Finite Group Databasebeta

← C3×#80907 #11867751

Subgroups — C3×#80907 #11867751

Order 1152.

999 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#918C211yesmaximal, characteristic, complemented
2C2×C3×#907C211yesmaximal, characteristic, complemented
3C3×#5629C211yesmaximal, characteristic
4C3×#5628C211yesmaximal, characteristic, complemented
5C32×#470C211yesmaximal, characteristic, complemented
6C3×#5188C211yesmaximal, characteristic, complemented
7C3×#5134C211yesmaximal, characteristic, complemented
8C3×#5051C211yesmaximal, characteristic, complemented
9C3×#5048C211yesmaximal, characteristic, complemented
10C3×#4864C211yesmaximal, characteristic, complemented
11C3×#4861C211yesmaximal, characteristic, complemented
12C3×#4816C211yesmaximal, characteristic, complemented
13C3×#4812C211yesmaximal, characteristic, complemented
14C3×#4804C211yesmaximal, characteristic, complemented
15C3×D3×#103C211yesmaximal, characteristic, complemented
16C3×#3063—31nomaximal
17#80907C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic
22C2×C32×M16C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic
24C32×C22⋊Q8C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C3×#924C2211yescharacteristic
31C22×C3×C3⋊C8C2211yescharacteristic
32C3×#918—24no—
33C3×#907—24no—
34C2×C3×#204C2211yescharacteristic
35C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
36C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
37C2×C3×D3×C8C2211yescharacteristic
38C2×C3×D3×C8C2211yescharacteristic
39C3×#897C2211yescharacteristic
40C3×#896—21no—
41C3×#895—21no—
42C3×#895C2211yescharacteristic
43C3×#894—21no—
44C3×#892C2211yescharacteristic
45C3×D3×C4⋊C4C2211yescharacteristic
46C3×#888—21no—
47C3×#885—21no—
48C3×#884—21no—
49C3×#884—21no—
50C3×#883—21no—
51C32×#106C2211yescharacteristic
52C32×#103C2211yescharacteristic
53C32×#103C2211yescharacteristic
54C3×#835C2211yescharacteristic
55C3×#835C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×#818C2211yescharacteristic
58C3×#816C2211yescharacteristic
59C3×#810C2211yescharacteristic
60C3×#809C2211yescharacteristic
61C3×#808C2211yescharacteristic
62C3×#807C2211yescharacteristic
63C2×C3×#137—31no—
64C2×C3×#131—31no—
65C3×#537—31no—
66C3×#536—31no—
67C2×#918C2×C311yescharacteristic, complemented
68C2×#907C2×C311yescharacteristic, complemented
69#5629C2×C311yescharacteristic
70#5628C2×C311yescharacteristic, complemented
71C3×#470—21no—
72C3×#470—31no—
73C3×#470D311yescharacteristic, complemented
74C3×#470C2×C311yescharacteristic, complemented
75C3×#468—31no—
76C3×#468—31no—
77C3×#467—31no—
78C3×#467—31no—
79C3×#465—31no—
80C3×#465—31no—
81C3×#428—31no—
82C3×#416—31no—
83C2×C3×#103—31no—
84#5188C2×C311yescharacteristic, complemented
85#5134C2×C311yescharacteristic, complemented
86#5051C2×C311yescharacteristic, complemented
87#5048C2×C311yescharacteristic, complemented
88#4864C2×C311yescharacteristic, complemented
89#4861C2×C311yescharacteristic, complemented
90#4816C2×C311yescharacteristic, complemented
91#4812C2×C311yescharacteristic, complemented
92#4804C2×C311yescharacteristic, complemented
93D3×#103C2×C311yescharacteristic, complemented
94C2×C32×Q8C2311yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67D411yescharacteristic
99C2×C3×#67D411yescharacteristic
100C3×#239—22no—
101C3×#239—22no—
102C3×D3×Q8—22no—
103C3×D3×Q8—22no—
104C3×#235—22no—
105C3×#235—22no—
106C2×C3×D12—21no—
107C2×C3×D12—21no—
108C2×C3×D12D411yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6—21no—
116C2×C3×Dic6D411yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C32×Q16—22no—
119C32×M16—22no—
120C2×C32×C8C2311yescharacteristic
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4—21no—
123C32×C4⋊C4—21no—
124C32×C4⋊C4C2311yescharacteristic
125C32×C4⋊C4C2311yescharacteristic
126C32×C22⋊C4—21no—
127C32×C22⋊C4—21no—
128C3×#217—21no—
129C3×#216—22no—
130C3×#215—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4—21no—
144C3×C4×Dic3—21no—
145C2×C3×C3⋊C8—22no—
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148C3×#204—22no—
149C3×ΓL(1,𝔽25)—22no—
150C3×ΓL(1,𝔽25)D414yescomplemented
151C3×D3×C8—22no—
152C3×D3×C8—22no—
153#3063—31noSylow
154C2×C3×#41—31no—
155C2×C3×#41—31no—
156C22×C3×Q8—31no—
157C2×#239C22×C311yescharacteristic
158C2×D3×Q8C22×C311yescharacteristic
159C2×#235C22×C311yescharacteristic
160C3×#137—64no—
161C2×C3×Q16—21no—
162C2×C3×Q16—31no—
163C2×C3×Q16C2×D311yescharacteristic
164C2×C3×Q16C22×C311yescharacteristic
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C3×#131—64no—
168C2×C3×M16—21no—
169C2×C3×M16—31no—
170C2×C3×M16—31no—
171C2×C3×M16C2×D311yescharacteristic
172C2×C3×M16C22×C311yescharacteristic
173C22×C3×C8—31no—
174C22×C3×C8—31no—
175C22×C3×C8—31no—
176C3×C4⋊Q8—61no—
177C3×#124—61no—
178C3×#123—61no—
179C3×#123—61no—
180C3×C22⋊Q8—21no—
181C3×C22⋊Q8—21no—
182C3×C22⋊Q8—31no—
183C3×C22⋊Q8—31no—
184C3×C22⋊Q8—31no—
185C3×C22⋊Q8—31no—
186C3×C22⋊Q8—61no—
187C3×C22⋊Q8C2×D311yescharacteristic
188C3×C22⋊Q8C2×D311yescharacteristic
189C3×C22⋊Q8C22×C311yescharacteristic
190C3×C22⋊Q8C22×C311yescharacteristic
191C3×#121—31no—
192C3×#121—31no—
193C3×#121—61no—
194C3×#121—61no—
195C3×#121—61no—
196C3×#117—31no—
197C2×C3×C4⋊C4—31no—
198#946C22×C311yescharacteristic
199#946C22×C311yescharacteristic
200C2×#216C22×C311yescharacteristic
201C2×#215C22×C311yescharacteristic
202#930C22×C311yescharacteristic
203#924C22×C311yescharacteristic
204C22×C3⋊C8C22×C311yescharacteristic
205#918—24no—
206#907—24no—
207C2×#204C22×C311yescharacteristic
208C2×ΓL(1,𝔽25)C22×C311yescharacteristic
209C2×ΓL(1,𝔽25)C22×C311yescharacteristic
210C2×D3×C8C22×C311yescharacteristic
211C2×D3×C8C22×C311yescharacteristic
212#897C22×C311yescharacteristic
213#896—21no—
214#895—21no—
215#895C22×C311yescharacteristic
216#894—21no—
217#892C22×C311yescharacteristic
218D3×C4⋊C4C22×C311yescharacteristic
219#888—21no—
220#885—21no—
221#884—21no—
222#884—21no—
223#883—21no—
224C3×#107—31no—
225C3×#107—31no—
226C3×#106—21no—
227C3×#106—31no—
228C3×#106C2×D311yescharacteristic
229C3×#106C22×C311yescharacteristic
230C3×#103—21no—
231C3×#103—21no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#103—31no—
236C3×#103C2×D311yescharacteristic
237C3×#103C2×D311yescharacteristic
238C3×#103C22×C311yescharacteristic
239C3×#103C22×C311yescharacteristic
240C3×#102—31no—
241C3×#102—31no—
242#835C22×C311yescharacteristic
243#835C22×C311yescharacteristic
244#821C22×C311yescharacteristic
245#818C22×C311yescharacteristic
246#816C22×C311yescharacteristic
247#810C22×C311yescharacteristic
248#809C22×C311yescharacteristic
249#808C22×C311yescharacteristic
250#807C22×C311yescharacteristic
251C23×C32C2×D411yescharacteristic
252C22×C3×D3—21no—
253C22×C3×D3C2×D411yescharacteristic
254C22×C3×D3C2×D411yescharacteristic
255C32×Q8—21no—
256C32×Q8—21no—
257C32×Q8—21no—
258C32×Q8—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267C3×#67—22no—
268C3×#67—22no—
269C3×#67—81no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—22no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—42no—
279C3×D12—81no—
280C3×C4×D3—21no—
281C3×C4×D3—21no—
282C3×C4×D3—42no—
283C3×C4×D3—42no—
284C3×C4×D3—81no—
285C3×C4×D3C2×D412yes—
286C3×C4×D3#4112yes—
287C3×Dic6—22no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—42no—
291C32×C8—21no—
292C32×C8C2×D412yes—
293C3×C3⋊C8—21no—
294C3×C3⋊C8C2×D412yes—
295C2×#137—31no—
296C2×#131—31no—
297#537—31no—
298#536—31no—
299#470—31no—
300#470C3×D311yescharacteristic, complemented
301#468—31no—
302#468—31no—
303#467—31no—
304#467—31no—
305#465—31no—
306#465—31no—
307#428—31no—
308#416—31no—
309C2×#103—31no—
310C3×#41—62no—
311C3×#41—62no—
312C3×#41—62no—
313C3×#41—62no—
314C2×C3×Q8—21no—
315C2×C3×Q8—21no—
316C2×C3×Q8—31no—
317C2×C3×Q8—31no—
318C2×C3×Q8—61no—
319C2×C3×Q8—62no—
320C2×C3×Q8—62no—
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C23×C311yescharacteristic
324C2×C3×Q8C23×C311yescharacteristic
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C22×C3×C4—21no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C22×C3×C4—61no—
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C23×C311yescharacteristic
340C2×#67—21no—
341C2×#67C3×D411yescharacteristic
342C2×#67C3×D411yescharacteristic
343#239—22no—
344#239—22no—
345D3×Q8—22no—
346D3×Q8—22no—
347#235—22no—
348#235—22no—
349C2×D12—21no—
350C2×D12—21no—
351C2×D12C3×D411yescharacteristic
352C2×D12C23×C311yescharacteristic
353C2×C4×D3—21no—
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×C4×D3C23×C311yescharacteristic
357C2×C4×D3C23×C311yescharacteristic
358C2×Dic6—21no—
359C2×Dic6C3×D411yescharacteristic
360C2×Dic6C23×C311yescharacteristic
361C3×Q16—22no—
362C3×Q16—22no—
363C3×Q16—42no—
364C3×Q16—62no—
365C3×SD16—62no—
366C3×SD16—62no—
367C3×M16—22no—
368C3×M16—22no—
369C3×M16—34no—
370C3×M16—42no—
371C3×M16—62no—
372C2×C3×C8—21no—
373C2×C3×C8—21no—
374C2×C3×C8—31no—
375C2×C3×C8—31no—
376C2×C3×C8—62no—
377C2×C3×C8—62no—
378C2×C3×C8—62no—
379C2×C3×C8C22×D311yescharacteristic
380C2×C3×C8C22×D311yescharacteristic
381C2×C3×C8C23×C311yescharacteristic
382C2×C3×C8C23×C311yescharacteristic
383C3×C4⋊C4—21no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—41no—
392C3×C4⋊C4—41no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4—61no—
395C3×C4⋊C4—61no—
396C3×C4⋊C4—61no—
397C3×C4⋊C4—61no—
398C3×C4⋊C4C22×D311yescharacteristic
399C3×C4⋊C4C22×D311yescharacteristic
400C3×C4⋊C4C23×C311yescharacteristic
401C3×C4⋊C4C23×C311yescharacteristic
402C3×C22⋊C4—21no—
403C3×C22⋊C4—21no—
404C3×C22⋊C4—21no—
405C3×C22⋊C4—21no—
406C3×C22⋊C4—41no—
407C3×C22⋊C4—41no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4—61no—
414C3×C22⋊C4—61no—
415C3×C42—61no—
416#217—21no—
417#216—22no—
418#215—22no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425C4⋊Dic3—21no—
426C4⋊Dic3C23×C311yescharacteristic
427C4⋊Dic3C23×C311yescharacteristic
428Dic3⋊C4—21no—
429Dic3⋊C4—21no—
430Dic3⋊C4—21no—
431Dic3⋊C4—21no—
432C4×Dic3—21no—
433C2×C3⋊C8—22no—
434C2×C3⋊C8C23×C311yescharacteristic
435C2×C3⋊C8C23×C311yescharacteristic
436#204—22no—
437ΓL(1,𝔽25)—22no—
438ΓL(1,𝔽25)C3×D414yescomplemented
439D3×C8—22no—
440D3×C8—22no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32C22×D411yescharacteristic
445C2×C3×D3—21no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3#12112yes—
454C32×C4—21no—
455C32×C4—41no—
456C32×C4—41no—
457C32×C4—41no—
458C32×C4—41no—
459C32×C4C22×D411yescharacteristic
460C32×C4C2×#4111yescharacteristic
461C3×Dic3—21no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3#12112yes—
466C2×#41—31no—
467C2×#41—31no—
468C22×Q8—31no—
469#137—64no—
470C2×Q16—31no—
471C2×Q16C2×C3×D311yescharacteristic
472C2×SD16—31no—
473C2×SD16—31no—
474#131—64no—
475C2×M16—31no—
476C2×M16—31no—
477C2×M16C2×C3×D311yescharacteristic
478C22×C8—31no—
479C22×C8—31no—
480C22×C8—31no—
481C4⋊Q8—61no—
482#124—61no—
483#123—61no—
484#123—61no—
485C22⋊Q8—31no—
486C22⋊Q8—31no—
487C22⋊Q8—31no—
488C22⋊Q8—31no—
489C22⋊Q8—61no—
490C22⋊Q8C2×C3×D311yescharacteristic
491C22⋊Q8C2×C3×D311yescharacteristic
492#121—31no—
493#121—31no—
494#121—61no—
495#121—61no—
496#121—61no—
497#117—31no—
498C2×C4⋊C4—31no—
499#107—31no—
500#107—31no—
501#106—31no—
502#106C2×C3×D311yescharacteristic
503#103—31no—
504#103—31no—
505#103—31no—
506#103—31no—
507#103C2×C3×D311yescharacteristic
508#103C2×C3×D311yescharacteristic
509#102—31no—
510#102—31no—
511C23×C3—21no—
512C23×C3—31no—
513C23×C3—31no—
514C23×C3—61no—
515C23×C3D3×D411yescharacteristic
516C23×C3C2×C3×D411yescharacteristic
517C22×D3—21no—
518C22×D3C2×C3×D411yescharacteristic
519C22×D3C2×C3×D411yescharacteristic
520C3×Q8—21no—
521C3×Q8—21no—
522C3×Q8—21no—
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×Q8—21no—
527C3×Q8—21no—
528C3×Q8—41no—
529C3×Q8—41no—
530C3×Q8—41no—
531C3×Q8—41no—
532C3×Q8—62no—
533C3×Q8—61no—
534C3×Q8—61no—
535C3×Q8—122no—
536C3×D4—62no—
537C3×D4—62no—
538C3×D4—62no—
539C3×D4—61no—
540C3×D4—61no—
541C3×D4—122no—
542C3×D4—241no—
543C3×D4—241no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—31no—
559C2×C3×C4—32no—
560C2×C3×C4—32no—
561C2×C3×C4—31no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—122no—
574C2×C3×C4—122no—
575C2×C3×C4—241no—
576C2×C3×C4D3×D411yescharacteristic
577C2×C3×C4C2×C3×D411yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579C2×C3×C4C24×C311yescharacteristic
580#67—22no—
581#67—22no—
582#67—81no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3C2×C3×D411yescharacteristic
587C2×Dic3C2×C3×D411yescharacteristic
588D12—22no—
589D12—21no—
590D12—21no—
591D12—42no—
592D12—81no—
593C4×D3—21no—
594C4×D3—21no—
595C4×D3—42no—
596C4×D3—42no—
597C4×D3—81no—
598C4×D3C2×C3×D412yes—
599C4×D3C3×#4112yes—
600Dic6—22no—
601Dic6—21no—
602Dic6—21no—
603Dic6—42no—
604C3×C8—21no—
605C3×C8—21no—
606C3×C8—22no—
607C3×C8—32no—
608C3×C8—41no—
609C3×C8—61no—
610C3×C8D3×D412yes—
611C3×C8C2×C3×D412yes—
612C3⋊C8—21no—
613C3⋊C8C2×C3×D412yes—
614C2×C32—41no—
615C2×C32C2×#12111yescharacteristic
616C2×C32#57711yescharacteristic
617C2×C32#57811yescharacteristic
618C3×D3—22no—
619C3×D3—41no—
620C3×D3—81no—
621#41—62no—
622#41—62no—
623#41—62no—
624#41—62no—
625C2×Q8—31no—
626C2×Q8—31no—
627C2×Q8—61no—
628C2×Q8—62no—
629C2×Q8—62no—
630C2×Q8C22×C3×D311yescharacteristic
631C2×Q8C22×C3×D311yescharacteristic
632C2×D4—31no—
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4—61no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4C22×C3×D311yescharacteristic
645Q16—22no—
646Q16—62no—
647SD16—62no—
648SD16—62no—
649M16—22no—
650M16—34no—
651M16—62no—
652C2×C8—31no—
653C2×C8—31no—
654C2×C8—62no—
655C2×C8—62no—
656C2×C8—62no—
657C2×C8C22×C3×D311yescharacteristic
658C2×C8C22×C3×D311yescharacteristic
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—31no—
662C4⋊C4—31no—
663C4⋊C4—61no—
664C4⋊C4—61no—
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4C22×C3×D311yescharacteristic
669C4⋊C4C22×C3×D311yescharacteristic
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—61no—
679C42—61no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—32no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3C2×D3×D411yescharacteristic
700C22×C3C22×C3×D411yescharacteristic
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3C3×#12112yes—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—32no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—61no—
725C3×C4—81no—
726C3×C4—81no—
727C3×C4—81no—
728C3×C4—81no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4—121no—
732C3×C4C2×D3×D411yescharacteristic
733C3×C4D3×#4111yescharacteristic
734C3×C4C22×C3×D411yescharacteristic
735C3×C4C2×C3×#4111yescharacteristic
736Dic3—21no—
737Dic3—41no—
738Dic3—41no—
739Dic3—41no—
740Dic3C3×#12112yes—
741C32#306311yescharacteristic, complemented, Sylow
742C23—31no—
743C23—31no—
744C23—61no—
745C23C3×D3×D411yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—62no—
751Q8—61no—
752Q8—61no—
753Q8—122no—
754D4—62no—
755D4—62no—
756D4—62no—
757D4—61no—
758D4—61no—
759D4—122no—
760D4—241no—
761D4—241no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—31no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—31no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—122no—
778C2×C4—122no—
779C2×C4—241no—
780C2×C4C3×D3×D411yescharacteristic
781C2×C4C23×C3×D311yescharacteristic
782C8—21no—
783C8—32no—
784C8—61no—
785C8C3×D3×D412yes—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—41no—
790C2×C3—41no—
791C2×C3—62no—
792C2×C3—81no—
793C2×C3—121no—
794C2×C3—241no—
795C2×C3D3×#12111yescharacteristic
796C2×C3#577811yescharacteristic
797C2×C3#577911yescharacteristic
798C2×C3C2×C3×#12111yescharacteristic
799C2×C3C3×#57711yescharacteristic
800C2×C3C3×#57811yescharacteristic
801D3—22no—
802D3—41no—
803D3—81no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—32no—
808C22—61no—
809C22—61no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22C2×C3×D3×D411yescharacteristic
817C4—21no—
818C4—32no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—61no—
824C4—121no—
825C4—121no—
826C4—121no—
827C4C2×C3×D3×D411yescharacteristic
828C4C3×D3×#4111yescharacteristic
829C3—21no—
830C3#8090711yescharacteristic, direct product factor
831C3C3×#306311yescharacteristic, complemented
832C2—41no—
833C2—62no—
834C2—121no—
835C2—241no—
836C2C3×D3×#12111yescharacteristic
837C2C3×#577811yescharacteristic
838C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#470C2
socleC22×C32C22×D4
prime radicalC3×#5629C2
hypercenterC3×#470D3
hypocenterC3C3×#3063
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#470

Complements

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

NH ≅ G/Ntype
1. C2×C3×#918C2semidirect
2. C2×C3×#907C2semidirect
4. C3×#5628C2semidirect
5. C32×#470C2semidirect
6. C3×#5188C2semidirect
7. C3×#5134C2semidirect
8. C3×#5051C2semidirect
9. C3×#5048C2semidirect
10. C3×#4864C2semidirect
11. C3×#4861C2semidirect
12. C3×#4816C2semidirect
13. C3×#4812C2semidirect
14. C3×#4804C2semidirect
15. C3×D3×#103C2semidirect
17. #80907C3direct (N × H)
67. C2×#918C2×C3semidirect
68. C2×#907C2×C3semidirect
70. #5628C2×C3semidirect
73. C3×#470D3semidirect
74. C3×#470C2×C3semidirect
84. #5188C2×C3semidirect
85. #5134C2×C3semidirect
86. #5051C2×C3semidirect
87. #5048C2×C3semidirect
88. #4864C2×C3semidirect
89. #4861C2×C3semidirect
90. #4816C2×C3semidirect
91. #4812C2×C3semidirect
92. #4804C2×C3semidirect
93. D3×#103C2×C3semidirect
150. C3×ΓL(1,𝔽25)D4semidirect
300. #470C3×D3semidirect
438. ΓL(1,𝔽25)C3×D4semidirect
741. C32#3063semidirect
830. C3#80907direct (N × H)
831. C3C3×#3063semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9182
C2×C3×#9072
C3×#56292
C3×#56282
C32×#4702
C3×#51882
C3×#51342
C3×#50512
C3×#50482
C3×#48642
C3×#48612
C3×#48162
C3×#48122
C3×#48042
C3×D3×#1032
C3×#30633
#809073