Finite Group Databasebeta

← #97×((C3⋊D3)⋊C3)⋊C2 #72268965

Subgroups — #97×((C3⋊D3)⋊C3)⋊C2 #72268965

Order 3456.

2526 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×((C3⋊D3)⋊C3)⋊C2C212yesmaximal
2C42×((C3⋊D3)⋊C3)⋊C2C211yesmaximal, characteristic
3#97×#272C211yesmaximal, characteristic, complemented
4#97×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
5#97×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
6#13138901C212yesmaximal, complemented
7#13138766C212yesmaximal, complemented
8#13138766C212yesmaximal, complemented
9#13137405C211yesmaximal, characteristic, complemented
10#13137368C211yesmaximal, characteristic, complemented
11#13137368C211yesmaximal, characteristic, complemented
12D32×#97—31nomaximal
13D32×#97—31nomaximal
14C2×C4×((C3⋊D3)⋊C3)⋊C2C412yes—
15C2×C4×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
16C2×C8×#272C2212yes—
17C42×#272C2211yescharacteristic
18C2×C8×(C3⋊D3)⋊C3C2212yes—
19C2×C8×(C3⋊D3)⋊C3C2212yes—
20C42×(C3⋊D3)⋊C3C2211yescharacteristic
21C42×(C3⋊D3)⋊C3C2211yescharacteristic
22C4×#6199C412yes—
23C4×#6199C2211yescharacteristic
24C4×((C3⋊D3)⋊C3)⋊C4C412yes—
25C4×((C3⋊D3)⋊C3)⋊C4C412yes—
26C4×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
27C4×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
28C2×#88434C2212yes—
29C2×((C3⋊D3)⋊C3)⋊C8C2212yes—
30C2×((C3⋊D3)⋊C3)⋊C8C2212yes—
31C8×((C3⋊D3)⋊C3)⋊C2C4116yescomplemented
32H(3,𝔽3)×#97C2211yescharacteristic, complemented
33#11720548C2212yescomplemented
34#11720520C2211yescharacteristic, complemented
35#63642⋊C3C2212yescomplemented
36#63642⋊C3C2212yescomplemented
37#63630⋊C3C2211yescharacteristic, complemented
38#63630⋊C3C2211yescharacteristic, complemented
39#11720312C2212yescomplemented
40#11720312C2212yescomplemented
41#11720303C2212yescomplemented
42C2×D32×C8—32no—
43C2×D32×C8—32no—
44C42×D32—31no—
45C42×D32—31no—
46C3⋊D3×#97D311yescharacteristic, complemented
47C3⋊D3×#97D311yescharacteristic, complemented
48C3×D3×#97—31no—
49C3×D3×#97—31no—
50C3×D3×#97—31no—
51C3×D3×#97—31no—
52C3×D3×#97—61no—
53#10590668—32no—
54#10590668—32no—
55D3×#815—32no—
56D3×#815—32no—
57D3×#815—32no—
58D3×#815—32no—
59#10590322—31no—
60#10590322—31no—
61D3×#803—31no—
62D3×#803—31no—
63D3×#803—31no—
64D3×#803—31no—
65C22×((C3⋊D3)⋊C3)⋊C2C2×C411yescharacteristic
66C2×C4×#272C2×C412yes—
67C2×C4×#272C2311yescharacteristic
68C2×C4×(C3⋊D3)⋊C3C2×C412yes—
69C2×C4×(C3⋊D3)⋊C3C2×C412yes—
70C2×C4×(C3⋊D3)⋊C3C2311yescharacteristic
71C2×C4×(C3⋊D3)⋊C3C2311yescharacteristic
72C2×#6199C2×C412yes—
73C2×#6199C2×C411yescharacteristic
74C2×((C3⋊D3)⋊C3)⋊C4C2×C412yes—
75C2×((C3⋊D3)⋊C3)⋊C4C2×C412yes—
76C2×((C3⋊D3)⋊C3)⋊C4C2×C411yescharacteristic
77C2×((C3⋊D3)⋊C3)⋊C4C2×C411yescharacteristic
78C4×((C3⋊D3)⋊C3)⋊C2—28no—
79C4×((C3⋊D3)⋊C3)⋊C2C2×C418yes—
80C2×C8×H(3,𝔽3)C2312yes—
81C42×H(3,𝔽3)C2311yescharacteristic
82C4×#1084C2×C412yes—
83C4×#1084C2311yescharacteristic
84C2×#6180C2312yes—
85C8×#272C2×C418yescomplemented
86C4×(C3⋊Dic3)⋊C3C2×C412yes—
87C4×(C3⋊Dic3)⋊C3C2×C412yes—
88C4×(C3⋊Dic3)⋊C3C2311yescharacteristic
89C4×(C3⋊Dic3)⋊C3C2311yescharacteristic
90C2×(C3⋊(C3⋊C8))⋊C3C2312yes—
91C2×(C3⋊(C3⋊C8))⋊C3C2312yes—
92C8×(C3⋊D3)⋊C3C2×C418yescomplemented
93C8×(C3⋊D3)⋊C3C2×C418yescomplemented
94#88447C2×C412yes—
95#88447C2×C412yes—
96#88447C2×C412yes—
97#88434C2×C418yescomplemented
98((C3⋊D3)⋊C3)⋊C8C2×C418yescomplemented
99((C3⋊D3)⋊C3)⋊C8C2×C418yescomplemented
100C2×D3×#97—91no—
101C2×D3×#97—91no—
102C2×D3×#97—91no—
103C2×C4×D32—31no—
104C2×C4×D32—31no—
105C2×C4×D32—32no—
106C2×C4×D32—32no—
107C2×C8×C3⋊D3C2×D312yes—
108C2×C8×C3⋊D3C2×D312yes—
109C42×C3⋊D3C2×D311yescharacteristic
110C42×C3⋊D3C2×D311yescharacteristic
111C2×C3×D3×C8—32no—
112C2×C3×D3×C8—32no—
113C2×C3×D3×C8—32no—
114C2×C3×D3×C8—32no—
115C2×C3×D3×C8—62no—
116C3×C42×D3—31no—
117C3×C42×D3—31no—
118C3×C42×D3—31no—
119C3×C42×D3—31no—
120C3×C42×D3—61no—
121C4×#624—32no—
122C4×#624—32no—
123C4×#624—31no—
124C4×#624—31no—
125C4×D3×Dic3—32no—
126C4×D3×Dic3—32no—
127C4×D3×Dic3—32no—
128C4×D3×Dic3—32no—
129C4×D3×Dic3—31no—
130C4×D3×Dic3—31no—
131C4×D3×Dic3—31no—
132C4×D3×Dic3—31no—
133C2×#3710—32no—
134C2×#3710—32no—
135C2×D3×C3⋊C8—32no—
136C2×D3×C3⋊C8—32no—
137C2×D3×C3⋊C8—32no—
138C2×D3×C3⋊C8—32no—
139D32×C8—316no—
140D32×C8—316no—
141C32×#97—21no—
142C32×#97C2×D311yescharacteristic, complemented
143C32×#97C2×D311yescharacteristic, complemented
144#63642C2×D312yescomplemented
145#63642C2×D312yescomplemented
146#63630C2×D311yescharacteristic, complemented
147#63630C2×D311yescharacteristic, complemented
148C3×#815—32no—
149C3×#815—32no—
150C3×#815—32no—
151C3×#815—32no—
152C3×#815—62no—
153C3×#803—31no—
154C3×#803—31no—
155C3×#803—31no—
156C3×#803—31no—
157C3×#803—61no—
158#63555—32no—
159#63555—32no—
160#63554—32no—
161#63554—32no—
162#63554—32no—
163#63554—32no—
164C22×#272C22×C411yescharacteristic
165C22×(C3⋊D3)⋊C3C22×C411yescharacteristic
166C22×(C3⋊D3)⋊C3C22×C411yescharacteristic
167C2×((C3⋊D3)⋊C3)⋊C2C4214yes—
168C2×((C3⋊D3)⋊C3)⋊C2M1618yes—
169C2×C4×H(3,𝔽3)C22×C412yes—
170C2×C4×H(3,𝔽3)C2411yescharacteristic
171C2×#1084C22×C412yes—
172C2×#1084C22×C411yescharacteristic
173C4×#272—24no—
174C4×#272C22×C414yes—
175C2×(C3⋊Dic3)⋊C3C22×C412yes—
176C2×(C3⋊Dic3)⋊C3C22×C412yes—
177C2×(C3⋊Dic3)⋊C3C22×C411yescharacteristic
178C2×(C3⋊Dic3)⋊C3C22×C411yescharacteristic
179C4×(C3⋊D3)⋊C3—24no—
180C4×(C3⋊D3)⋊C3—24no—
181C4×(C3⋊D3)⋊C3C22×C414yes—
182C4×(C3⋊D3)⋊C3C22×C414yes—
183#6199—24no—
184#6199C4214yes—
185((C3⋊D3)⋊C3)⋊C4—24no—
186((C3⋊D3)⋊C3)⋊C4—24no—
187((C3⋊D3)⋊C3)⋊C4C4214yes—
188((C3⋊D3)⋊C3)⋊C4C4214yes—
189C8×H(3,𝔽3)C22×C414yescomplemented
190#6180C22×C414yescomplemented
191(C3⋊(C3⋊C8))⋊C3C22×C414yescomplemented
192(C3⋊(C3⋊C8))⋊C3C22×C414yescomplemented
193C22×D3×C8—92no—
194C22×D3×C8—92no—
195C22×D3×C8—92no—
196C2×C42×D3—91no—
197C2×C42×D3—91no—
198C2×C42×D3—91no—
199C2×C3×#97—91no—
200C2×C3×#97—91no—
201C2×C3×#97—91no—
202C2×#815—92no—
203C2×#815—92no—
204C2×#815—92no—
205C2×#803—91no—
206C2×#803—91no—
207C2×#803—91no—
208D3×#97—31no—
209D3×#97—31no—
210D3×#97—31no—
211D3×#97—31no—
212D3×#97—61no—
213D3×#97—91no—
214D3×#97—91no—
215D3×#97—91no—
216D3×#97—91no—
217D3×#97—92no—
218D3×#97—92no—
219D3×#97—92no—
220D3×#97—92no—
221D3×#97—91no—
222D3×#97—91no—
223D3×#97—92no—
224D3×#97—92no—
225D3×#97—91no—
226D3×#97—181no—
227C22×D32—31no—
228C22×D32—31no—
229C2×C4×C3⋊D3C4×D312yes—
230C2×C4×C3⋊D3C4×D312yes—
231C2×C4×C3⋊D3C22×D311yescharacteristic
232C2×C4×C3⋊D3C22×D311yescharacteristic
233C2×C3×C4×D3—31no—
234C2×C3×C4×D3—31no—
235C2×C3×C4×D3—31no—
236C2×C3×C4×D3—31no—
237C2×C3×C4×D3—32no—
238C2×C3×C4×D3—32no—
239C2×C3×C4×D3—32no—
240C2×C3×C4×D3—32no—
241C2×C3×C4×D3—61no—
242C2×C3×C4×D3—62no—
243C2×#624—31no—
244C2×#624—31no—
245C2×#624—32no—
246C2×#624—32no—
247C2×D3×Dic3—31no—
248C2×D3×Dic3—31no—
249C2×D3×Dic3—31no—
250C2×D3×Dic3—31no—
251C2×D3×Dic3—32no—
252C2×D3×Dic3—32no—
253C2×D3×Dic3—32no—
254C2×D3×Dic3—32no—
255C4×D32—38no—
256C4×D32—38no—
257C4×D32—68no—
258C4×D32—68no—
259C2×C32×C8—22no—
260C2×C32×C8C22×D312yes—
261C2×C32×C8C22×D312yes—
262C32×C42—21no—
263C32×C42C22×D311yescharacteristic
264C32×C42C22×D311yescharacteristic
265C4×C3⋊Dic3C4×D312yes—
266C4×C3⋊Dic3C4×D312yes—
267C4×C3⋊Dic3C22×D311yescharacteristic
268C4×C3⋊Dic3C22×D311yescharacteristic
269C2×C3⋊(C3⋊C8)C22×D312yes—
270C2×C3⋊(C3⋊C8)C22×D312yes—
271C8×C3⋊D3C4×D318yescomplemented
272C8×C3⋊D3C4×D318yescomplemented
273C3×C4×Dic3—32no—
274C3×C4×Dic3—32no—
275C3×C4×Dic3—32no—
276C3×C4×Dic3—32no—
277C3×C4×Dic3—31no—
278C3×C4×Dic3—31no—
279C3×C4×Dic3—31no—
280C3×C4×Dic3—31no—
281C3×C4×Dic3—61no—
282C3×C4×Dic3—62no—
283C2×C3×C3⋊C8—32no—
284C2×C3×C3⋊C8—32no—
285C2×C3×C3⋊C8—32no—
286C2×C3×C3⋊C8—32no—
287C2×C3×C3⋊C8—62no—
288C3×D3×C8—38no—
289C3×D3×C8—38no—
290C3×D3×C8—38no—
291C3×D3×C8—38no—
292C3×D3×C8—68no—
293Dic32—32no—
294Dic32—32no—
295Dic32—32no—
296Dic32—32no—
297Dic32—32no—
298Dic32—32no—
299#3710—38no—
300#3710—38no—
301D3×C3⋊C8—38no—
302D3×C3⋊C8—38no—
303D3×C3⋊C8—38no—
304D3×C3⋊C8—38no—
305C22×#97—271noSylow
306C22×H(3,𝔽3)C23×C411yescharacteristic
307C2×#272C2×C4212yes—
308C2×#272C2×M1614yes—
309C2×(C3⋊D3)⋊C3C2×C4212yes—
310C2×(C3⋊D3)⋊C3C2×C4212yes—
311C2×(C3⋊D3)⋊C3C2×M1614yes—
312C2×(C3⋊D3)⋊C3C2×M1614yes—
313((C3⋊D3)⋊C3)⋊C2#97116yesdirect product factor
314C4×H(3,𝔽3)—22no—
315C4×H(3,𝔽3)C23×C412yes—
316#1084—22no—
317#1084C2×C4212yes—
318(C3⋊Dic3)⋊C3—22no—
319(C3⋊Dic3)⋊C3—22no—
320(C3⋊Dic3)⋊C3C2×C4212yes—
321(C3⋊Dic3)⋊C3C2×C4212yes—
322C22×C4×D3—91no—
323C22×C4×D3—92no—
324C22×C4×D3—91no—
325C22×C4×D3—91no—
326C22×C4×D3—92no—
327C22×C4×D3—92no—
328C22×C3×C8—92no—
329C22×C3×C8—92no—
330C22×C3×C8—92no—
331C2×C3×C42—91no—
332C2×C3×C42—91no—
333C2×C3×C42—91no—
334C2×C4×Dic3—92no—
335C2×C4×Dic3—91no—
336C2×C4×Dic3—92no—
337C2×C4×Dic3—91no—
338C2×C4×Dic3—92no—
339C2×C4×Dic3—91no—
340C22×C3⋊C8—92no—
341C22×C3⋊C8—92no—
342C22×C3⋊C8—92no—
343C2×D3×C8—32no—
344C2×D3×C8—32no—
345C2×D3×C8—32no—
346C2×D3×C8—32no—
347C2×D3×C8—62no—
348C2×D3×C8—92no—
349C2×D3×C8—916no—
350C2×D3×C8—916no—
351C2×D3×C8—916no—
352C2×D3×C8—92no—
353C2×D3×C8—92no—
354C2×D3×C8—92no—
355C2×D3×C8—92no—
356C2×D3×C8—92no—
357C2×D3×C8—92no—
358C2×D3×C8—182no—
359C42×D3—31no—
360C42×D3—31no—
361C42×D3—31no—
362C42×D3—31no—
363C42×D3—61no—
364C42×D3—91no—
365C42×D3—91no—
366C42×D3—91no—
367C42×D3—92no—
368C42×D3—92no—
369C42×D3—91no—
370C42×D3—92no—
371C42×D3—91no—
372C42×D3—92no—
373C42×D3—91no—
374C42×D3—92no—
375C42×D3—91no—
376C42×D3—92no—
377C42×D3—181no—
378C3×#97—31no—
379C3×#97—61no—
380C3×#97—91no—
381C3×#97—91no—
382C3×#97—92no—
383C3×#97—92no—
384C3×#97—92no—
385C3×#97—91no—
386C3×#97—121no—
387C3×#97D3211yescharacteristic
388#815—32no—
389#815—32no—
390#815—32no—
391#815—32no—
392#815—62no—
393#815—92no—
394#815—92no—
395#815—92no—
396#815—92no—
397#815—92no—
398#815—92no—
399#815—92no—
400#815—182no—
401#803—31no—
402#803—31no—
403#803—31no—
404#803—31no—
405#803—61no—
406#803—91no—
407#803—92no—
408#803—92no—
409#803—92no—
410#803—181no—
411C22×C3⋊D3C2×C4×D311yescharacteristic
412C22×C3⋊D3C2×C4×D311yescharacteristic
413C22×C3×D3—31no—
414C22×C3×D3—31no—
415C22×C3×D3—31no—
416C22×C3×D3—31no—
417C22×C3×D3—61no—
418C2×D32—34no—
419C2×D32—34no—
420C2×D32—38no—
421C2×D32—38no—
422C2×C32×C4—21no—
423C2×C32×C4—22no—
424C2×C32×C4C2×C4×D312yes—
425C2×C32×C4C2×C4×D312yes—
426C2×C32×C4C23×D311yescharacteristic
427C2×C32×C4C23×D311yescharacteristic
428C2×C3⋊Dic3C2×C4×D312yes—
429C2×C3⋊Dic3C2×C4×D311yescharacteristic
430C2×C3⋊Dic3C2×C4×D312yes—
431C2×C3⋊Dic3C2×C4×D311yescharacteristic
432C4×C3⋊D3—24no—
433C4×C3⋊D3—24no—
434C4×C3⋊D3C2×C4×D314yes—
435C4×C3⋊D3C2×C4×D314yes—
436C2×C3×Dic3—31no—
437C2×C3×Dic3—31no—
438C2×C3×Dic3—31no—
439C2×C3×Dic3—31no—
440C2×C3×Dic3—32no—
441C2×C3×Dic3—32no—
442C2×C3×Dic3—32no—
443C2×C3×Dic3—32no—
444C2×C3×Dic3—61no—
445C2×C3×Dic3—62no—
446C3×C4×D3—34no—
447C3×C4×D3—34no—
448C3×C4×D3—34no—
449C3×C4×D3—34no—
450C3×C4×D3—64no—
451C3×C4×D3—64no—
452C3×C4×D3—64no—
453C3×C4×D3—64no—
454C3×C4×D3—64no—
455C3×C4×D3—124no—
456#624—34no—
457#624—34no—
458#624—64no—
459#624—64no—
460D3×Dic3—34no—
461D3×Dic3—34no—
462D3×Dic3—34no—
463D3×Dic3—34no—
464D3×Dic3—64no—
465D3×Dic3—64no—
466D3×Dic3—64no—
467D3×Dic3—64no—
468C32×C8—24no—
469C32×C8C2×C4×D314yescomplemented
470C32×C8C2×C4×D314yescomplemented
471C3⋊(C3⋊C8)C2×C4×D314yescomplemented
472C3⋊(C3⋊C8)C2×C4×D314yescomplemented
473C3×C3⋊C8—34no—
474C3×C3⋊C8—34no—
475C3×C3⋊C8—34no—
476C3×C3⋊C8—34no—
477C3×C3⋊C8—64no—
478C23×C8—272no—
479C22×C42—271no—
480C2×#97—91no—
481C2×#97—91no—
482C2×#97—91no—
483C2×#97—271no—
484C2×#97—271no—
485C2×#97—271no—
486C2×#97—272no—
487C2×#97—272no—
488C2×#97—272no—
489C2×H(3,𝔽3)C22×C4211yescharacteristic
490C2×H(3,𝔽3)C22×M1612yes—
491#272C2×#9714yescomplemented
492(C3⋊D3)⋊C3C2×#9714yescomplemented
493(C3⋊D3)⋊C3C2×#9714yescomplemented
494C23×D3—91no—
495C23×D3—91no—
496C23×D3—91no—
497C22×C3×C4—91no—
498C22×C3×C4—92no—
499C22×C3×C4—91no—
500C22×C3×C4—92no—
501C22×C3×C4—91no—
502C22×C3×C4—92no—
503C22×Dic3—91no—
504C22×Dic3—92no—
505C22×Dic3—91no—
506C22×Dic3—91no—
507C22×Dic3—92no—
508C22×Dic3—92no—
509C2×C4×D3—31no—
510C2×C4×D3—31no—
511C2×C4×D3—31no—
512C2×C4×D3—31no—
513C2×C4×D3—32no—
514C2×C4×D3—32no—
515C2×C4×D3—32no—
516C2×C4×D3—32no—
517C2×C4×D3—61no—
518C2×C4×D3—62no—
519C2×C4×D3—91no—
520C2×C4×D3—92no—
521C2×C4×D3—98no—
522C2×C4×D3—98no—
523C2×C4×D3—98no—
524C2×C4×D3—91no—
525C2×C4×D3—91no—
526C2×C4×D3—91no—
527C2×C4×D3—91no—
528C2×C4×D3—91no—
529C2×C4×D3—91no—
530C2×C4×D3—92no—
531C2×C4×D3—92no—
532C2×C4×D3—92no—
533C2×C4×D3—92no—
534C2×C4×D3—92no—
535C2×C4×D3—92no—
536C2×C4×D3—181no—
537C2×C4×D3—182no—
538C2×C4×D3—188no—
539C2×C4×D3—188no—
540C2×C4×D3—188no—
541C2×C3×C8—32no—
542C2×C3×C8—62no—
543C2×C3×C8—98no—
544C2×C3×C8—98no—
545C2×C3×C8—92no—
546C2×C3×C8—92no—
547C2×C3×C8—92no—
548C2×C3×C8—98no—
549C2×C3×C8—122no—
550C2×C3×C8C2×D3212yes—
551C3×C42—31no—
552C3×C42—61no—
553C3×C42—91no—
554C3×C42—92no—
555C3×C42—91no—
556C3×C42—92no—
557C3×C42—91no—
558C3×C42—92no—
559C3×C42—121no—
560C3×C42C2×D3211yescharacteristic
561C4×Dic3—31no—
562C4×Dic3—32no—
563C4×Dic3—31no—
564C4×Dic3—32no—
565C4×Dic3—31no—
566C4×Dic3—31no—
567C4×Dic3—32no—
568C4×Dic3—32no—
569C4×Dic3—61no—
570C4×Dic3—62no—
571C4×Dic3—91no—
572C4×Dic3—92no—
573C4×Dic3—92no—
574C4×Dic3—92no—
575C4×Dic3—92no—
576C4×Dic3—92no—
577C4×Dic3—92no—
578C4×Dic3—92no—
579C4×Dic3—92no—
580C4×Dic3—92no—
581C4×Dic3—92no—
582C4×Dic3—181no—
583C4×Dic3—182no—
584C2×C3⋊C8—32no—
585C2×C3⋊C8—32no—
586C2×C3⋊C8—32no—
587C2×C3⋊C8—32no—
588C2×C3⋊C8—62no—
589C2×C3⋊C8—92no—
590C2×C3⋊C8—98no—
591C2×C3⋊C8—98no—
592C2×C3⋊C8—98no—
593C2×C3⋊C8—182no—
594D3×C8—38no—
595D3×C8—38no—
596D3×C8—38no—
597D3×C8—38no—
598D3×C8—68no—
599D3×C8—98no—
600D3×C8—98no—
601D3×C8—98no—
602D3×C8—98no—
603D3×C8—98no—
604D3×C8—98no—
605D3×C8—98no—
606D3×C8—188no—
607C22×C32—21no—
608C22×C32C22×C4×D311yescharacteristic
609C22×C32C22×C4×D311yescharacteristic
610C2×C3⋊D3C42×D312yes—
611C2×C3⋊D3C42×D312yes—
612C2×C3⋊D3D3×M1614yes—
613C2×C3⋊D3D3×M1614yes—
614C2×C3×D3—32no—
615C2×C3×D3—32no—
616C2×C3×D3—32no—
617C2×C3×D3—32no—
618C2×C3×D3—34no—
619C2×C3×D3—34no—
620C2×C3×D3—34no—
621C2×C3×D3—34no—
622C2×C3×D3—62no—
623C2×C3×D3—64no—
624D32—316no—
625D32—316no—
626C32×C4—22no—
627C32×C4—22no—
628C32×C4—22no—
629C32×C4—42no—
630C32×C4C22×C4×D312yes—
631C32×C4C22×C4×D312yes—
632C3⋊Dic3—22no—
633C3⋊Dic3—22no—
634C3⋊Dic3C42×D312yes—
635C3⋊Dic3C42×D312yes—
636C3×Dic3—32no—
637C3×Dic3—32no—
638C3×Dic3—32no—
639C3×Dic3—32no—
640C3×Dic3—62no—
641C3×Dic3—62no—
642C3×Dic3—62no—
643C3×Dic3—62no—
644C3×Dic3—62no—
645C3×Dic3—122no—
646C23×C4—271no—
647C23×C4—272no—
648C22×C8—92no—
649C22×C8—92no—
650C22×C8—92no—
651C22×C8—2716no—
652C22×C8—272no—
653C22×C8—272no—
654C22×C8—272no—
655C2×C42—91no—
656C2×C42—91no—
657C2×C42—91no—
658C2×C42—271no—
659C2×C42—271no—
660C2×C42—271no—
661C2×C42—272no—
662C2×C42—272no—
663C2×C42—272no—
664#97—92no—
665#97—92no—
666#97—92no—
667#97—91no—
668#97—91no—
669#97—91no—
670#97—272no—
671#97—272no—
672#97—272no—
673#97((C3⋊D3)⋊C3)⋊C211yescharacteristic, direct product factor
674H(3,𝔽3)C22×#9711yescharacteristic, complemented, Sylow
675C23×C3—91no—
676C23×C3—91no—
677C23×C3—91no—
678C22×D3—31no—
679C22×D3—31no—
680C22×D3—31no—
681C22×D3—31no—
682C22×D3—61no—
683C22×D3—91no—
684C22×D3—94no—
685C22×D3—98no—
686C22×D3—94no—
687C22×D3—98no—
688C22×D3—94no—
689C22×D3—98no—
690C22×D3—181no—
691C2×C3×C4—31no—
692C2×C3×C4—32no—
693C2×C3×C4—61no—
694C2×C3×C4—62no—
695C2×C3×C4—94no—
696C2×C3×C4—94no—
697C2×C3×C4—91no—
698C2×C3×C4—91no—
699C2×C3×C4—91no—
700C2×C3×C4—94no—
701C2×C3×C4—92no—
702C2×C3×C4—92no—
703C2×C3×C4—92no—
704C2×C3×C4—121no—
705C2×C3×C4—122no—
706C2×C3×C4—184no—
707C2×C3×C4—184no—
708C2×C3×C4—184no—
709C2×C3×C4C4×D3212yes—
710C2×C3×C4C22×D3211yescharacteristic
711C2×Dic3—31no—
712C2×Dic3—31no—
713C2×Dic3—31no—
714C2×Dic3—31no—
715C2×Dic3—32no—
716C2×Dic3—32no—
717C2×Dic3—32no—
718C2×Dic3—32no—
719C2×Dic3—61no—
720C2×Dic3—62no—
721C2×Dic3—91no—
722C2×Dic3—92no—
723C2×Dic3—94no—
724C2×Dic3—94no—
725C2×Dic3—94no—
726C2×Dic3—181no—
727C2×Dic3—182no—
728C2×Dic3—184no—
729C2×Dic3—184no—
730C2×Dic3—184no—
731C4×D3—34no—
732C4×D3—34no—
733C4×D3—34no—
734C4×D3—34no—
735C4×D3—64no—
736C4×D3—64no—
737C4×D3—64no—
738C4×D3—64no—
739C4×D3—64no—
740C4×D3—94no—
741C4×D3—94no—
742C4×D3—94no—
743C4×D3—94no—
744C4×D3—94no—
745C4×D3—94no—
746C4×D3—94no—
747C4×D3—124no—
748C4×D3—184no—
749C4×D3—184no—
750C4×D3—184no—
751C4×D3—184no—
752C4×D3—184no—
753C4×D3—184no—
754C4×D3—184no—
755C4×D3—184no—
756C4×D3—364no—
757C3×C8—34no—
758C3×C8—64no—
759C3×C8—94no—
760C3×C8—94no—
761C3×C8—94no—
762C3×C8—124no—
763C3×C8C4×D3214yes—
764C3⋊C8—34no—
765C3⋊C8—34no—
766C3⋊C8—34no—
767C3⋊C8—34no—
768C3⋊C8—64no—
769C3⋊C8—94no—
770C3⋊C8—184no—
771C2×C32—22no—
772C2×C32—21no—
773C2×C32C2×C42×D311yescharacteristic
774C2×C32C2×C42×D311yescharacteristic
775C2×C32C2×D3×M1612yes—
776C2×C32C2×D3×M1612yes—
777C3⋊D3D3×#9714yescomplemented
778C3⋊D3D3×#9714yescomplemented
779C3×D3—34no—
780C3×D3—34no—
781C3×D3—34no—
782C3×D3—34no—
783C3×D3—64no—
784C24—271no—
785C22×C4—91no—
786C22×C4—91no—
787C22×C4—91no—
788C22×C4—92no—
789C22×C4—92no—
790C22×C4—92no—
791C22×C4—278no—
792C22×C4—271no—
793C22×C4—271no—
794C22×C4—271no—
795C22×C4—272no—
796C22×C4—272no—
797C22×C4—272no—
798C22×C4—548no—
799C2×C8—92no—
800C2×C8—92no—
801C2×C8—92no—
802C2×C8—98no—
803C2×C8—98no—
804C2×C8—98no—
805C2×C8—278no—
806C2×C8—278no—
807C2×C8—278no—
808C2×C8C2×((C3⋊D3)⋊C3)⋊C212yes—
809C42—91no—
810C42—91no—
811C42—91no—
812C42—92no—
813C42—92no—
814C42—92no—
815C42—272no—
816C42—272no—
817C42—272no—
818C42C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
819C22×C3—31no—
820C22×C3—61no—
821C22×C3—92no—
822C22×C3—94no—
823C22×C3—92no—
824C22×C3—94no—
825C22×C3—94no—
826C22×C3—92no—
827C22×C3—121no—
828C22×C3C2×C4×D3211yescharacteristic
829C2×D3—32no—
830C2×D3—34no—
831C2×D3—32no—
832C2×D3—34no—
833C2×D3—34no—
834C2×D3—34no—
835C2×D3—32no—
836C2×D3—32no—
837C2×D3—62no—
838C2×D3—64no—
839C2×D3—92no—
840C2×D3—94no—
841C2×D3—916no—
842C2×D3—916no—
843C2×D3—916no—
844C2×D3—182no—
845C2×D3—184no—
846C3×C4—22no—
847C3×C4—32no—
848C3×C4—62no—
849C3×C4—62no—
850C3×C4—92no—
851C3×C4—92no—
852C3×C4—92no—
853C3×C4—122no—
854C3×C4—122no—
855C3×C4—182no—
856C3×C4—182no—
857C3×C4—182no—
858C3×C4—242no—
859C3×C4C2×C4×D3212yes—
860Dic3—32no—
861Dic3—32no—
862Dic3—32no—
863Dic3—32no—
864Dic3—62no—
865Dic3—62no—
866Dic3—62no—
867Dic3—62no—
868Dic3—62no—
869Dic3—92no—
870Dic3—122no—
871Dic3—182no—
872Dic3—182no—
873Dic3—362no—
874C32—21no—
875C32C2×D3×#9711yescharacteristic, complemented
876C32C2×D3×#9711yescharacteristic, complemented
877C23—91no—
878C23—91no—
879C23—91no—
880C23—274no—
881C23—278no—
882C2×C4—91no—
883C2×C4—91no—
884C2×C4—91no—
885C2×C4—94no—
886C2×C4—94no—
887C2×C4—94no—
888C2×C4—92no—
889C2×C4—92no—
890C2×C4—92no—
891C2×C4—184no—
892C2×C4—184no—
893C2×C4—184no—
894C2×C4—274no—
895C2×C4—274no—
896C2×C4—274no—
897C2×C4—544no—
898C2×C4—544no—
899C2×C4—544no—
900C2×C4C4×((C3⋊D3)⋊C3)⋊C212yes—
901C2×C4C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
902C8—94no—
903C8—94no—
904C8—94no—
905C8C4×((C3⋊D3)⋊C3)⋊C214yescomplemented
906C2×C3—32no—
907C2×C3—31no—
908C2×C3—62no—
909C2×C3—61no—
910C2×C3—94no—
911C2×C3—94no—
912C2×C3—94no—
913C2×C3—122no—
914C2×C3—121no—
915C2×C3C42×D3211yescharacteristic
916C2×C3D32×M1612yes—
917D3—34no—
918D3—34no—
919D3—34no—
920D3—34no—
921D3—64no—
922D3—94no—
923D3—184no—
924C22—94no—
925C22—94no—
926C22—94no—
927C22—92no—
928C22—92no—
929C22—92no—
930C22—2716no—
931C22C2×C4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
932C4—22no—
933C4—92no—
934C4—92no—
935C4—92no—
936C4—182no—
937C4—182no—
938C4—182no—
939C4C2×C4×((C3⋊D3)⋊C3)⋊C212yes—
940C3—31no—
941C3—61no—
942C3—121no—
943C3D32×#9711yescharacteristic
944C2—94no—
945C2—94no—
946C2—94no—
947C2C42×((C3⋊D3)⋊C3)⋊C211yescharacteristic
948C2M16×((C3⋊D3)⋊C3)⋊C212yes—
subgroupG/H
centerC2×C4C22×((C3⋊D3)⋊C3)⋊C2
commutatorC2×H(3,𝔽3)C22×C42
FrattiniC2×C3×C4C22×D32
FittingH(3,𝔽3)×#97C22
socleC22×C3C2×C4×D32
prime radicalC22×((C3⋊D3)⋊C3)⋊C2C2×C4
cosocleC2×C4×H(3,𝔽3)C24
hypercenter#97((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C22×#97
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
3. #97×#272C2semidirect
4. #97×(C3⋊D3)⋊C3C2semidirect
5. #97×(C3⋊D3)⋊C3C2semidirect
6. #13138901C2semidirect
7. #13138766C2semidirect
8. #13138766C2semidirect
9. #13137405C2semidirect
10. #13137368C2semidirect
11. #13137368C2semidirect
31. C8×((C3⋊D3)⋊C3)⋊C2C4semidirect
32. H(3,𝔽3)×#97C22semidirect
33. #11720548C22semidirect
34. #11720520C22semidirect
35. #63642⋊C3C22semidirect
36. #63642⋊C3C22semidirect
37. #63630⋊C3C22semidirect
38. #63630⋊C3C22semidirect
39. #11720312C22semidirect
40. #11720312C22semidirect
41. #11720303C22semidirect
46. C3⋊D3×#97D3semidirect
47. C3⋊D3×#97D3semidirect
85. C8×#272C2×C4semidirect
92. C8×(C3⋊D3)⋊C3C2×C4semidirect
93. C8×(C3⋊D3)⋊C3C2×C4semidirect
97. #88434C2×C4semidirect
98. ((C3⋊D3)⋊C3)⋊C8C2×C4semidirect
99. ((C3⋊D3)⋊C3)⋊C8C2×C4semidirect
142. C32×#97C2×D3semidirect
143. C32×#97C2×D3semidirect
144. #63642C2×D3semidirect
145. #63642C2×D3semidirect
146. #63630C2×D3semidirect
147. #63630C2×D3semidirect
189. C8×H(3,𝔽3)C22×C4semidirect
190. #6180C22×C4semidirect
191. (C3⋊(C3⋊C8))⋊C3C22×C4semidirect
192. (C3⋊(C3⋊C8))⋊C3C22×C4semidirect
271. C8×C3⋊D3C4×D3semidirect
272. C8×C3⋊D3C4×D3semidirect
313. ((C3⋊D3)⋊C3)⋊C2#97direct (N × H)
469. C32×C8C2×C4×D3semidirect
470. C32×C8C2×C4×D3semidirect
471. C3⋊(C3⋊C8)C2×C4×D3semidirect
472. C3⋊(C3⋊C8)C2×C4×D3semidirect
491. #272C2×#97semidirect
492. (C3⋊D3)⋊C3C2×#97semidirect
493. (C3⋊D3)⋊C3C2×#97semidirect
673. #97((C3⋊D3)⋊C3)⋊C2direct (N × H)
674. H(3,𝔽3)C22×#97semidirect
777. C3⋊D3D3×#97semidirect
778. C3⋊D3D3×#97semidirect
875. C32C2×D3×#97semidirect
876. C32C2×D3×#97semidirect
905. C8C4×((C3⋊D3)⋊C3)⋊C2semidirect

Maximal subgroups

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

subgroupindex
C2×C8×((C3⋊D3)⋊C3)⋊C22
C42×((C3⋊D3)⋊C3)⋊C22
#97×#2722
#97×(C3⋊D3)⋊C32
#131389012
#131387662
#131374052
#131373682
D32×#973