66631C2211yescharacteristic
41#66631C2211yescharacteristic
42#66631C2211yescharacteristic
43C4⋊Dic21C2211yescharacteristic
44#66629C2211yescharacteristic
45#66629C2211yescharacteristic
46#66629C2211yescharacteristic
47#66629C2211yescharacteristic
48#66629C2211yescharacteristic
49#66629C2211yescharacteristic
50C4×Dic21C2211yescharacteristic
51C4×Dic21C2211yescharacteristic
52C7×#121D311yescharacteristic, complemented
53#6503—31no—
54#6502—31no—
55#6502—31no—
56#6502—31no—
57#6501—31no—
58#6498—31no—
59#6492—31no—
60C4×C22⋊D7—31no—
61#6457—31no—
62#6452—31no—
63#6447—31no—
64#6446—31no—
65(C22⋊D7)⋊C4—31no—
66#6440—31no—
67#5615—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C23×C3×C7C2311yescharacteristic
70C23×C3×C7C2311yescharacteristic
71C22×D21C2311yescharacteristic
72C22×D21C2311yescharacteristic
73C3×C7×D4—41no—
74C3×C7×D4—41no—
75C3×C7×D4—41no—
76C2×C3×C4×C7—41no—
77C2×C3×C4×C7C2311yescharacteristic
78C2×C3×C4×C7C2311yescharacteristic
79C2×C3×C4×C7C2311yescharacteristic
80C2×C3×C4×C7C2311yescharacteristic
81#4268—22no—
82#4268—22no—
83#4268—41no—
84#4268—41no—
85#4268—41no—
86#4268—41no—
87C2×Dic21—22no—
88C2×Dic21—41no—
89C2×Dic21C2311yescharacteristic
90C2×Dic21C2311yescharacteristic
91C2×Dic21C2311yescharacteristic
92C2×Dic21C2311yescharacteristic
93C2×Dic21C2311yescharacteristic
94C2×Dic21C2311yescharacteristic
95D84—41no—
96C4×D21—41no—
97C4×D21—41no—
98C2×C7×D4C2×D311yescharacteristic
99C2×C7×D4C2×D311yescharacteristic
100C2×C7×D4C2×D311yescharacteristic
101C22×C4×C7C2×D311yescharacteristic
102C2×C22⋊D7—31no—
103C2×C22⋊D7—31no—
104C2×C22⋊D7—31no—
105C2×C22⋊D7—31no—
106C2×C22⋊D7—31no—
107C2×C22⋊D7—31no—
108C22×Dic7—31no—
109C22×Dic7—31no—
110C2×D28—31no—
111C2×C4×D7—31no—
112C2×C4×D7—31no—
113C7×C4⋊C4C2×D311yescharacteristic
114C7×C22⋊C4C2×D311yescharacteristic
115C7×C22⋊C4C2×D311yescharacteristic
116C22⋊Dic7—31no—
117C22⋊Dic7—31no—
118C22⋊Dic7—31no—
119C22⋊Dic7—31no—
120(C2×D7)⋊C4—31no—
121(C2×D7)⋊C4—31no—
122(C2×D7)⋊C4—31no—
123(C2×D7)⋊C4—31no—
124C4⋊Dic7—31no—
125Dic7⋊C4—31no—
126Dic7⋊C4—31no—
127Dic7⋊C4—31no—
128Dic7⋊C4—31no—
129Dic7⋊C4—31no—
130Dic7⋊C4—31no—
131C4×Dic7—31no—
132C4×Dic7—31no—
133C3×#121D711yescharacteristic, complemented
134#940—71no—
135#939—71no—
136#939—71no—
137#939—71no—
138#938—71no—
139#935—71no—
140#929—71no—
141C4×#67—71no—
142#894—71no—
143#889—71no—
144#884—71no—
145#883—71no—
146#67⋊C4—71no—
147#877—71no—
148C22×C3×C7—21no—
149C22×C3×C7—21no—
150C22×C3×C7—21no—
151C22×C3×C7—21no—
152C22×C3×C7—21no—
153C22×C3×C7—21no—
154C22×C3×C7—21no—
155C22×C3×C7—21no—
156C22×C3×C7—21no—
157C22×C3×C7C2411yescharacteristic
158C2×D21—21no—
159C2×D21—21no—
160C2×D21—21no—
161C2×D21—21no—
162C2×D21—21no—
163C2×D21—21no—
164C3×C4×C7—21no—
165C3×C4×C7—21no—
166C3×C4×C7—21no—
167C3×C4×C7—21no—
168Dic21—21no—
169Dic21—21no—
170Dic21—21no—
171Dic21—21no—
172Dic21—21no—
173Dic21#4112yes—
174#540—211noSylow
175C23×C7C22×D311yescharacteristic
176C23×C7C22×D311yescharacteristic
177C23×C7C22×D311yescharacteristic
178C22×D7—31no—
179C22×D7—31no—
180C7×D4—41no—
181C7×D4—41no—
182C7×D4—41no—
183C2×C4×C7—41no—
184C2×C4×C7C22×D311yescharacteristic
185C2×C4×C7C22×D311yescharacteristic
186C2×C4×C7C22×D311yescharacteristic
187C2×C4×C7C22×D311yescharacteristic
188C22⋊D7—62no—
189C22⋊D7—62no—
190C22⋊D7—121no—
191C22⋊D7—121no—
192C22⋊D7—121no—
193C22⋊D7—121no—
194C2×Dic7—31no—
195C2×Dic7—31no—
196C2×Dic7—31no—
197C2×Dic7—31no—
198C2×Dic7—31no—
199C2×Dic7—31no—
200C2×Dic7—62no—
201C2×Dic7—121no—
202D28—121no—
203C4×D7—121no—
204C4×D7—121no—
205C2×C3×D4C2×D711yescharacteristic
206C2×C3×D4C2×D711yescharacteristic
207C2×C3×D4C2×D711yescharacteristic
208C22×C3×C4C2×D711yescharacteristic
209C2×#67—71no—
210C2×#67—71no—
211C2×#67—71no—
212C2×#67—71no—
213C2×#67—71no—
214C2×#67—71no—
215C22×Dic3—71no—
216C22×Dic3—71no—
217C2×D12—71no—
218C2×C4×D3—71no—
219C2×C4×D3—71no—
220C3×C4⋊C4C2×D711yescharacteristic
221C3×C22⋊C4C2×D711yescharacteristic
222C3×C22⋊C4C2×D711yescharacteristic
223#217—71no—
224#217—71no—
225#217—71no—
226#217—71no—
227(C2×D3)⋊C4—71no—
228(C2×D3)⋊C4—71no—
229(C2×D3)⋊C4—71no—
230(C2×D3)⋊C4—71no—
231C4⋊Dic3—71no—
232Dic3⋊C4—71no—
233Dic3⋊C4—71no—
234Dic3⋊C4—71no—
235Dic3⋊C4—71no—
236Dic3⋊C4—71no—
237Dic3⋊C4—71no—
238C4×Dic3—71no—
239C4×Dic3—71no—
240C2×C3×C7—41no—
241C2×C3×C7—41no—
242C2×C3×C7—41no—
243C2×C3×C7C2×#4111yescharacteristic
244C2×C3×C7H(5,𝔽2)11yescharacteristic
245C2×C3×C7H(5,𝔽2)11yescharacteristic
246D21—41no—
247D21—41no—
248#127—211no—
249#125—211no—
250#123—211no—
251#123—211no—
252#123—211no—
253#123—211no—
254#121—211no—
255#121—211no—
256#121—211no—
257#121—211no—
258#121—211no—
259#121D2111yescharacteristic, complemented
260C4×D4—211no—
261C4×D4—211no—
262#117—211no—
263C22×C7—21no—
264C22×C7—21no—
265C22×C7—21no—
266C22×C7—21no—
267C22×C7—21no—
268C22×C7—21no—
269C22×C7—21no—
270C22×C7—21no—
271C22×C7—21no—
272C22×C7C23×D311yescharacteristic
273C2×D7—61no—
274C2×D7—61no—
275C2×D7—61no—
276C2×D7—61no—
277C2×D7—61no—
278C2×D7—61no—
279C4×C7—21no—
280C4×C7—21no—
281C4×C7—21no—
282C4×C7—21no—
283Dic7—32no—
284Dic7—61no—
285Dic7—61no—
286Dic7—61no—
287Dic7—61no—
288Dic7—61no—
289C23×C3C22×D711yescharacteristic
290C23×C3C22×D711yescharacteristic
291C23×C3C22×D711yescharacteristic
292C22×D3—71no—
293C22×D3—71no—
294C3×D4—41no—
295C3×D4—41no—
296C3×D4—41no—
297C2×C3×C4—41no—
298C2×C3×C4C22×D711yescharacteristic
299C2×C3×C4C22×D711yescharacteristic
300C2×C3×C4C22×D711yescharacteristic
301C2×C3×C4C22×D711yescharacteristic
302#67—142no—
303#67—142no—
304#67—281no—
305#67—281no—
306#67—281no—
307#67—281no—
308C2×Dic3—71no—
309C2×Dic3—71no—
310C2×Dic3—71no—
311C2×Dic3—71no—
312C2×Dic3—71no—
313C2×Dic3—71no—
314C2×Dic3—142no—
315C2×Dic3—281no—
316D12—281no—
317C4×D3—281no—
318C4×D3—281no—
319C3×C7#54011yescharacteristic, complemented, Hall
320C2×D4—211no—
321C2×D4—211no—
322C2×D4—211no—
323C2×D4—211no—
324C2×D4—211no—
325C2×D4—211no—
326C2×D4—211no—
327C2×D4C2×D2111yescharacteristic
328C2×D4C2×D2111yescharacteristic
329C2×D4C2×D2111yescharacteristic
330C22×C4—211no—
331C22×C4—211no—
332C22×C4—211no—
333C22×C4—211no—
334C22×C4C2×D2111yescharacteristic
335C4⋊C4—211no—
336C4⋊C4—211no—
337C4⋊C4—211no—
338C4⋊C4—211no—
339C4⋊C4—211no—
340C4⋊C4—211no—
341C4⋊C4—211no—
342C4⋊C4C2×D2111yescharacteristic
343C22⋊C4—211no—
344C22⋊C4—211no—
345C22⋊C4—211no—
346C22⋊C4—211no—
347C22⋊C4—211no—
348C22⋊C4—211no—
349C22⋊C4—211no—
350C22⋊C4—211no—
351C22⋊C4C2×D2111yescharacteristic
352C22⋊C4C2×D2111yescharacteristic
353C42—211no—
354C42—211no—
355C2×C7—41no—
356C2×C7—41no—
357C2×C7—41no—
358C2×C7#100411yescharacteristic
359C2×C7#100411yescharacteristic
360C2×C7D3×#4111yescharacteristic
361D7—121no—
362D7—121no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3C23×D711yescharacteristic
373C2×D3—141no—
374C2×D3—141no—
375C2×D3—141no—
376C2×D3—141no—
377C2×D3—141no—
378C2×D3—141no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383Dic3—72no—
384Dic3—141no—
385Dic3—141no—
386Dic3—141no—
387Dic3—141no—
388Dic3—141no—
389C23—211no—
390C23—211no—
391C23C22×D2111yescharacteristic
392C23C22×D2111yescharacteristic
393C23C22×D2111yescharacteristic
394D4—41no—
395D4—41no—
396D4—41no—
397D4—422no—
398D4—422no—
399D4—841no—
400D4—841no—
401D4—841no—
402D4—841no—
403D4—841no—
404C2×C4—41no—
405C2×C4—211no—
406C2×C4—211no—
407C2×C4—211no—
408C2×C4—211no—
409C2×C4—211no—
410C2×C4—211no—
411C2×C4—422no—
412C2×C4—841no—
413C2×C4—841no—
414C2×C4—841no—
415C2×C4C22×D2111yescharacteristic
416C2×C4C22×D2111yescharacteristic
417C2×C4C22×D2111yescharacteristic
418C2×C4C22×D2111yescharacteristic
419C7#561511yescharacteristic, complemented, Sylow
420C2×C3—41no—
421C2×C3—41no—
422C2×C3—41no—
423C2×C3#654811yescharacteristic
424C2×C3#654811yescharacteristic
425C2×C3D7×#4111yescharacteristic
426D3—281no—
427D3—281no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—421no—
438C22—421no—
439C22—421no—
440C22—421no—
441C22—421no—
442C22—421no—
443C22C23×D2111yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—212no—
449C4—421no—
450C4—421no—
451C4—421no—
452C4—421no—
453C4—421no—
454C3#9030611yescharacteristic, complemented, Sylow
455C2—41no—
456C2—41no—
457C2—41no—
458C2—841no—
459C2—841no—
460C2#1062165711yescharacteristic
461C2#1062165711yescharacteristic
462C2#41×D2111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D21
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×#121C2
hypercenter#121D21
hypocenterC3×C7#540
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×C7×#121C2semidirect
2. #10621423C2semidirect
3. #10621422C2semidirect
4. #10621422C2semidirect
5. #10621422C2semidirect
6. #10621421C2semidirect
7. #10621418C2semidirect
8. #10621412C2semidirect
9. C4×#4268C2semidirect
10. #10621377C2semidirect
11. #10621372C2semidirect
12. #10621367C2semidirect
13. #10621366C2semidirect
14. #10621364C2semidirect
15. #10621360C2semidirect
52. C7×#121D3semidirect
133. C3×#121D7semidirect
259. #121D21semidirect
319. C3×C7#540semidirect
419. C7#5615semidirect
454. C3#90306semidirect

Maximal subgroups

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

subgroupindex
C3×C7×#1212
#106214232
#106214222
#106214212
#106214182
#106214122
C4×#42682
#106213772
#106213722
#106213672
#106213662
#106213642
#106213602
#903063
#56157