Finite Group Databasebeta

← #13149434

Subgroups — #13149434

Order 1728.

847 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721757C211yesmaximal, characteristic, complemented
2C4⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic
3#64098⋊C3C211yesmaximal, characteristic, complemented
4#11721129C211yesmaximal, characteristic
5#11721119C211yesmaximal, characteristic
6#11721119C211yesmaximal, characteristic
7#11721119C211yesmaximal, characteristic
8#11721119C211yesmaximal, characteristic
9C4×((C3⋊D3)⋊C3)⋊C4C211yesmaximal, characteristic
10#11721098C211yesmaximal, characteristic, complemented
11#11721091C211yesmaximal, characteristic, complemented
12#11721087C211yesmaximal, characteristic, complemented
13#11721086C211yesmaximal, characteristic, complemented
14#11721086C211yesmaximal, characteristic, complemented
15#11721085C211yesmaximal, characteristic, complemented
16#10594399—31nomaximal
17D3×#889—31nomaximal
18C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
19C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
20C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
21C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
22C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
23C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
24C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
25C4⋊C4×H(3,𝔽3)C2211yescharacteristic
26C4⋊#1084C2211yescharacteristic
27#88540C2211yescharacteristic
28#88540C2211yescharacteristic
29#88540C2211yescharacteristic
30#88540C2211yescharacteristic
31C4×#1084C2211yescharacteristic
32C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
33C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
34#3750⋊C3C2211yescharacteristic
35#3750⋊C3C2211yescharacteristic
36#3750⋊C3C2211yescharacteristic
37#3750⋊C3C2211yescharacteristic
38#3750⋊C3C2211yescharacteristic
39#3750⋊C3C2211yescharacteristic
40C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
41#88449C2211yescharacteristic
42#88449C2211yescharacteristic
43#88449C2211yescharacteristic
44#88449C2211yescharacteristic
45#88448C2211yescharacteristic
46#88448C2211yescharacteristic
47#88448C2211yescharacteristic
48#88448C2211yescharacteristic
49#88448C2211yescharacteristic
50#88448C2211yescharacteristic
51#88447C2211yescharacteristic
52#88447C2211yescharacteristic
53C4⋊C4×C3⋊D3D311yescharacteristic
54#64098D311yescharacteristic, complemented
55C3×D3×C4⋊C4—31no—
56C3×#889—31no—
57C3×#889—31no—
58C3×#889—31no—
59C3×#889—61no—
60#63900—31no—
61D3×C4⋊Dic3—31no—
62#63883—31no—
63#63883—31no—
64#63883—31no—
65#63883—31no—
66C4×#624—31no—
67D3×Dic3⋊C4—31no—
68D3×Dic3⋊C4—31no—
69D3×Dic3⋊C4—31no—
70D3×Dic3⋊C4—31no—
71C4×D3×Dic3—31no—
72#63870—31no—
73#63867—31no—
74#63867—31no—
75#63867—31no—
76#63847—31no—
77#63847—31no—
78#63846—31no—
79#63846—31no—
80#63846—31no—
81#63845—31no—
82#63845—31no—
83#63845—31no—
84C22×(C3⋊D3)⋊C3C2311yescharacteristic
85C2×C4×H(3,𝔽3)C2311yescharacteristic
86C2×C4×H(3,𝔽3)C2311yescharacteristic
87C2×C4×H(3,𝔽3)C2311yescharacteristic
88C2×#1084C2311yescharacteristic
89C2×#1084C2311yescharacteristic
90C2×#1084C2311yescharacteristic
91C2×#1084C2311yescharacteristic
92C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
93C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
94C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
95C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
96C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
97C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C4×(C3⋊D3)⋊C3—22no—
100C4×(C3⋊D3)⋊C3—22no—
101C4×(C3⋊D3)⋊C3—22no—
102((C3⋊D3)⋊C3)⋊C4—22no—
103((C3⋊D3)⋊C3)⋊C4—22no—
104((C3⋊D3)⋊C3)⋊C4—22no—
105((C3⋊D3)⋊C3)⋊C4Q814yes—
106D3×#125—91no—
107D3×#125—91no—
108C2×#889—91no—
109C2×C4×C3⋊D3C2×D311yescharacteristic
110C2×C4×C3⋊D3C2×D311yescharacteristic
111C2×C4×C3⋊D3C2×D311yescharacteristic
112C2×C3×C4×D3—31no—
113C2×C3×C4×D3—31no—
114C2×C3×C4×D3—31no—
115C2×#624—31no—
116C2×#624—31no—
117C2×#624—31no—
118C2×#624—31no—
119C2×D3×Dic3—31no—
120C2×D3×Dic3—31no—
121C2×D3×Dic3—31no—
122C2×D3×Dic3—31no—
123C32×C4⋊C4—21no—
124C32×C4⋊C4C2×D311yescharacteristic
125C32×C4⋊C4C2×D311yescharacteristic
126C4⋊(C3⋊Dic3)C2×D311yescharacteristic
127C4⋊(C3⋊Dic3)C2×D311yescharacteristic
128#3750C2×D311yescharacteristic
129#3750C2×D311yescharacteristic
130#3750C2×D311yescharacteristic
131#3750C2×D311yescharacteristic
132#3750C2×D311yescharacteristic
133#3750C2×D311yescharacteristic
134C4×C3⋊Dic3C2×D311yescharacteristic
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—61no—
140C3×Dic3⋊C4—31no—
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4—31no—
143C3×Dic3⋊C4—31no—
144C3×Dic3⋊C4—31no—
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4—31no—
148C3×Dic3⋊C4—31no—
149C3×Dic3⋊C4—31no—
150C3×Dic3⋊C4—31no—
151C3×Dic3⋊C4—31no—
152C3×Dic3⋊C4—31no—
153C3×Dic3⋊C4—31no—
154C3×Dic3⋊C4—61no—
155C3×Dic3⋊C4—61no—
156C3×Dic3⋊C4—61no—
157C3×Dic3⋊C4—61no—
158C3×C4×Dic3—31no—
159C3×C4×Dic3—31no—
160C3×C4×Dic3—31no—
161C3×C4×Dic3—61no—
162#3724—31no—
163#3724—31no—
164#3724—31no—
165#3724—31no—
166#3724—31no—
167#3724—31no—
168Dic3⋊Dic3—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—31no—
171Dic3⋊Dic3—31no—
172Dic3⋊Dic3—31no—
173Dic3⋊Dic3—31no—
174Dic3⋊Dic3—31no—
175Dic3⋊Dic3—31no—
176Dic3⋊Dic3—31no—
177Dic3⋊Dic3—31no—
178Dic3⋊Dic3—31no—
179Dic3⋊Dic3—31no—
180Dic3⋊Dic3—31no—
181Dic3⋊Dic3—31no—
182Dic32—31no—
183Dic32—31no—
184Dic32—31no—
185Dic32—31no—
186C22×H(3,𝔽3)C2411yescharacteristic
187C2×(C3⋊D3)⋊C3C2×Q812yes—
188C2×(C3⋊D3)⋊C3#4112yes—
189C2×(C3⋊D3)⋊C3#4112yes—
190C4×H(3,𝔽3)—21no—
191C4×H(3,𝔽3)—21no—
192C4×H(3,𝔽3)—21no—
193#1084—21no—
194#1084—21no—
195#1084—21no—
196#1084C2×Q812yes—
197(C3⋊Dic3)⋊C3—21no—
198(C3⋊Dic3)⋊C3—21no—
199(C3⋊Dic3)⋊C3—21no—
200(C3⋊Dic3)⋊C3—21no—
201(C3⋊Dic3)⋊C3—21no—
202(C3⋊Dic3)⋊C3—21no—
203(C3⋊Dic3)⋊C3C2×Q812yes—
204C3×#125—91no—
205C3×#125—91no—
206C2×C3×C4⋊C4—91no—
207C2×C4⋊Dic3—91no—
208C2×Dic3⋊C4—91no—
209C2×Dic3⋊C4—91no—
210C2×Dic3⋊C4—91no—
211C2×Dic3⋊C4—91no—
212C2×C4×Dic3—91no—
213D3×C4⋊C4—31no—
214D3×C4⋊C4—91no—
215D3×C4⋊C4—91no—
216D3×C4⋊C4—91no—
217D3×C4⋊C4—91no—
218D3×C4⋊C4—91no—
219D3×C4⋊C4—91no—
220D3×C4⋊C4—91no—
221D3×C4⋊C4—91no—
222D3×C4⋊C4—91no—
223D3×C4⋊C4—91no—
224D3×C4⋊C4—91no—
225#890—91no—
226#890—91no—
227#890—91no—
228#890—91no—
229#889—31no—
230#889—31no—
231#889—31no—
232#889—61no—
233#889—91no—
234#889—91no—
235#889—91no—
236#889—91no—
237#889—91no—
238#889—91no—
239#889—91no—
240#889—91no—
241#889—91no—
242#889—91no—
243#889—91no—
244#889—91no—
245#889—91no—
246C42×D3—91no—
247C42×D3—91no—
248#870—91no—
249#870—91no—
250C22×C3⋊D3C22×D311yescharacteristic
251C22×C3×D3—31no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D311yescharacteristic
263C2×C3⋊Dic3C22×D311yescharacteristic
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D311yescharacteristic
266C2×C3⋊Dic3C22×D311yescharacteristic
267C2×C3⋊Dic3C22×D311yescharacteristic
268C4×C3⋊D3—22no—
269C4×C3⋊D3—22no—
270C4×C3⋊D3—22no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—61no—
289C2×C3×Dic3—61no—
290C3×C4×D3—62no—
291C3×C4×D3—62no—
292C3×C4×D3—62no—
293#624—34no—
294#624—62no—
295#624—62no—
296#624—62no—
297D3×Dic3—34no—
298D3×Dic3—62no—
299D3×Dic3—62no—
300D3×Dic3—62no—
301C2×#125—271noSylow
302C2×H(3,𝔽3)C22×Q811yescharacteristic
303C2×H(3,𝔽3)C2×#4111yescharacteristic
304C2×H(3,𝔽3)C2×#4111yescharacteristic
305(C3⋊D3)⋊C3#12514yescomplemented
306C22×C3×C4—91no—
307C22×C3×C4—91no—
308C22×C3×C4—91no—
309C22×Dic3—91no—
310C22×Dic3—91no—
311C22×Dic3—91no—
312C22×Dic3—91no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—91no—
317C2×C4×D3—91no—
318C2×C4×D3—91no—
319C2×C4×D3—91no—
320C2×C4×D3—91no—
321C2×C4×D3—91no—
322C2×C4×D3—91no—
323C2×C4×D3—91no—
324C2×C4×D3—91no—
325C2×C4×D3—91no—
326C2×C4×D3—91no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—91no—
331C3×C4⋊C4—91no—
332C3×C4⋊C4—91no—
333C3×C4⋊C4—91no—
334C3×C4⋊C4—91no—
335C3×C4⋊C4—91no—
336C3×C4⋊C4—91no—
337C3×C4⋊C4—91no—
338C3×C4⋊C4—91no—
339C3×C4⋊C4—91no—
340C3×C4⋊C4—91no—
341C3×C4⋊C4—91no—
342C3×C4⋊C4—91no—
343C3×C4⋊C4D3211yescharacteristic
344C3×C42—91no—
345C3×C42—91no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—61no—
351C4⋊Dic3—91no—
352C4⋊Dic3—91no—
353C4⋊Dic3—91no—
354C4⋊Dic3—91no—
355C4⋊Dic3—91no—
356C4⋊Dic3—91no—
357C4⋊Dic3—91no—
358C4⋊Dic3—91no—
359C4⋊Dic3—91no—
360C4⋊Dic3—91no—
361C4⋊Dic3—91no—
362C4⋊Dic3—91no—
363Dic3⋊C4—31no—
364Dic3⋊C4—31no—
365Dic3⋊C4—31no—
366Dic3⋊C4—31no—
367Dic3⋊C4—31no—
368Dic3⋊C4—31no—
369Dic3⋊C4—31no—
370Dic3⋊C4—31no—
371Dic3⋊C4—31no—
372Dic3⋊C4—31no—
373Dic3⋊C4—31no—
374Dic3⋊C4—31no—
375Dic3⋊C4—31no—
376Dic3⋊C4—31no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—91no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407C4×Dic3—31no—
408C4×Dic3—31no—
409C4×Dic3—31no—
410C4×Dic3—61no—
411C4×Dic3—91no—
412C4×Dic3—91no—
413C4×Dic3—91no—
414C4×Dic3—91no—
415C4×Dic3—91no—
416C4×Dic3—91no—
417C4×Dic3—91no—
418C22×C32—21no—
419C22×C32C23×D311yescharacteristic
420C22×C32C23×D311yescharacteristic
421C2×C3⋊D3#23512yes—
422C2×C3⋊D3#23712yes—
423C2×C3⋊D3D3×Q812yes—
424C2×C3×D3—32no—
425C2×C3×D3—32no—
426C2×C3×D3—32no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—41no—
434C32×C4—41no—
435C32×C4—41no—
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—21no—
439C3⋊Dic3—21no—
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3D3×Q812yes—
443C3×Dic3—32no—
444C3×Dic3—32no—
445C3×Dic3—32no—
446C3×Dic3—62no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C3×Dic3—61no—
450C3×Dic3—61no—
451C3×Dic3—61no—
452C3×Dic3—61no—
453C3×Dic3—61no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C3×Dic3—61no—
458C3×Dic3—61no—
459C3×Dic3—121no—
460C3×Dic3—121no—
461C3×Dic3—121no—
462#125—91no—
463#125—91no—
464#125—271no—
465#125—271no—
466#125—271no—
467#125—271no—
468#125—271no—
469#125—271no—
470C2×C4⋊C4—91no—
471C2×C4⋊C4—271no—
472C2×C4⋊C4—271no—
473C2×C4⋊C4—271no—
474C2×C4⋊C4—271no—
475C2×C4⋊C4—271no—
476C2×C42—271no—
477H(3,𝔽3)C2×#12511yescharacteristic, complemented, Sylow
478C23×C3—91no—
479C22×D3—31no—
480C22×D3—91no—
481C2×C3×C4—31no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—91no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—91no—
495C2×C3×C4—91no—
496C2×C3×C4—91no—
497C2×C3×C4—91no—
498C2×C3×C4—91no—
499C2×C3×C4—91no—
500C2×C3×C4—91no—
501C2×C3×C4—182no—
502C2×C3×C4—182no—
503C2×C3×C4—182no—
504C2×C3×C4C2×D3211yescharacteristic
505C2×C3×C4C2×D3211yescharacteristic
506C2×C3×C4C2×D3211yescharacteristic
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—91no—
527C2×Dic3—91no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—94no—
534C2×Dic3—182no—
535C2×Dic3—182no—
536C2×Dic3—182no—
537C4×D3—62no—
538C4×D3—62no—
539C4×D3—62no—
540C4×D3—94no—
541C4×D3—94no—
542C4×D3—182no—
543C4×D3—182no—
544C4×D3—182no—
545C4×D3—182no—
546C4×D3—182no—
547C4×D3—182no—
548C4×D3—182no—
549C4×D3—182no—
550C4×D3—182no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—21no—
554C2×C32C2×#23511yescharacteristic
555C2×C32C2×#23711yescharacteristic
556C2×C32C2×D3×Q811yescharacteristic
557C2×C32C2×D3×Q811yescharacteristic
558C2×C32D3×#4111yescharacteristic
559C2×C32D3×#4111yescharacteristic
560C3⋊D3#88914yescomplemented
561C3×D3—34no—
562C22×C4—91no—
563C22×C4—91no—
564C22×C4—91no—
565C22×C4—271no—
566C22×C4—271no—
567C22×C4—271no—
568C22×C4—271no—
569C4⋊C4—91no—
570C4⋊C4—91no—
571C4⋊C4—91no—
572C4⋊C4—91no—
573C4⋊C4—91no—
574C4⋊C4—91no—
575C4⋊C4—91no—
576C4⋊C4—91no—
577C4⋊C4—91no—
578C4⋊C4—91no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C4⋊C4—91no—
582C4⋊C4—271no—
583C4⋊C4—271no—
584C4⋊C4—271no—
585C4⋊C4—271no—
586C4⋊C4—271no—
587C4⋊C4—271no—
588C4⋊C4—271no—
589C4⋊C4—271no—
590C4⋊C4—271no—
591C4⋊C4—271no—
592C4⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
593C42—91no—
594C42—91no—
595C42—271no—
596C42—271no—
597C22×C3—31no—
598C22×C3—31no—
599C22×C3—61no—
600C22×C3—92no—
601C22×C3—92no—
602C22×C3—92no—
603C22×C3C22×D3211yescharacteristic
604C2×D3—32no—
605C2×D3—32no—
606C2×D3—32no—
607C2×D3—92no—
608C2×D3—92no—
609C2×D3—92no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—61no—
614C3×C4—61no—
615C3×C4—61no—
616C3×C4—61no—
617C3×C4—61no—
618C3×C4—61no—
619C3×C4—92no—
620C3×C4—92no—
621C3×C4—121no—
622C3×C4—121no—
623C3×C4—121no—
624C3×C4—181no—
625C3×C4—181no—
626C3×C4—181no—
627C3×C4—181no—
628C3×C4—181no—
629C3×C4—181no—
630C3×C4—181no—
631C3×C4—181no—
632C3×C4—181no—
633Dic3—32no—
634Dic3—32no—
635Dic3—32no—
636Dic3—62no—
637Dic3—61no—
638Dic3—61no—
639Dic3—61no—
640Dic3—61no—
641Dic3—61no—
642Dic3—61no—
643Dic3—61no—
644Dic3—61no—
645Dic3—61no—
646Dic3—61no—
647Dic3—61no—
648Dic3—61no—
649Dic3—92no—
650Dic3—121no—
651Dic3—121no—
652Dic3—121no—
653Dic3—181no—
654Dic3—181no—
655Dic3—181no—
656Dic3—181no—
657Dic3—181no—
658Dic3—181no—
659C32—21no—
660C32C2×#88911yescharacteristic, complemented
661C32D3×#12511yescharacteristic, complemented
662C23—91no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—91no—
667C2×C4—91no—
668C2×C4—91no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—91no—
672C2×C4—91no—
673C2×C4—91no—
674C2×C4—182no—
675C2×C4—182no—
676C2×C4—182no—
677C2×C4—274no—
678C2×C4—542no—
679C2×C4—542no—
680C2×C4—542no—
681C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
682C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
683C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
684C2×C3—31no—
685C2×C3—31no—
686C2×C3—31no—
687C2×C3—31no—
688C2×C3—31no—
689C2×C3—31no—
690C2×C3—61no—
691C2×C3—61no—
692C2×C3—61no—
693C2×C3—94no—
694C2×C3D3×#23511yescharacteristic
695C2×C3D3×#23711yescharacteristic
696C2×C3D32×Q811yescharacteristic
697D3—34no—
698D3—94no—
699C22—92no—
700C22—92no—
701C22—92no—
702C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
703C4—21no—
704C4—21no—
705C4—21no—
706C4—92no—
707C4—92no—
708C4—181no—
709C4—181no—
710C4—181no—
711C4—181no—
712C4—181no—
713C4—181no—
714C4—181no—
715C4—181no—
716C4—181no—
717C3—31no—
718C3—31no—
719C3—61no—
720C3D3×#88911yescharacteristic
721C2—94no—
722C2#1172249011yescharacteristic
723C2#1172250411yescharacteristic
724C2Q8×((C3⋊D3)⋊C3)⋊C211yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC4⋊C4×H(3,𝔽3)C22
prime radicalC22×(C3⋊D3)⋊C3C23
hypercenterC4⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C2×#125
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721757C2semidirect
3. #64098⋊C3C2semidirect
10. #11721098C2semidirect
11. #11721091C2semidirect
12. #11721087C2semidirect
13. #11721086C2semidirect
14. #11721086C2semidirect
15. #11721085C2semidirect
54. #64098D3semidirect
305. (C3⋊D3)⋊C3#125semidirect
477. H(3,𝔽3)C2×#125semidirect
560. C3⋊D3#889semidirect
660. C32C2×#889semidirect
661. C32D3×#125semidirect

Maximal subgroups

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

subgroupindex
#117217572
C4⋊C4×(C3⋊D3)⋊C32
#64098⋊C32
#117211292
#117211192
C4×((C3⋊D3)⋊C3)⋊C42
#117210982
#117210912
#117210872
#117210862
#117210852
#105943993
D3×#8893