Finite Group Databasebeta

← #10596126⋊C3 #13153046

Subgroups — #10596126⋊C3 #13153046

Order 1728.

1100 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3830⋊C3C211yesmaximal, characteristic, complemented
2C2×#3828⋊C3C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×#123C211yesmaximal, characteristic, complemented
4#64148⋊C3C211yesmaximal, characteristic, complemented
5C2×#3750⋊C3C211yesmaximal, characteristic, complemented
6#64105⋊C3C211yesmaximal, characteristic, complemented
7#64103⋊C3C211yesmaximal, characteristic, complemented
8C4⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
9#64097⋊C3C211yesmaximal, characteristic, complemented
10#64095⋊C3C211yesmaximal, characteristic, complemented
11#64093⋊C3C211yesmaximal, characteristic, complemented
12#64092⋊C3C211yesmaximal, characteristic, complemented
13#64090⋊C3C211yesmaximal, characteristic, complemented
14#64090⋊C3C211yesmaximal, characteristic, complemented
15#64087⋊C3C211yesmaximal, characteristic, complemented
16#10596126C311yesmaximal, characteristic, complemented
17C3×#5655—31nomaximal
18C2×D4×H(3,𝔽3)C2211yescharacteristic
19C22×C4×H(3,𝔽3)C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic
21C2×#638⋊C3C2211yescharacteristic
22C2×#638⋊C3C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic
24C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
25C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
26C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
27#3830⋊C3—24no—
28#3828⋊C3—24no—
29C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
30C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
31C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
32C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
33C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
34C2×#634⋊C3C2211yescharacteristic
35C2×#634⋊C3C2211yescharacteristic
36C4⋊C4×H(3,𝔽3)C2211yescharacteristic
37C4⋊C4×H(3,𝔽3)C2211yescharacteristic
38C22⋊C4×H(3,𝔽3)C2211yescharacteristic
39C22⋊C4×H(3,𝔽3)C2211yescharacteristic
40C22⋊C4×H(3,𝔽3)C2211yescharacteristic
41#3757⋊C3C2211yescharacteristic
42#3752⋊C3C2211yescharacteristic
43#3752⋊C3C2211yescharacteristic
44#3752⋊C3C2211yescharacteristic
45#3752⋊C3C2211yescharacteristic
46C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
47C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
48#3750⋊C3C2211yescharacteristic
49#3750⋊C3C2211yescharacteristic
50#3750⋊C3C2211yescharacteristic
51#3750⋊C3C2211yescharacteristic
52#3750⋊C3C2211yescharacteristic
53#3750⋊C3C2211yescharacteristic
54C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
55C2×#3830C2×C311yescharacteristic, complemented
56C2×#3828C2×C311yescharacteristic, complemented
57C2×C3×#237—31no—
58C2×C3×#235—31no—
59C32×#123—21no—
60C32×#123D311yescharacteristic, complemented
61C32×#123C2×C311yescharacteristic, complemented
62#64148C2×C311yescharacteristic, complemented
63C2×#3750C2×C311yescharacteristic, complemented
64#64105C2×C311yescharacteristic, complemented
65#64103C2×C311yescharacteristic, complemented
66C4⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
67#64097C2×C311yescharacteristic, complemented
68#64095C2×C311yescharacteristic, complemented
69#64093C2×C311yescharacteristic, complemented
70#64092C2×C311yescharacteristic, complemented
71#64090C2×C311yescharacteristic, complemented
72#64090C2×C311yescharacteristic, complemented
73#64087C2×C311yescharacteristic, complemented
74C3×#939—31no—
75C2×C3×Dic3⋊C4—31no—
76C3×#896—31no—
77C3×#894—31no—
78C3×D3×C4⋊C4—31no—
79C3×#888—31no—
80C3×#886—31no—
81C3×#884—31no—
82C3×#883—31no—
83C3×#67⋊C4—31no—
84C3×#67⋊C4—31no—
85C3×#878—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C23×H(3,𝔽3)C2311yescharacteristic
88C22×(C3⋊D3)⋊C3C2311yescharacteristic
89C22×(C3⋊D3)⋊C3C2311yescharacteristic
90D4×H(3,𝔽3)—22no—
91C2×C4×H(3,𝔽3)—22no—
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×C4×H(3,𝔽3)C2311yescharacteristic
95C2×C4×H(3,𝔽3)C2311yescharacteristic
96C2×C4×H(3,𝔽3)C2311yescharacteristic
97#638⋊C3—22no—
98#638⋊C3—22no—
99#638⋊C3—22no—
100#638⋊C3D414yescomplemented
101C2×(C3⋊Dic3)⋊C3—22no—
102C2×(C3⋊Dic3)⋊C3—22no—
103C2×(C3⋊Dic3)⋊C3—22no—
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
110C4⋊((C3⋊D3)⋊C3)—22no—
111C4×(C3⋊D3)⋊C3—22no—
112C4×(C3⋊D3)⋊C3—22no—
113C4×(C3⋊D3)⋊C3—22no—
114C4×(C3⋊D3)⋊C3—22no—
115#634⋊C3—22no—
116#634⋊C3—22no—
117C3×#547—91no—
118#5655—31no—
119#5655—91no—
120C2×C32×D4—21no—
121C2×C32×D4C2×D311yescharacteristic
122C2×C32×D4C22×C311yescharacteristic
123C22×C32×C4—21no—
124C22×C32×C4C2×D311yescharacteristic
125C22×C32×C4C22×C311yescharacteristic
126C2×#638C22×C311yescharacteristic
127C2×#638C22×C311yescharacteristic
128C2×#638C22×C311yescharacteristic
129C2×#638C22×C311yescharacteristic
130C22×C3⋊Dic3C22×C311yescharacteristic
131C22×C3⋊Dic3C22×C311yescharacteristic
132C22×C3⋊Dic3C22×C311yescharacteristic
133#3830—24no—
134#3828—24no—
135C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
136C2×C4×C3⋊D3C22×C311yescharacteristic
137C2×C4×C3⋊D3C22×C311yescharacteristic
138C2×C4×C3⋊D3C22×C311yescharacteristic
139C2×C4×C3⋊D3C22×C311yescharacteristic
140C2×#634C22×C311yescharacteristic
141C2×#634C22×C311yescharacteristic
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C22×C3×Dic3—31no—
147C22×C3×Dic3—31no—
148C22×C3×Dic3—31no—
149C3×#237—64no—
150C3×#235—64no—
151C2×C3×D12—31no—
152C2×C3×C4×D3—31no—
153C2×C3×C4×D3—31no—
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—31no—
156C2×C3×Dic6—31no—
157C2×C3×Dic6—31no—
158C32×C4⋊C4—21no—
159C32×C4⋊C4—21no—
160C32×C4⋊C4C2×D311yescharacteristic
161C32×C4⋊C4C2×D311yescharacteristic
162C32×C4⋊C4C22×C311yescharacteristic
163C32×C4⋊C4C22×C311yescharacteristic
164C32×C22⋊C4—21no—
165C32×C22⋊C4—21no—
166C32×C22⋊C4—21no—
167C32×C22⋊C4C2×D311yescharacteristic
168C32×C22⋊C4C2×D311yescharacteristic
169C32×C22⋊C4C2×D311yescharacteristic
170C32×C22⋊C4C22×C311yescharacteristic
171C32×C22⋊C4C22×C311yescharacteristic
172C32×C22⋊C4C22×C311yescharacteristic
173#3757C22×C311yescharacteristic
174#3752C22×C311yescharacteristic
175#3752C22×C311yescharacteristic
176#3752C22×C311yescharacteristic
177#3752C22×C311yescharacteristic
178C4⋊(C3⋊Dic3)C22×C311yescharacteristic
179C4⋊(C3⋊Dic3)C22×C311yescharacteristic
180#3750C22×C311yescharacteristic
181#3750C22×C311yescharacteristic
182#3750C22×C311yescharacteristic
183#3750C22×C311yescharacteristic
184#3750C22×C311yescharacteristic
185#3750C22×C311yescharacteristic
186C4×C3⋊Dic3C22×C311yescharacteristic
187C3×#217—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—31no—
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×C4×Dic3—31no—
201C22×H(3,𝔽3)—21no—
202C22×H(3,𝔽3)—21no—
203C22×H(3,𝔽3)—21no—
204C22×H(3,𝔽3)—21no—
205C22×H(3,𝔽3)—21no—
206C22×H(3,𝔽3)C2×D412yes—
207C22×H(3,𝔽3)C2411yescharacteristic
208C2×(C3⋊D3)⋊C3—21no—
209C2×(C3⋊D3)⋊C3—21no—
210C2×(C3⋊D3)⋊C3—21no—
211C2×(C3⋊D3)⋊C3—21no—
212C2×(C3⋊D3)⋊C3—21no—
213C2×(C3⋊D3)⋊C3C2×D412yes—
214C4×H(3,𝔽3)—21no—
215C4×H(3,𝔽3)—21no—
216C4×H(3,𝔽3)—21no—
217C4×H(3,𝔽3)—21no—
218C4×H(3,𝔽3)—21no—
219(C3⋊Dic3)⋊C3—21no—
220(C3⋊Dic3)⋊C3—21no—
221(C3⋊Dic3)⋊C3—21no—
222(C3⋊Dic3)⋊C3—21no—
223(C3⋊Dic3)⋊C3C2×D412yes—
224(C3⋊Dic3)⋊C3#4112yescomplemented
225C2×C3×#41—91no—
226C2×C3×#41—91no—
227C2×#237—31no—
228C2×#237—91no—
229C2×#235—31no—
230C2×#235—91no—
231C3×C4⋊Q8—91no—
232C3×#123—31no—
233C3×#123—31no—
234C3×#123—61no—
235C3×#123—91no—
236C3×#123—91no—
237C3×#123—91no—
238C3×#123C3×D311yescharacteristic
239C3×C22⋊Q8—91no—
240C3×C22⋊Q8—91no—
241C3×#121—91no—
242C3×#121—91no—
243C3×C4×D4—91no—
244C3×C4×D4—91no—
245C2×C3×C4⋊C4—91no—
246C2×C3×C4⋊C4—91no—
247#939—31no—
248#939—91no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—91no—
251#896—31no—
252#896—91no—
253#894—31no—
254#894—91no—
255D3×C4⋊C4—31no—
256D3×C4⋊C4—91no—
257#888—31no—
258#888—91no—
259#886—31no—
260#886—91no—
261#884—31no—
262#884—91no—
263#883—31no—
264#883—91no—
265#67⋊C4—31no—
266#67⋊C4—31no—
267#67⋊C4—91no—
268#67⋊C4—91no—
269#878—31no—
270#878—91no—
271C23×C32—21no—
272C23×C32—21no—
273C23×C32C22×D311yescharacteristic
274C23×C32C22×D311yescharacteristic
275C23×C32C23×C311yescharacteristic
276C23×C32C23×C311yescharacteristic
277C22×C3⋊D3C23×C311yescharacteristic
278C22×C3⋊D3C23×C311yescharacteristic
279C22×C3×D3—31no—
280C22×C3×D3—31no—
281C32×D4—22no—
282C32×D4—22no—
283C32×D4—42no—
284C2×C32×C4—22no—
285C2×C32×C4—22no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4—42no—
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C22×D311yescharacteristic
295C2×C32×C4C22×D311yescharacteristic
296C2×C32×C4C22×D311yescharacteristic
297C2×C32×C4C23×C311yescharacteristic
298C2×C32×C4C23×C311yescharacteristic
299C2×C32×C4C23×C311yescharacteristic
300C2×C32×C4C23×C311yescharacteristic
301C2×C32×C4C23×C311yescharacteristic
302#638—22no—
303#638—22no—
304#638—22no—
305#638C3×D414yescomplemented
306C2×C3⋊Dic3—22no—
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3C23×C311yescharacteristic
310C2×C3⋊Dic3C23×C311yescharacteristic
311C2×C3⋊Dic3C23×C311yescharacteristic
312C2×C3⋊Dic3C23×C311yescharacteristic
313C2×C3⋊Dic3C23×C311yescharacteristic
314C2×C3⋊Dic3C23×C311yescharacteristic
315C4⋊(C3⋊D3)—22no—
316C4×C3⋊D3—22no—
317C4×C3⋊D3—22no—
318C4×C3⋊D3—22no—
319C4×C3⋊D3—22no—
320#634—22no—
321#634—22no—
322C3×#67—34no—
323C3×#67—62no—
324C3×#67—62no—
325C3×#67—62no—
326C2×C3×Dic3—31no—
327C2×C3×Dic3—31no—
328C2×C3×Dic3—31no—
329C2×C3×Dic3—31no—
330C2×C3×Dic3—31no—
331C2×C3×Dic3—31no—
332C2×C3×Dic3—62no—
333C2×C3×Dic3—62no—
334C2×C3×Dic3—62no—
335C3×D12—62no—
336C3×C4×D3—62no—
337C3×C4×D3—62no—
338C3×C4×D3—62no—
339C3×C4×D3—62no—
340C3×Dic6—62no—
341C3×Dic6—62no—
342#547—91noSylow
343C2×H(3,𝔽3)—22no—
344C2×H(3,𝔽3)—41no—
345C2×H(3,𝔽3)C22×D411yescharacteristic
346C2×H(3,𝔽3)C2×#4111yescharacteristic
347C2×H(3,𝔽3)2−1+411yescharacteristic
348(C3⋊D3)⋊C3—22no—
349(C3⋊D3)⋊C3—41no—
350C3×#41—184no—
351C3×#41—184no—
352C2×C3×Q8—91no—
353C2×C3×Q8—91no—
354C2×C3×D4—31no—
355C2×C3×D4—31no—
356C2×C3×D4—61no—
357C2×C3×D4—91no—
358C2×C3×D4—91no—
359C2×C3×D4—91no—
360C2×C3×D4—91no—
361C2×C3×D4—91no—
362C2×C3×D4C2×C3×D311yescharacteristic
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—61no—
366C22×C3×C4—91no—
367C22×C3×C4—91no—
368C22×C3×C4—91no—
369C22×C3×C4—91no—
370C22×C3×C4—91no—
371C22×C3×C4—91no—
372C22×C3×C4—91no—
373C22×C3×C4C2×C3×D311yescharacteristic
374C2×#67—31no—
375C2×#67—31no—
376C2×#67—31no—
377C2×#67—31no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—91no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—91no—
386C22×Dic3—91no—
387C22×Dic3—91no—
388#237—64no—
389#237—184no—
390#235—64no—
391#235—184no—
392C2×D12—31no—
393C2×D12—91no—
394C2×C4×D3—31no—
395C2×C4×D3—31no—
396C2×C4×D3—31no—
397C2×C4×D3—31no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×Dic6—31no—
403C2×Dic6—31no—
404C2×Dic6—91no—
405C2×Dic6—91no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4—31no—
409C3×C4⋊C4—31no—
410C3×C4⋊C4—61no—
411C3×C4⋊C4—61no—
412C3×C4⋊C4—91no—
413C3×C4⋊C4—91no—
414C3×C4⋊C4—91no—
415C3×C4⋊C4—91no—
416C3×C4⋊C4—91no—
417C3×C4⋊C4—91no—
418C3×C4⋊C4—91no—
419C3×C4⋊C4—91no—
420C3×C4⋊C4C2×C3×D311yescharacteristic
421C3×C4⋊C4C2×C3×D311yescharacteristic
422C3×C22⋊C4—31no—
423C3×C22⋊C4—31no—
424C3×C22⋊C4—31no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—31no—
427C3×C22⋊C4—31no—
428C3×C22⋊C4—61no—
429C3×C22⋊C4—61no—
430C3×C22⋊C4—61no—
431C3×C22⋊C4—91no—
432C3×C22⋊C4—91no—
433C3×C22⋊C4—91no—
434C3×C22⋊C4—91no—
435C3×C22⋊C4—91no—
436C3×C22⋊C4C2×C3×D311yescharacteristic
437C3×C22⋊C4C2×C3×D311yescharacteristic
438C3×C22⋊C4C2×C3×D311yescharacteristic
439C3×C42—91no—
440#217—31no—
441#217—91no—
442(C2×D3)⋊C4—31no—
443(C2×D3)⋊C4—31no—
444(C2×D3)⋊C4—31no—
445(C2×D3)⋊C4—31no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—91no—
448(C2×D3)⋊C4—91no—
449(C2×D3)⋊C4—91no—
450C4⋊Dic3—31no—
451C4⋊Dic3—31no—
452C4⋊Dic3—91no—
453C4⋊Dic3—91no—
454Dic3⋊C4—31no—
455Dic3⋊C4—31no—
456Dic3⋊C4—31no—
457Dic3⋊C4—31no—
458Dic3⋊C4—31no—
459Dic3⋊C4—31no—
460Dic3⋊C4—91no—
461Dic3⋊C4—91no—
462Dic3⋊C4—91no—
463Dic3⋊C4—91no—
464Dic3⋊C4—91no—
465Dic3⋊C4—91no—
466C4×Dic3—31no—
467C4×Dic3—91no—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32—21no—
471C22×C32—21no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—21no—
479C22×C32—22no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32D3×D412yes—
486C22×C32C2×C3×D412yes—
487C22×C32C23×D311yescharacteristic
488C22×C32C24×C311yescharacteristic
489C2×C3⋊D3—21no—
490C2×C3⋊D3—21no—
491C2×C3⋊D3—21no—
492C2×C3⋊D3—21no—
493C2×C3⋊D3—21no—
494C2×C3⋊D3C2×C3×D412yes—
495C2×C3×D3—32no—
496C2×C3×D3—61no—
497C2×C3×D3—61no—
498C2×C3×D3—61no—
499C2×C3×D3—61no—
500C2×C3×D3—61no—
501C32×C4—21no—
502C32×C4—21no—
503C32×C4—21no—
504C32×C4—21no—
505C32×C4—21no—
506C32×C4—21no—
507C32×C4—21no—
508C32×C4—21no—
509C32×C4—21no—
510C32×C4—21no—
511C32×C4—41no—
512C32×C4—41no—
513C32×C4—41no—
514C32×C4—41no—
515C32×C4—41no—
516C3⋊Dic3—21no—
517C3⋊Dic3—21no—
518C3⋊Dic3—21no—
519C3⋊Dic3—21no—
520C3⋊Dic3C2×C3×D412yes—
521C3⋊Dic3C3×#4112yescomplemented
522C3×Dic3—32no—
523C3×Dic3—32no—
524C3×Dic3—61no—
525C3×Dic3—61no—
526C3×Dic3—61no—
527C3×Dic3—61no—
528C2×#41—91no—
529C2×#41—91no—
530C4⋊Q8—91no—
531#123—91no—
532#123—91no—
533#123—91no—
534#123(C3⋊D3)⋊C311yescharacteristic, complemented
535C22⋊Q8—91no—
536C22⋊Q8—91no—
537#121—91no—
538#121—91no—
539C4×D4—91no—
540C4×D4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543H(3,𝔽3)#54711yescharacteristic, complemented, Sylow
544C23×C3—31no—
545C23×C3—31no—
546C23×C3—31no—
547C23×C3—31no—
548C23×C3—61no—
549C23×C3—61no—
550C23×C3—91no—
551C23×C3—91no—
552C23×C3C22×C3×D311yescharacteristic
553C23×C3C22×C3×D311yescharacteristic
554C22×D3—31no—
555C22×D3—31no—
556C22×D3—91no—
557C22×D3—91no—
558C3×Q8—182no—
559C3×Q8—182no—
560C3×D4—22no—
561C3×D4—62no—
562C3×D4—62no—
563C3×D4—94no—
564C3×D4—122no—
565C3×D4—182no—
566C3×D4—182no—
567C3×D4—182no—
568C3×D4—182no—
569C2×C3×C4—22no—
570C2×C3×C4—31no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—62no—
581C2×C3×C4—62no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—91no—
588C2×C3×C4—91no—
589C2×C3×C4—91no—
590C2×C3×C4—91no—
591C2×C3×C4—91no—
592C2×C3×C4—91no—
593C2×C3×C4—122no—
594C2×C3×C4—182no—
595C2×C3×C4—182no—
596C2×C3×C4—182no—
597C2×C3×C4—182no—
598C2×C3×C4—182no—
599C2×C3×C4—182no—
600C2×C3×C4—182no—
601C2×C3×C4C22×C3×D311yescharacteristic
602C2×C3×C4C22×C3×D311yescharacteristic
603C2×C3×C4C22×C3×D311yescharacteristic
604C2×C3×C4C22×C3×D311yescharacteristic
605C2×C3×C4C22×C3×D311yescharacteristic
606#67—34no—
607#67—62no—
608#67—62no—
609#67—62no—
610#67—94no—
611#67—182no—
612#67—182no—
613#67—182no—
614C2×Dic3—31no—
615C2×Dic3—31no—
616C2×Dic3—31no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—62no—
621C2×Dic3—62no—
622C2×Dic3—62no—
623C2×Dic3—91no—
624C2×Dic3—91no—
625C2×Dic3—91no—
626C2×Dic3—91no—
627C2×Dic3—91no—
628C2×Dic3—91no—
629C2×Dic3—182no—
630C2×Dic3—182no—
631C2×Dic3—182no—
632D12—62no—
633D12—182no—
634C4×D3—62no—
635C4×D3—62no—
636C4×D3—62no—
637C4×D3—62no—
638C4×D3—182no—
639C4×D3—182no—
640C4×D3—182no—
641C4×D3—182no—
642Dic6—62no—
643Dic6—62no—
644Dic6—182no—
645Dic6—182no—
646C2×C32—22no—
647C2×C32—22no—
648C2×C32—21no—
649C2×C32—21no—
650C2×C32—21no—
651C2×C32—42no—
652C2×C32—41no—
653C2×C32—41no—
654C2×C32—81no—
655C2×C32C2×D3×D411yescharacteristic
656C2×C32D3×#4111yescharacteristic
657C2×C32#101011yescharacteristic
658C2×C32C22×C3×D411yescharacteristic
659C2×C32C2×C3×#4111yescharacteristic
660C2×C32C3×2−1+411yescharacteristic
661C3⋊D3—22no—
662C3⋊D3—41no—
663C3×D3—62no—
664C3×D3—121no—
665#41—184no—
666#41—184no—
667C2×Q8—91no—
668C2×Q8—91no—
669C2×D4—91no—
670C2×D4—91no—
671C2×D4—91no—
672C2×D4—91no—
673C2×D4—91no—
674C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
675C22×C4—91no—
676C22×C4—91no—
677C22×C4—91no—
678C22×C4—91no—
679C22×C4—91no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
683C4⋊C4—91no—
684C4⋊C4—91no—
685C4⋊C4—91no—
686C4⋊C4—91no—
687C4⋊C4—91no—
688C4⋊C4—91no—
689C4⋊C4—91no—
690C4⋊C4—91no—
691C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
692C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
693C22⋊C4—91no—
694C22⋊C4—91no—
695C22⋊C4—91no—
696C22⋊C4—91no—
697C22⋊C4—91no—
698C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
699C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
700C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
701C42—91no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—31no—
708C22×C3—31no—
709C22×C3—32no—
710C22×C3—32no—
711C22×C3—61no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—62no—
723C22×C3—92no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—181no—
730C22×C3—181no—
731C22×C3—181no—
732C22×C3—181no—
733C22×C3—181no—
734C22×C3C3×D3×D412yes—
735C22×C3C23×C3×D311yescharacteristic
736C2×D3—32no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—92no—
743C2×D3—181no—
744C2×D3—181no—
745C2×D3—181no—
746C2×D3—181no—
747C2×D3—181no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—61no—
754C3×C4—61no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—61no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—61no—
761C3×C4—61no—
762C3×C4—61no—
763C3×C4—92no—
764C3×C4—92no—
765C3×C4—121no—
766C3×C4—121no—
767C3×C4—121no—
768C3×C4—121no—
769C3×C4—121no—
770C3×C4—181no—
771C3×C4—181no—
772C3×C4—181no—
773C3×C4—181no—
774Dic3—32no—
775Dic3—32no—
776Dic3—61no—
777Dic3—61no—
778Dic3—61no—
779Dic3—61no—
780Dic3—92no—
781Dic3—92no—
782Dic3—181no—
783Dic3—181no—
784Dic3—181no—
785Dic3—181no—
786C32—21no—
787C32#565511yescharacteristic, complemented
788C32C3×#54711yescharacteristic, complemented
789C23—91no—
790C23—91no—
791C23C22×(C3⋊D3)⋊C311yescharacteristic
792C23C22×(C3⋊D3)⋊C311yescharacteristic
793Q8—182no—
794Q8—182no—
795D4—22no—
796D4—94no—
797D4—182no—
798D4—182no—
799D4—182no—
800D4—182no—
801C2×C4—22no—
802C2×C4—91no—
803C2×C4—91no—
804C2×C4—91no—
805C2×C4—91no—
806C2×C4—91no—
807C2×C4—91no—
808C2×C4—182no—
809C2×C4—182no—
810C2×C4—182no—
811C2×C4—182no—
812C2×C4—182no—
813C2×C4—182no—
814C2×C4—182no—
815C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
816C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
817C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
818C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
819C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
820C2×C3—22no—
821C2×C3—31no—
822C2×C3—31no—
823C2×C3—31no—
824C2×C3—31no—
825C2×C3—31no—
826C2×C3—31no—
827C2×C3—41no—
828C2×C3—62no—
829C2×C3—62no—
830C2×C3—61no—
831C2×C3—61no—
832C2×C3—61no—
833C2×C3—122no—
834C2×C3—121no—
835C2×C3—121no—
836C2×C3—182no—
837C2×C3—241no—
838C2×C3—361no—
839C2×C3C2×C3×D3×D411yescharacteristic
840C2×C3C3×D3×#4111yescharacteristic
841C2×C3C3×#101011yescharacteristic
842D3—62no—
843D3—121no—
844D3—182no—
845D3—361no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—92no—
852C22—181no—
853C22—181no—
854C22—181no—
855C22—181no—
856C22—181no—
857C22D4×(C3⋊D3)⋊C312yes—
858C22C23×(C3⋊D3)⋊C311yescharacteristic
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—92no—
865C4—92no—
866C4—181no—
867C4—181no—
868C4—181no—
869C4—181no—
870C3—31no—
871C3—31no—
872C3—61no—
873C3C3×#565511yescharacteristic
874C2—22no—
875C2—41no—
876C2—182no—
877C2—361no—
878C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
879C2#41×(C3⋊D3)⋊C311yescharacteristic
880C2#1172263911yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#123C2
hypercenter#123(C3⋊D3)⋊C3
hypocenterC32C3×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#3830⋊C3C2semidirect
2. C2×#3828⋊C3C2semidirect
3. H(3,𝔽3)×#123C2semidirect
4. #64148⋊C3C2semidirect
5. C2×#3750⋊C3C2semidirect
6. #64105⋊C3C2semidirect
7. #64103⋊C3C2semidirect
8. C4⋊C4×(C3⋊D3)⋊C3C2semidirect
9. #64097⋊C3C2semidirect
10. #64095⋊C3C2semidirect
11. #64093⋊C3C2semidirect
12. #64092⋊C3C2semidirect
13. #64090⋊C3C2semidirect
14. #64090⋊C3C2semidirect
15. #64087⋊C3C2semidirect
16. #10596126C3semidirect
55. C2×#3830C2×C3semidirect
56. C2×#3828C2×C3semidirect
60. C32×#123D3semidirect
61. C32×#123C2×C3semidirect
62. #64148C2×C3semidirect
63. C2×#3750C2×C3semidirect
64. #64105C2×C3semidirect
65. #64103C2×C3semidirect
66. C4⋊C4×C3⋊D3C2×C3semidirect
67. #64097C2×C3semidirect
68. #64095C2×C3semidirect
69. #64093C2×C3semidirect
70. #64092C2×C3semidirect
71. #64090C2×C3semidirect
72. #64090C2×C3semidirect
73. #64087C2×C3semidirect
100. #638⋊C3D4semidirect
224. (C3⋊Dic3)⋊C3#41semidirect
305. #638C3×D4semidirect
521. C3⋊Dic3C3×#41semidirect
534. #123(C3⋊D3)⋊C3semidirect
543. H(3,𝔽3)#547semidirect
787. C32#5655semidirect
788. C32C3×#547semidirect

Maximal subgroups

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

subgroupindex
C2×#3830⋊C32
C2×#3828⋊C32
H(3,𝔽3)×#1232
#64148⋊C32
C2×#3750⋊C32
#64105⋊C32
#64103⋊C32
C4⋊C4×(C3⋊D3)⋊C32
#64097⋊C32
#64095⋊C32
#64093⋊C32
#64092⋊C32
#64090⋊C32
#64087⋊C32
#105961263
C3×#56553