Finite Group Databasebeta

← C2×#33955 #7623921

Subgroups — C2×#33955 #7623921

Order 512.

1270 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3383C211yesmaximal, characteristic, complemented
2C2×#3380C211yesmaximal, characteristic
3#33955C2116yesmaximal, direct product factor
4C2×#2255C211yesmaximal, characteristic, complemented
5C2×#2255C211yesmaximal, characteristic, complemented
6C2×#2253C211yesmaximal, characteristic, complemented
7C2×#2229C211yesmaximal, characteristic, complemented
8C2×#2229C211yesmaximal, characteristic, complemented
9C2×#2225C211yesmaximal, characteristic, complemented
10C2×#2228C211yesmaximal, characteristic
11C2×#2228C211yesmaximal, characteristic
12C2×#2226C211yesmaximal, characteristic
13C2×#2183C211yesmaximal, characteristic, complemented
14C2×#2175C211yesmaximal, characteristic
15C2×#2175C211yesmaximal, characteristic
16C2×C4×SD32C211yesmaximal, characteristic
17C2×#557—21no—
18C2×#554—21no—
19C22×SD32C2211yescharacteristic
20#3383—24no—
21#3383C2218yescomplemented
22#3380—24no—
23#3380C2218yes—
24C2×#500C2211yescharacteristic
25C2×#500C2211yescharacteristic
26C2×#499C2211yescharacteristic
27C2×#499C2211yescharacteristic
28C2×#499C2211yescharacteristic
29C2×#499C2211yescharacteristic
30C2×#479—21no—
31C2×#479—21no—
32C2×#475—21no—
33C2×#478—21no—
34C2×#478—21no—
35C2×#476—21no—
36C2×C8×Q8C2211yescharacteristic
37C2×C4×Q16C2211yescharacteristic
38C2×C4×Q16C2211yescharacteristic
39C2×C4×Q16C2211yescharacteristic
40C2×C4×D8C2211yescharacteristic
41C2×C4×D8C2211yescharacteristic
42C2×C4×D8C2211yescharacteristic
43#2255C2218yescomplemented
44#2255C2218yescomplemented
45#2253C2218yescomplemented
46#2229C2218yescomplemented
47#2229C2218yescomplemented
48#2228C2218yes—
49#2228C2218yes—
50#2226C2218yes—
51#2225C2218yescomplemented
52#2183C2218yescomplemented
53#2175C2218yes—
54#2175C2218yes—
55C4×SD32C2218yes—
56C2×#367C2211yescharacteristic
57C2×#367C2211yescharacteristic
58C2×#367C2211yescharacteristic
59C2×#367C2211yescharacteristic
60C2×#367C2211yescharacteristic
61C2×#366C2211yescharacteristic
62C2×#366C2211yescharacteristic
63C2×#366C2211yescharacteristic
64C2×#366C2211yescharacteristic
65C2×C4⋊C16C2211yescharacteristic
66C2×C4⋊C16C2211yescharacteristic
67C2×C4⋊C16C2211yescharacteristic
68C2×#358C2211yescharacteristic
69C2×#358C2211yescharacteristic
70C2×#358C2211yescharacteristic
71C2×#357C2211yescharacteristic
72C2×#357C2211yescharacteristic
73C2×#357C2211yescharacteristic
74C2×#346C2211yescharacteristic
75C2×#346C2211yescharacteristic
76C2×C4×C16C2211yescharacteristic
77C22×Q16C2311yescharacteristic
78C22×D8C2311yescharacteristic
79#557—28no—
80#557—44no—
81#554—28no—
82#554—44no—
83C2×C4⋊Q8—21no—
84C2×C4⋊Q8—21no—
85C2×C4⋊Q8—41no—
86C2×#125—21no—
87C2×#125—21no—
88C2×#125—21no—
89C2×#125—21no—
90C2×#125—41no—
91C2×#125—41no—
92C2×C22⋊Q8—41no—
93C2×C22⋊Q8—41no—
94C2×C22⋊Q8—41no—
95C2×C4×Q8—21no—
96C2×C4×Q8—21no—
97C2×C4×Q8—21no—
98C2×C4×Q8—41no—
99C2×C4×Q8D411yescharacteristic
100C2×C4×D4—21no—
101C2×C4×D4—21no—
102C2×C4×D4—21no—
103C22×C4⋊C4—41no—
104C2×SD32Q818yescomplemented
105C2×SD32C2314yes—
106C22×C16C2311yescharacteristic
107C22×C16C2311yescharacteristic
108C22×C16C2311yescharacteristic
109C22×C16C2311yescharacteristic
110#500—22no—
111#500—22no—
112#500C2314yes—
113#500C2314yes—
114#499—22no—
115#499—22no—
116#499—22no—
117#499—22no—
118#499C2314yes—
119#499C2314yes—
120#499C2314yes—
121#499C2314yes—
122#479—28no—
123#479—28no—
124#478—28no—
125#478—28no—
126#476—28no—
127#475—28no—
128C8×Q8D414yes—
129C8×Q8C2314yes—
130C4×Q16—22no—
131C4×Q16—22no—
132C4×Q16—22no—
133C4×Q16C2314yes—
134C4×Q16C2314yes—
135C4×Q16C2314yes—
136C4×D8—22no—
137C4×D8—22no—
138C4×D8—22no—
139C4×D8C2314yes—
140C4×D8C2314yes—
141C4×D8C2314yes—
142C2×#107—21no—
143C2×#107—21no—
144C2×#107C2311yescharacteristic
145C2×#107C2311yescharacteristic
146C2×#107C2311yescharacteristic
147C2×#107C2311yescharacteristic
148C2×#107C2311yescharacteristic
149C2×#107C2311yescharacteristic
150C2×#106—21no—
151C2×#106—21no—
152C2×#106—21no—
153C2×#106—21no—
154C2×C4⋊C8D411yescharacteristic
155C2×C4⋊C8D411yescharacteristic
156C2×C4⋊C8D411yescharacteristic
157C2×#103—21no—
158C2×#103—21no—
159C2×#103—21no—
160C2×#102—21no—
161C2×#102—21no—
162C2×#102—21no—
163C2×C4×C8C2311yescharacteristic
164C2×C4×C8C2311yescharacteristic
165C2×C4×C8C2311yescharacteristic
166#367C2314yes—
167#367C2314yes—
168#367C2314yes—
169#367C2314yes—
170#367C2314yes—
171#366C2314yes—
172#366C2314yes—
173#366C2314yes—
174#366C2314yes—
175C4⋊C16C2314yes—
176C4⋊C16C2314yes—
177C4⋊C16C2314yes—
178#358C2314yes—
179#358C2314yes—
180#358C2314yes—
181#357C2314yes—
182#357C2314yes—
183#357C2314yes—
184#346C2314yes—
185#346C2314yes—
186C4×C16C2314yes—
187C22×Q8—21no—
188C22×Q8—41no—
189C22×Q8—41no—
190C22×Q8D811yescharacteristic
191C22×D4—21no—
192C23×C4—41no—
193C23×C4—41no—
194C23×C4—41no—
195C2×Q16—21no—
196C2×Q16—22no—
197C2×Q16C2×Q814yes—
198C2×Q16C2412yes—
199C2×D8—21no—
200C2×D8—22no—
201C2×D8C2×Q814yes—
202C2×D8C2412yes—
203C22×C8C2×D411yescharacteristic
204C22×C8C2×D411yescharacteristic
205C22×C8C2×D411yescharacteristic
206C22×C8C2411yescharacteristic
207C4⋊Q8—24no—
208C4⋊Q8—24no—
209C4⋊Q8—48no—
210C4⋊Q8—42no—
211C4⋊Q8—42no—
212#125—24no—
213#125—24no—
214#125—24no—
215#125—24no—
216#125—48no—
217#125—48no—
218#125—42no—
219#125—42no—
220#125—42no—
221#125—42no—
222C22⋊Q8—48no—
223C22⋊Q8—48no—
224C22⋊Q8—48no—
225C4×Q8—24no—
226C4×Q8—24no—
227C4×Q8—24no—
228C4×Q8—48no—
229C4×Q8—42no—
230C4×Q8—42no—
231C4×Q8—42no—
232C4×Q8D814yes—
233C4×Q8C2×D414yes—
234C4×D4—24no—
235C4×D4—24no—
236C4×D4—24no—
237C4×D4—42no—
238C4×D4—42no—
239C4×D4—42no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—41no—
247C2×C4⋊C4—41no—
248C2×C4⋊C4—41no—
249C2×C4⋊C4—41no—
250C2×C4⋊C4—41no—
251C2×C4⋊C4—41no—
252C2×C4⋊C4—41no—
253C2×C4⋊C4—41no—
254C2×C4⋊C4—41no—
255C2×C4⋊C4—41no—
256C2×C4⋊C4—41no—
257C2×C4⋊C4—41no—
258C2×C4⋊C4—41no—
259C2×C4⋊C4—48no—
260C2×C4⋊C4D811yescharacteristic
261C2×C4⋊C4D811yescharacteristic
262C2×C4⋊C4D811yescharacteristic
263C2×C22⋊C4—41no—
264C2×C22⋊C4—41no—
265C2×C22⋊C4—41no—
266C2×C42—41no—
267C2×C42—41no—
268C2×C42—41no—
269C2×C42C2×D411yescharacteristic
270C2×C42C2×D411yescharacteristic
271C2×C42C2×D411yescharacteristic
272SD32C2×Q8116yescomplemented
273C2×C16—22no—
274C2×C16—22no—
275C2×C16—22no—
276C2×C16C2×Q814yes—
277C2×C16C2412yes—
278C2×C16C2412yes—
279C2×C16C2412yes—
280C2×C16C2412yes—
281#107—24no—
282#107—24no—
283#107—21no—
284#107—21no—
285#107—21no—
286#107—21no—
287#107—21no—
288#107—21no—
289#107C2412yes—
290#107C2412yes—
291#107C2412yes—
292#107C2412yes—
293#107C2412yes—
294#107C2412yes—
295#106—24no—
296#106—24no—
297#106—24no—
298#106—24no—
299C4⋊C8C2×D414yes—
300C4⋊C8C2×D414yes—
301C4⋊C8C2×D414yes—
302#103—24no—
303#103—24no—
304#103—24no—
305#102—24no—
306#102—24no—
307#102—24no—
308C4×C8C2×D412yes—
309C4×C8C2×D412yes—
310C4×C8C2×D412yes—
311C4×C8C2412yes—
312C4×C8C2412yes—
313C4×C8C2412yes—
314C24—41no—
315C2×Q8—24no—
316C2×Q8—22no—
317C2×Q8—42no—
318C2×Q8—41no—
319C2×Q8—44no—
320C2×Q8—44no—
321C2×Q8—42no—
322C2×Q8—84no—
323C2×Q8—162no—
324C2×Q8C2×D814yes—
325C2×D4—24no—
326C2×D4—22no—
327C2×D4—41no—
328C2×D4—42no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—44no—
337C22×C4—44no—
338C22×C4—44no—
339C22×C4—84no—
340C22×C4—162no—
341C22×C4—162no—
342C22×C4C2×D811yescharacteristic
343C22×C4C2×D811yescharacteristic
344C22×C4C2×D811yescharacteristic
345C22×C4C2×D811yescharacteristic
346C22×C4C2×D811yescharacteristic
347C22×C4C2×D811yescharacteristic
348C22×C4C22×D411yescharacteristic
349Q16—24no—
350Q16—22no—
351Q16C22×Q814yes—
352D8—24no—
353D8—22no—
354D8C22×Q814yes—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8C22×D412yes—
359C2×C8C22×D412yes—
360C2×C8C22×D412yes—
361C2×C8C22×D411yescharacteristic
362C2×C8C22×Q812yes—
363C2×C82−1+412yes—
364C2×C8C2511yescharacteristic
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—44no—
378C4⋊C4—44no—
379C4⋊C4—44no—
380C4⋊C4—44no—
381C4⋊C4—44no—
382C4⋊C4—44no—
383C4⋊C4—44no—
384C4⋊C4—44no—
385C4⋊C4—44no—
386C4⋊C4—44no—
387C4⋊C4—44no—
388C4⋊C4—44no—
389C4⋊C4—44no—
390C4⋊C4C2×D814yes—
391C4⋊C4C2×D814yes—
392C4⋊C4C2×D814yes—
393C22⋊C4—44no—
394C22⋊C4—44no—
395C22⋊C4—44no—
396C42—44no—
397C42—44no—
398C42—44no—
399C42C2×D812yes—
400C42C2×D812yes—
401C42C2×D812yes—
402C42C22×D412yes—
403C42C22×D412yes—
404C42C22×D412yes—
405C16—22no—
406C16—22no—
407C16—22no—
408C16C22×Q814yes—
409C23—44no—
410C23—42no—
411C23—82no—
412C23—82no—
413C23C22×D811yescharacteristic
414Q8—24no—
415Q8—44no—
416Q8—44no—
417Q8—42no—
418Q8—88no—
419Q8—164no—
420D4—24no—
421D4—44no—
422D4—42no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—88no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—164no—
445C2×C4—164no—
446C2×C4D4×Q812yes—
447C2×C4C22×D812yes—
448C2×C4C22×D812yes—
449C2×C4C22×D812yes—
450C2×C4C22×D812yes—
451C2×C4C22×D812yes—
452C2×C4C22×D812yes—
453C2×C4C22×D811yescharacteristic
454C2×C4#57812yes—
455C2×C4C23×D411yescharacteristic
456C8—22no—
457C8—22no—
458C8—22no—
459C8D4×Q812yes—
460C8C23×Q811yescharacteristic
461C8C2×2−1+411yescharacteristic
462C22—44no—
463C22—88no—
464C22—82no—
465C22—82no—
466C22Q8×D812yes—
467C22#341412yes—
468C22#341612yes—
469C22C23×D811yescharacteristic
470C4—22no—
471C4—22no—
472C4—22no—
473C4—22no—
474C4—22no—
475C4—22no—
476C4—44no—
477C4—82no—
478C4—82no—
479C4—82no—
480C4—82no—
481C4—82no—
482C4—82no—
483C4Q8×D812yes—
484C4C2×D4×Q811yescharacteristic
485C4C2×#57811yescharacteristic
486C2—84no—
487C2#3395514yesdirect product factor
488C2C2×Q8×D811yescharacteristic
489C2C2×#341411yescharacteristic
490C2C2×#341611yescharacteristic
subgroupG/H
center, socleC23C22×D8
commutator, Frattini, cosocleC2×C8C25
prime radicalC22×D8C23
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3383C2semidirect
3. #33955C2direct (N × H)
4. C2×#2255C2semidirect
5. C2×#2255C2semidirect
6. C2×#2253C2semidirect
7. C2×#2229C2semidirect
8. C2×#2229C2semidirect
9. C2×#2225C2semidirect
13. C2×#2183C2semidirect
21. #3383C22semidirect
43. #2255C22semidirect
44. #2255C22semidirect
45. #2253C22semidirect
46. #2229C22semidirect
47. #2229C22semidirect
51. #2225C22semidirect
52. #2183C22semidirect
104. C2×SD32Q8semidirect
272. SD32C2×Q8semidirect
487. C2#33955direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#33832
C2×#33802
#339552
C2×#22552
C2×#22532
C2×#22292
C2×#22252
C2×#22282
C2×#22262
C2×#21832
C2×#21752
C2×C4×SD322