Finite Group Databasebeta

← C107×#23000 #41048964

Subgroups — C107×#23000 #41048964

Order 27392.

958 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#464×C107C211yesmaximal, characteristic
2C2×C4×Q16×C107C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C107C211yesmaximal, characteristic
4C107×#2367C211yesmaximal, characteristic
5C107×#2351C211yesmaximal, characteristic, complemented
6C107×#1958C211yesmaximal, characteristic
7C107×#1949C211yesmaximal, characteristic, complemented
8C107×#1934C211yesmaximal, characteristic
9C107×#1933C211yesmaximal, characteristic, complemented
10C107×#1880C211yesmaximal, characteristic
11C107×#1878C211yesmaximal, characteristic, complemented
12C107×#1865C211yesmaximal, characteristic, complemented
13C107×#1862C211yesmaximal, characteristic
14C8×C4⋊C4×C107C211yesmaximal, characteristic, complemented
15C4×#103×C107C211yesmaximal, characteristic, complemented
16C22×Q16×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C2×#124×C107C2211yescharacteristic
19C2×C4×Q8×C107C2211yescharacteristic
20C2×C4×Q8×C107C2211yescharacteristic
21C2×C4×Q8×C107C2211yescharacteristic
22C2×C4×Q8×C107C2211yescharacteristic
23C2×C4×D4×C107C2211yescharacteristic
24#464×C107C418yescomplemented
25C4×Q16×C107—24no—
26C4×SD16×C107—24no—
27C2×#107×C107C2211yescharacteristic
28C2×#106×C107C2211yescharacteristic
29C2×C4⋊C8×C107C2211yescharacteristic
30C2×#103×C107C2211yescharacteristic
31C2×#103×C107C2211yescharacteristic
32C2×#103×C107C2211yescharacteristic
33C2×#103×C107C2211yescharacteristic
34C2×#103×C107C2211yescharacteristic
35C2×#102×C107C2211yescharacteristic
36C2×#102×C107C2211yescharacteristic
37C2×#102×C107C2211yescharacteristic
38C2×C4×C8×C107C2211yescharacteristic
39C2×C4×C8×C107C2211yescharacteristic
40C2×C4×C8×C107C2211yescharacteristic
41#391×C107C2211yescharacteristic
42#390×C107C2211yescharacteristic
43#389×C107—21no—
44#389×C107—21no—
45#389×C107C2211yescharacteristic
46#389×C107C2211yescharacteristic
47#388×C107—21no—
48#388×C107—21no—
49#385×C107—21no—
50#382×C107—21no—
51#382×C107C2211yescharacteristic
52C4×C4⋊C4×C107—21no—
53C4×C4⋊C4×C107C2211yescharacteristic
54C4×C4⋊C4×C107C2211yescharacteristic
55C4×C22⋊C4×C107—21no—
56#340×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#340×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic
60#336×C107C2211yescharacteristic
61#336×C107C2211yescharacteristic
62C22×Q8×C107C2311yescharacteristic
63C22×Q8×C107C2311yescharacteristic
64C22×D4×C107C2311yescharacteristic
65C23×C4×C107—21no—
66C2×Q16×C107—22no—
67C2×Q16×C107—22no—
68C2×Q16×C107C2×C414yescomplemented
69C2×SD16×C107—22no—
70C2×SD16×C107—22no—
71C2×SD16×C107C2×C414yes—
72C22×C8×C107C2311yescharacteristic
73C22×C8×C107C2311yescharacteristic
74C22×C8×C107C2311yescharacteristic
75C22×C8×C107C2311yescharacteristic
76#124×C107—22no—
77#124×C107C2×C414yes—
78C4×Q8×C107—22no—
79C4×Q8×C107—22no—
80C4×Q8×C107—22no—
81C4×Q8×C107—22no—
82C4×Q8×C107—41no—
83C4×Q8×C107—41no—
84C4×Q8×C107—41no—
85C4×Q8×C107C2×C414yescomplemented
86C4×D4×C107—22no—
87C4×D4×C107—41no—
88C2×C4⋊C4×C107—21no—
89C2×C4⋊C4×C107—21no—
90C2×C4⋊C4×C107—21no—
91C2×C4⋊C4×C107—21no—
92C2×C4⋊C4×C107—21no—
93C2×C4⋊C4×C107—21no—
94C2×C4⋊C4×C107D411yescharacteristic
95C2×C4⋊C4×C107D411yescharacteristic
96C2×C4⋊C4×C107C2311yescharacteristic
97C2×C4⋊C4×C107C2311yescharacteristic
98C2×C4⋊C4×C107C2311yescharacteristic
99C2×C4⋊C4×C107C2311yescharacteristic
100C2×C4⋊C4×C107C2311yescharacteristic
101C2×C22⋊C4×C107—21no—
102C2×C22⋊C4×C107—21no—
103C2×C22⋊C4×C107—21no—
104C2×C22⋊C4×C107—21no—
105C2×C22⋊C4×C107—21no—
106C2×C42×C107—21no—
107C2×C42×C107—21no—
108C2×C42×C107—21no—
109C2×C42×C107—21no—
110C2×C42×C107—21no—
111C2×C42×C107C2311yescharacteristic
112C2×C42×C107C2311yescharacteristic
113C2×C42×C107C2311yescharacteristic
114#107×C107—22no—
115#106×C107—22no—
116C4⋊C8×C107C2×C414yescomplemented
117#103×C107—22no—
118#103×C107—22no—
119#103×C107—41no—
120#103×C107C2×C414yescomplemented
121#103×C107D414yes—
122#102×C107—22no—
123#102×C107—41no—
124#102×C107C2×C414yes—
125C4×C8×C107—22no—
126C4×C8×C107—22no—
127C4×C8×C107—22no—
128#95×C107—21no—
129#95×C107—21no—
130#95×C107—21no—
131#95×C107—21no—
132#95×C107—21no—
133#95×C107—21no—
134#95×C107—21no—
135#95×C107D411yescharacteristic
136#95×C107D411yescharacteristic
137C24×C107—21no—
138C2×Q8×C107—21no—
139C2×Q8×C107—21no—
140C2×Q8×C107—21no—
141C2×Q8×C107—21no—
142C2×Q8×C107—21no—
143C2×Q8×C107—21no—
144C2×Q8×C107—21no—
145C2×Q8×C107—21no—
146C2×Q8×C107C22×C412yes—
147C2×Q8×C107C22×C412yes—
148C2×Q8×C107C2×D412yes—
149C2×Q8×C107#4112yes—
150C2×D4×C107—21no—
151C2×D4×C107—21no—
152C2×D4×C107—21no—
153C2×D4×C107—21no—
154C2×D4×C107—21no—
155C2×D4×C107C22×C412yes—
156C22×C4×C107—21no—
157C22×C4×C107—21no—
158C22×C4×C107—21no—
159C22×C4×C107—21no—
160C22×C4×C107—21no—
161C22×C4×C107—21no—
162C22×C4×C107—21no—
163C22×C4×C107—42no—
164C22×C4×C107—42no—
165C22×C4×C107—81no—
166C22×C4×C107C2×D411yescharacteristic
167C22×C4×C107C2×D411yescharacteristic
168C22×C4×C107C2×D411yescharacteristic
169C22×C4×C107C2×D411yescharacteristic
170C22×C4×C107C2×D411yescharacteristic
171C22×C4×C107C2×D411yescharacteristic
172C22×C4×C107C2411yescharacteristic
173Q16×C107—28no—
174SD16×C107—28no—
175C2×C8×C107—21no—
176C2×C8×C107—21no—
177C2×C8×C107—21no—
178C2×C8×C107—21no—
179C2×C8×C107—21no—
180C2×C8×C107—21no—
181C2×C8×C107—21no—
182C2×C8×C107—21no—
183C2×C8×C107—21no—
184C2×C8×C107C22×C412yes—
185C2×C8×C107C22×C412yes—
186C2×C8×C107C2×D412yes—
187C4⋊C4×C107—24no—
188C4⋊C4×C107—22no—
189C4⋊C4×C107—22no—
190C4⋊C4×C107—21no—
191C4⋊C4×C107—21no—
192C4⋊C4×C107—21no—
193C4⋊C4×C107—21no—
194C4⋊C4×C107—21no—
195C4⋊C4×C107—21no—
196C4⋊C4×C107—21no—
197C4⋊C4×C107—21no—
198C4⋊C4×C107—42no—
199C4⋊C4×C107—42no—
200C4⋊C4×C107—42no—
201C4⋊C4×C107—42no—
202C4⋊C4×C107—42no—
203C4⋊C4×C107C22×C412yes—
204C4⋊C4×C107C2×D412yes—
205C22⋊C4×C107—24no—
206C22⋊C4×C107—24no—
207C22⋊C4×C107—42no—
208C22⋊C4×C107—42no—
209C22⋊C4×C107—81no—
210C42×C107—24no—
211C42×C107—21no—
212C42×C107—21no—
213C42×C107—21no—
214C42×C107—21no—
215C42×C107—42no—
216C42×C107—42no—
217C42×C107—42no—
218C42×C107—81no—
219C42×C107C22×C412yes—
220C42×C107#4112yes—
221C23×C107—22no—
222C23×C107—41no—
223C23×C107—41no—
224C23×C107—41no—
225C23×C107—41no—
226C23×C107—41no—
227C23×C107—41no—
228C23×C107C22×D411yescharacteristic
229Q8×C107—22no—
230Q8×C107—22no—
231Q8×C107—22no—
232Q8×C107—22no—
233Q8×C107—22no—
234Q8×C107—41no—
235Q8×C107—41no—
236Q8×C107C4×D414yes—
237D4×C107—22no—
238D4×C107—22no—
239D4×C107—41no—
240D4×C107—41no—
241C2×C4×C107—22no—
242C2×C4×C107—21no—
243C2×C4×C107—21no—
244C2×C4×C107—22no—
245C2×C4×C107—22no—
246C2×C4×C107—21no—
247C2×C4×C107—21no—
248C2×C4×C107—21no—
249C2×C4×C107—21no—
250C2×C4×C107—21no—
251C2×C4×C107—21no—
252C2×C4×C107—22no—
253C2×C4×C107—22no—
254C2×C4×C107—21no—
255C2×C4×C107—21no—
256C2×C4×C107—22no—
257C2×C4×C107—21no—
258C2×C4×C107—21no—
259C2×C4×C107—21no—
260C2×C4×C107—21no—
261C2×C4×C107—41no—
262C2×C4×C107—41no—
263C2×C4×C107—41no—
264C2×C4×C107—41no—
265C2×C4×C107—41no—
266C2×C4×C107—41no—
267C2×C4×C107—41no—
268C2×C4×C107—41no—
269C2×C4×C107—41no—
270C2×C4×C107—41no—
271C2×C4×C107—41no—
272C2×C4×C107—41no—
273C2×C4×C107—41no—
274C2×C4×C107—41no—
275C2×C4×C107—41no—
276C2×C4×C107—84no—
277C2×C4×C107C4×D412yes—
278C2×C4×C107C4×D412yes—
279C2×C4×C107#13512yes—
280C2×C4×C107#13512yes—
281C2×C4×C107C23×C411yescharacteristic
282C2×C4×C107C22×D411yescharacteristic
283C2×C4×C107C2×#4111yescharacteristic
284C2×C4×C107C2×#4111yescharacteristic
285C2×C4×C107H(5,𝔽2)11yescharacteristic
286C2×C4×C1072−1+411yescharacteristic
287C8×C107—22no—
288C8×C107—22no—
289C8×C107—22no—
290C8×C107—41no—
291C22×C107—42no—
292C22×C107—42no—
293C22×C107—42no—
294C22×C107—81no—
295C22×C107—81no—
296C22×C107—81no—
297C22×C107—81no—
298C22×C107C2×C4×D411yescharacteristic
299C22×C107D4211yescharacteristic
300C22×C107#54811yescharacteristic
301C22×C107C2×#13511yescharacteristic
302C22×C107C2×#13511yescharacteristic
303C22×C107#57711yescharacteristic
304C22×C107#57811yescharacteristic
305C4×C107—24no—
306C4×C107—22no—
307C4×C107—22no—
308C4×C107—22no—
309C4×C107—22no—
310C4×C107—42no—
311C4×C107—42no—
312C4×C107—41no—
313C4×C107—42no—
314C4×C107—41no—
315C4×C107—81no—
316C4×C107—81no—
317C4×C107—81no—
318C4×C107C2×C4×D411yescharacteristic
319C4×C107#52011yescharacteristic
320C4×C107#54711yescharacteristic
321C4×C107#55311yescharacteristic
322#23000C10711yesmaximal, characteristic, direct product factor, Sylow
323C2×C107—82no—
324C2×C107#236111yescharacteristic
325C2×C107C4×#13511yescharacteristic
326C2×C107#294711yescharacteristic
327C2×C107#328211yescharacteristic
328C2×C107#328511yescharacteristic
329C2×C107#336411yescharacteristic
330C2×C107#336511yescharacteristic
331C2×#464C2×C10711yescharacteristic
332C2×C4×Q16C2×C10711yescharacteristic, complemented
333C2×C4×SD16C2×C10711yescharacteristic
334#2367C2×C10711yescharacteristic
335#2351C2×C10711yescharacteristic, complemented
336#1958C2×C10711yescharacteristic
337#1949C2×C10711yescharacteristic, complemented
338#1934C2×C10711yescharacteristic
339#1933C2×C10711yescharacteristic, complemented
340#1880C2×C10711yescharacteristic
341#1878C2×C10711yescharacteristic, complemented
342#1865C2×C10711yescharacteristic, complemented
343#1862C2×C10711yescharacteristic
344C8×C4⋊C4C2×C10711yescharacteristic, complemented
345C4×#103C2×C10711yescharacteristic, complemented
346C107#2300011yescharacteristic, direct product factor, Sylow
347C22×Q16C22×C10711yescharacteristic
348C22×SD16C22×C10711yescharacteristic
349C2×#124C22×C10711yescharacteristic
350C2×C4×Q8C22×C10711yescharacteristic
351C2×C4×Q8C22×C10711yescharacteristic
352C2×C4×Q8C22×C10711yescharacteristic
353C2×C4×Q8C22×C10711yescharacteristic
354C2×C4×D4C22×C10711yescharacteristic
355#464C4×C10718yescomplemented
356C4×Q16—24no—
357C4×SD16—24no—
358C2×#107C22×C10711yescharacteristic
359C2×#106C22×C10711yescharacteristic
360C2×C4⋊C8C22×C10711yescharacteristic
361C2×#103C22×C10711yescharacteristic
362C2×#103C22×C10711yescharacteristic
363C2×#103C22×C10711yescharacteristic
364C2×#103C22×C10711yescharacteristic
365C2×#103C22×C10711yescharacteristic
366C2×#102C22×C10711yescharacteristic
367C2×#102C22×C10711yescharacteristic
368C2×#102C22×C10711yescharacteristic
369C2×C4×C8C22×C10711yescharacteristic
370C2×C4×C8C22×C10711yescharacteristic
371C2×C4×C8C22×C10711yescharacteristic
372#391C22×C10711yescharacteristic
373#390C22×C10711yescharacteristic
374#389—21no—
375#389—21no—
376#389C22×C10711yescharacteristic
377#389C22×C10711yescharacteristic
378#388—21no—
379#388—21no—
380#385—21no—
381#382—21no—
382#382C22×C10711yescharacteristic
383C4×C4⋊C4—21no—
384C4×C4⋊C4C22×C10711yescharacteristic
385C4×C4⋊C4C22×C10711yescharacteristic
386C4×C22⋊C4—21no—
387#340C22×C10711yescharacteristic
388#340C22×C10711yescharacteristic
389#340C22×C10711yescharacteristic
390#340C22×C10711yescharacteristic
391#336C22×C10711yescharacteristic
392#336C22×C10711yescharacteristic
393C22×Q8C23×C10711yescharacteristic
394C22×Q8C23×C10711yescharacteristic
395C22×D4C23×C10711yescharacteristic
396C23×C4—21no—
397C2×Q16—22no—
398C2×Q16—22no—
399C2×Q16C2×C4×C10714yescomplemented
400C2×SD16—22no—
401C2×SD16—22no—
402C2×SD16C2×C4×C10714yes—
403C22×C8C23×C10711yescharacteristic
404C22×C8C23×C10711yescharacteristic
405C22×C8C23×C10711yescharacteristic
406C22×C8C23×C10711yescharacteristic
407#124—22no—
408#124C2×C4×C10714yes—
409C4×Q8—22no—
410C4×Q8—22no—
411C4×Q8—22no—
412C4×Q8—22no—
413C4×Q8—41no—
414C4×Q8—41no—
415C4×Q8—41no—
416C4×Q8C2×C4×C10714yescomplemented
417C4×D4—22no—
418C4×D4—41no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4D4×C10711yescharacteristic
426C2×C4⋊C4D4×C10711yescharacteristic
427C2×C4⋊C4C23×C10711yescharacteristic
428C2×C4⋊C4C23×C10711yescharacteristic
429C2×C4⋊C4C23×C10711yescharacteristic
430C2×C4⋊C4C23×C10711yescharacteristic
431C2×C4⋊C4C23×C10711yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42C23×C10711yescharacteristic
443C2×C42C23×C10711yescharacteristic
444C2×C42C23×C10711yescharacteristic
445#107—22no—
446#106—22no—
447C4⋊C8C2×C4×C10714yescomplemented
448#103—22no—
449#103—22no—
450#103—41no—
451#103C2×C4×C10714yescomplemented
452#103D4×C10714yes—
453#102—22no—
454#102—41no—
455#102C2×C4×C10714yes—
456C4×C8—22no—
457C4×C8—22no—
458C4×C8—22no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95D4×C10711yescharacteristic
467#95D4×C10711yescharacteristic
468C24—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8C22×C4×C10712yes—
478C2×Q8C22×C4×C10712yes—
479C2×Q8C2×D4×C10712yes—
480C2×Q8#41×C10712yes—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4C22×C4×C10712yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—81no—
497C22×C4C2×D4×C10711yescharacteristic
498C22×C4C2×D4×C10711yescharacteristic
499C22×C4C2×D4×C10711yescharacteristic
500C22×C4C2×D4×C10711yescharacteristic
501C22×C4C2×D4×C10711yescharacteristic
502C22×C4C2×D4×C10711yescharacteristic
503C22×C4C24×C10711yescharacteristic
504Q16—28no—
505SD16—28no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8C22×C4×C10712yes—
516C2×C8C22×C4×C10712yes—
517C2×C8C2×D4×C10712yes—
518C4⋊C4—24no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4C22×C4×C10712yes—
535C4⋊C4C2×D4×C10712yes—
536C22⋊C4—24no—
537C22⋊C4—24no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—81no—
541C42—24no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—42no—
547C42—42no—
548C42—42no—
549C42—81no—
550C42C22×C4×C10712yes—
551C42#41×C10712yes—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23C22×D4×C10711yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—22no—
563Q8—22no—
564Q8—22no—
565Q8—41no—
566Q8—41no—
567Q8C4×D4×C10714yes—
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—84no—
608C2×C4C4×D4×C10712yes—
609C2×C4C4×D4×C10712yes—
610C2×C4#135×C10712yes—
611C2×C4#135×C10712yes—
612C2×C4C23×C4×C10711yescharacteristic
613C2×C4C22×D4×C10711yescharacteristic
614C2×C4C2×#41×C10711yescharacteristic
615C2×C4C2×#41×C10711yescharacteristic
616C2×C4H(5,𝔽2)×C10711yescharacteristic
617C2×C42−1+4×C10711yescharacteristic
618C8—22no—
619C8—22no—
620C8—22no—
621C8—41no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22C2×C4×D4×C10711yescharacteristic
630C22D42×C10711yescharacteristic
631C22#548×C10711yescharacteristic
632C22C2×#135×C10711yescharacteristic
633C22C2×#135×C10711yescharacteristic
634C22#577×C10711yescharacteristic
635C22#578×C10711yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—22no—
640C4—24no—
641C4—42no—
642C4—41no—
643C4—42no—
644C4—41no—
645C4—42no—
646C4—81no—
647C4—81no—
648C4—81no—
649C4C2×C4×D4×C10711yescharacteristic
650C4#520×C10711yescharacteristic
651C4#547×C10711yescharacteristic
652C4#553×C10711yescharacteristic
653C2—82no—
654C2C107×#236111yescharacteristic
655C2C4×#135×C10711yescharacteristic
656C2C107×#294711yescharacteristic
657C2C107×#328211yescharacteristic
658C2C107×#328511yescharacteristic
659C2C107×#336411yescharacteristic
660C2C107×#336511yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
prime radicalC22×D4×C107C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C4×C4⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q16×C107C2semidirect
5. C107×#2351C2semidirect
7. C107×#1949C2semidirect
9. C107×#1933C2semidirect
11. C107×#1878C2semidirect
12. C107×#1865C2semidirect
14. C8×C4⋊C4×C107C2semidirect
15. C4×#103×C107C2semidirect
24. #464×C107C4semidirect
68. C2×Q16×C107C2×C4semidirect
85. C4×Q8×C107C2×C4semidirect
116. C4⋊C8×C107C2×C4semidirect
120. #103×C107C2×C4semidirect
322. #23000C107direct (N × H)
332. C2×C4×Q16C2×C107semidirect
335. #2351C2×C107semidirect
337. #1949C2×C107semidirect
339. #1933C2×C107semidirect
341. #1878C2×C107semidirect
342. #1865C2×C107semidirect
344. C8×C4⋊C4C2×C107semidirect
345. C4×#103C2×C107semidirect
346. C107#23000direct (N × H)
355. #464C4×C107semidirect
399. C2×Q16C2×C4×C107semidirect
416. C4×Q8C2×C4×C107semidirect
447. C4⋊C8C2×C4×C107semidirect
451. #103C2×C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#464×C1072
C2×C4×Q16×C1072
C2×C4×SD16×C1072
C107×#23672
C107×#23512
C107×#19582
C107×#19492
C107×#19342
C107×#19332
C107×#18802
C107×#18782
C107×#18652
C107×#18622
C8×C4⋊C4×C1072
C4×#103×C1072
#23000107