Finite Group Databasebeta

← C107×#25389 #41051353

Subgroups — C107×#25389 #41051353

Order 27392.

1052 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#467×C107C211yesmaximal, characteristic, complemented
2C2×#465×C107C211yesmaximal, characteristic, complemented
3C2×#464×C107C211yesmaximal, characteristic, complemented
4C2×C8×D4×C107C211yesmaximal, characteristic, complemented
5C107×#2540C211yesmaximal, characteristic
6C107×#2536C211yesmaximal, characteristic, complemented
7C107×#2035C211yesmaximal, characteristic, complemented
8C107×#2033C211yesmaximal, characteristic, complemented
9C107×#2001C211yesmaximal, characteristic, complemented
10C107×#2000C211yesmaximal, characteristic, complemented
11C107×#1958C211yesmaximal, characteristic, complemented
12C107×#1949C211yesmaximal, characteristic, complemented
13C107×#1893C211yesmaximal, characteristic, complemented
14C107×#1892C211yesmaximal, characteristic, complemented
15C4×#103×C107C211yesmaximal, characteristic, complemented
16C22×Q16×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C23×C8×C107C2211yescharacteristic
19C23×C8×C107C2211yescharacteristic
20C2×#124×C107C2211yescharacteristic
21C2×C22⋊Q8×C107C2211yescharacteristic
22C2×C22⋊Q8×C107C2211yescharacteristic
23C2×C22⋊Q8×C107C2211yescharacteristic
24C2×C22⋊Q8×C107C2211yescharacteristic
25C2×#121×C107C2211yescharacteristic
26C2×#121×C107C2211yescharacteristic
27C2×C4×Q8×C107C2211yescharacteristic
28C2×C4×D4×C107C2211yescharacteristic
29#467×C107—24no—
30#465×C107—24no—
31#464×C107—24no—
32C8×D4×C107—24no—
33C2×#107×C107C2211yescharacteristic
34C2×#106×C107C2211yescharacteristic
35C2×C4⋊C8×C107C2211yescharacteristic
36C2×#103×C107C2211yescharacteristic
37C2×#103×C107C2211yescharacteristic
38C2×#103×C107C2211yescharacteristic
39C2×#103×C107C2211yescharacteristic
40C2×#103×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×#102×C107C2211yescharacteristic
44C2×C22⋊C8×C107C2211yescharacteristic
45C2×C22⋊C8×C107C2211yescharacteristic
46C2×C4×C8×C107C2211yescharacteristic
47#399×C107—21no—
48#398×C107—21no—
49#394×C107—21no—
50#392×C107—21no—
51#390×C107—21no—
52#390×C107—21no—
53#388×C107—21no—
54#388×C107—21no—
55#382×C107C2211yescharacteristic
56#380×C107C2211yescharacteristic
57#380×C107C2211yescharacteristic
58C4×C4⋊C4×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic
60#340×C107C2211yescharacteristic
61#340×C107C2211yescharacteristic
62#340×C107C2211yescharacteristic
63C22×Q8×C107C2311yescharacteristic
64C22×Q8×C107C2311yescharacteristic
65C22×D4×C107—21no—
66C22×D4×C107—21no—
67C22×D4×C107D411yescharacteristic
68C22×D4×C107C2311yescharacteristic
69C23×C4×C107C2311yescharacteristic
70C23×C4×C107C2311yescharacteristic
71C2×Q16×C107—22no—
72C2×Q16×C107—22no—
73C2×Q16×C107—41no—
74C2×SD16×C107—22no—
75C2×SD16×C107—22no—
76C2×SD16×C107—41no—
77C22×C8×C107—22no—
78C22×C8×C107—22no—
79C22×C8×C107—22no—
80C22×C8×C107—22no—
81C22×C8×C107—41no—
82C22×C8×C107—41no—
83C22×C8×C107C2311yescharacteristic
84C22×C8×C107C2311yescharacteristic
85C22×C8×C107C2311yescharacteristic
86C22×C8×C107C2311yescharacteristic
87#124×C107—22no—
88#124×C107—22no—
89C22⋊Q8×C107—22no—
90C22⋊Q8×C107—22no—
91C22⋊Q8×C107—22no—
92C22⋊Q8×C107—22no—
93C22⋊Q8×C107—41no—
94C22⋊Q8×C107—41no—
95C22⋊Q8×C107—41no—
96C22⋊Q8×C107—41no—
97#121×C107—22no—
98#121×C107—22no—
99#121×C107—41no—
100#121×C107—41no—
101C4×Q8×C107—22no—
102C4×Q8×C107—22no—
103C4×D4×C107—22no—
104C4×D4×C107—22no—
105C2×C4⋊C4×C107—21no—
106C2×C4⋊C4×C107—21no—
107C2×C4⋊C4×C107—21no—
108C2×C4⋊C4×C107—21no—
109C2×C4⋊C4×C107—21no—
110C2×C4⋊C4×C107D411yescharacteristic
111C2×C4⋊C4×C107C2311yescharacteristic
112C2×C4⋊C4×C107C2311yescharacteristic
113C2×C4⋊C4×C107C2311yescharacteristic
114C2×C4⋊C4×C107C2311yescharacteristic
115C2×C4⋊C4×C107C2311yescharacteristic
116C2×C22⋊C4×C107—21no—
117C2×C22⋊C4×C107—21no—
118C2×C22⋊C4×C107—21no—
119C2×C22⋊C4×C107—21no—
120C2×C22⋊C4×C107—21no—
121C2×C22⋊C4×C107—21no—
122C2×C22⋊C4×C107—21no—
123C2×C22⋊C4×C107—21no—
124C2×C22⋊C4×C107—21no—
125C2×C22⋊C4×C107—21no—
126C2×C22⋊C4×C107D411yescharacteristic
127C2×C22⋊C4×C107D411yescharacteristic
128C2×C42×C107—21no—
129C2×C42×C107—21no—
130C2×C42×C107C2311yescharacteristic
131#107×C107—22no—
132#106×C107—22no—
133C4⋊C8×C107D414yescomplemented
134#103×C107—22no—
135#103×C107—22no—
136#103×C107—22no—
137#103×C107—41no—
138#103×C107D414yescomplemented
139#102×C107—22no—
140#102×C107—22no—
141#102×C107—41no—
142C22⋊C8×C107—22no—
143C22⋊C8×C107—22no—
144C4×C8×C107—22no—
145#95×C107—21no—
146#95×C107—21no—
147#95×C107—21no—
148#95×C107—21no—
149#95×C107—21no—
150C24×C107—21no—
151C24×C107C2×D411yescharacteristic
152C24×C107C2×D411yescharacteristic
153C2×Q8×C107—21no—
154C2×Q8×C107—21no—
155C2×Q8×C107—21no—
156C2×Q8×C107—21no—
157C2×Q8×C107—21no—
158C2×Q8×C107—21no—
159C2×Q8×C107—21no—
160C2×Q8×C107—21no—
161C2×Q8×C107—21no—
162C2×Q8×C107—21no—
163C2×Q8×C107—21no—
164C2×Q8×C107C2×D412yes—
165C2×D4×C107—22no—
166C2×D4×C107—22no—
167C2×D4×C107—22no—
168C2×D4×C107—21no—
169C2×D4×C107—21no—
170C2×D4×C107—21no—
171C2×D4×C107—21no—
172C2×D4×C107—21no—
173C2×D4×C107—21no—
174C2×D4×C107—42no—
175C2×D4×C107—42no—
176C2×D4×C107—42no—
177C2×D4×C107—42no—
178C2×D4×C107—81no—
179C2×D4×C107—81no—
180C22×C4×C107—21no—
181C22×C4×C107—21no—
182C22×C4×C107—21no—
183C22×C4×C107—21no—
184C22×C4×C107—21no—
185C22×C4×C107—21no—
186C22×C4×C107—21no—
187C22×C4×C107—21no—
188C22×C4×C107—21no—
189C22×C4×C107—21no—
190C22×C4×C107—21no—
191C22×C4×C107—21no—
192C22×C4×C107—21no—
193C22×C4×C107—21no—
194C22×C4×C107—21no—
195C22×C4×C107—21no—
196C22×C4×C107—21no—
197C22×C4×C107—21no—
198C22×C4×C107—21no—
199C22×C4×C107C2×D411yescharacteristic
200C22×C4×C107C2×D411yescharacteristic
201C22×C4×C107C2×D411yescharacteristic
202C22×C4×C107C2×D411yescharacteristic
203C22×C4×C107C2411yescharacteristic
204Q16×C107—44no—
205SD16×C107—44no—
206C2×C8×C107—21no—
207C2×C8×C107—21no—
208C2×C8×C107—21no—
209C2×C8×C107—21no—
210C2×C8×C107—21no—
211C2×C8×C107—21no—
212C2×C8×C107—21no—
213C2×C8×C107—21no—
214C2×C8×C107—21no—
215C2×C8×C107—44no—
216C2×C8×C107—44no—
217C2×C8×C107C2×D412yes—
218C2×C8×C107C2×D412yes—
219C2×C8×C107C2×D412yes—
220C4⋊C4×C107—22no—
221C4⋊C4×C107—21no—
222C4⋊C4×C107—21no—
223C4⋊C4×C107—21no—
224C4⋊C4×C107—21no—
225C4⋊C4×C107—21no—
226C4⋊C4×C107—21no—
227C4⋊C4×C107—21no—
228C4⋊C4×C107—21no—
229C4⋊C4×C107—42no—
230C4⋊C4×C107—42no—
231C4⋊C4×C107—42no—
232C4⋊C4×C107—42no—
233C4⋊C4×C107—42no—
234C4⋊C4×C107C2×D412yes—
235C4⋊C4×C107#4112yes—
236C22⋊C4×C107—22no—
237C22⋊C4×C107—22no—
238C22⋊C4×C107—42no—
239C22⋊C4×C107—42no—
240C22⋊C4×C107—42no—
241C22⋊C4×C107—42no—
242C22⋊C4×C107—42no—
243C22⋊C4×C107—42no—
244C22⋊C4×C107—42no—
245C22⋊C4×C107—42no—
246C22⋊C4×C107—42no—
247C22⋊C4×C107—42no—
248C42×C107—42no—
249C42×C107—81no—
250C42×C107C2×D412yes—
251C42×C107#4112yes—
252C23×C107—21no—
253C23×C107—21no—
254C23×C107—21no—
255C23×C107—21no—
256C23×C107—21no—
257C23×C107—21no—
258C23×C107—21no—
259C23×C107—21no—
260C23×C107—21no—
261C23×C107—21no—
262C23×C107—21no—
263C23×C107—21no—
264C23×C107—41no—
265C23×C107—41no—
266C23×C107—41no—
267C23×C107—41no—
268C23×C107—41no—
269C23×C107—41no—
270C23×C107—41no—
271C23×C107#13512yes—
272C23×C107#13512yes—
273C23×C107C22×D411yescharacteristic
274Q8×C107—22no—
275Q8×C107—22no—
276Q8×C107—41no—
277Q8×C107—41no—
278Q8×C107—41no—
279Q8×C107—41no—
280Q8×C107—41no—
281Q8×C107—41no—
282D4×C107—28no—
283D4×C107—41no—
284D4×C107—41no—
285D4×C107—41no—
286D4×C107—41no—
287D4×C107—84no—
288D4×C107—84no—
289C2×C4×C107—21no—
290C2×C4×C107—21no—
291C2×C4×C107—21no—
292C2×C4×C107—21no—
293C2×C4×C107—21no—
294C2×C4×C107—21no—
295C2×C4×C107—22no—
296C2×C4×C107—21no—
297C2×C4×C107—22no—
298C2×C4×C107—21no—
299C2×C4×C107—22no—
300C2×C4×C107—21no—
301C2×C4×C107—21no—
302C2×C4×C107—41no—
303C2×C4×C107—41no—
304C2×C4×C107—41no—
305C2×C4×C107—41no—
306C2×C4×C107—41no—
307C2×C4×C107—41no—
308C2×C4×C107—41no—
309C2×C4×C107—41no—
310C2×C4×C107—41no—
311C2×C4×C107—41no—
312C2×C4×C107—41no—
313C2×C4×C107—41no—
314C2×C4×C107—41no—
315C2×C4×C107—41no—
316C2×C4×C107—41no—
317C2×C4×C107—41no—
318C2×C4×C107—41no—
319C2×C4×C107—41no—
320C2×C4×C107—41no—
321C2×C4×C107—41no—
322C2×C4×C107—41no—
323C2×C4×C107—41no—
324C2×C4×C107—41no—
325C2×C4×C107—41no—
326C2×C4×C107—41no—
327C2×C4×C107—41no—
328C2×C4×C107#12112yes—
329C2×C4×C107#12112yes—
330C2×C4×C107C22×D411yescharacteristic
331C2×C4×C107C22×D411yescharacteristic
332C2×C4×C107C2×#4111yescharacteristic
333C2×C4×C107C2×#4111yescharacteristic
334C2×C4×C107H(5,𝔽2)11yescharacteristic
335C2×C4×C107H(5,𝔽2)11yescharacteristic
336C8×C107—22no—
337C8×C107—22no—
338C8×C107—22no—
339C8×C107—41no—
340C22×C107—22no—
341C22×C107—22no—
342C22×C107—22no—
343C22×C107—22no—
344C22×C107—22no—
345C22×C107—22no—
346C22×C107—41no—
347C22×C107—41no—
348C22×C107—41no—
349C22×C107—41no—
350C22×C107—41no—
351C22×C107—41no—
352C22×C107—41no—
353C22×C107—41no—
354C22×C107—81no—
355C22×C107—81no—
356C22×C107—81no—
357C22×C107—81no—
358C22×C107—81no—
359C22×C107—81no—
360C22×C107—81no—
361C22×C107C2×#12111yescharacteristic
362C22×C107D4211yescharacteristic
363C22×C107#54611yescharacteristic
364C22×C107C2×#13511yescharacteristic
365C22×C107C2×#13511yescharacteristic
366C22×C107#57711yescharacteristic
367C22×C107#57811yescharacteristic
368C4×C107—22no—
369C4×C107—22no—
370C4×C107—41no—
371C4×C107—41no—
372C4×C107—42no—
373C4×C107—42no—
374C4×C107—42no—
375C4×C107—81no—
376C4×C107—81no—
377C4×C107—81no—
378C4×C107—81no—
379C4×C107#53211yescharacteristic
380C4×C107#54011yescharacteristic
381C4×C107D4211yescharacteristic
382C4×C107#55011yescharacteristic
383#25389C10711yesmaximal, characteristic, direct product factor, Sylow
384C2×C107—42no—
385C2×C107—42no—
386C2×C107—161no—
387C2×C107#242811yescharacteristic
388C2×C107#305011yescharacteristic
389C2×C107#306311yescharacteristic
390C2×C107#328211yescharacteristic
391C2×C107#328511yescharacteristic
392C2×C107#329611yescharacteristic
393C2×C107#330011yescharacteristic
394C2×#467C2×C10711yescharacteristic, complemented
395C2×#465C2×C10711yescharacteristic, complemented
396C2×#464C2×C10711yescharacteristic, complemented
397C2×C8×D4C2×C10711yescharacteristic, complemented
398#2540C2×C10711yescharacteristic
399#2536C2×C10711yescharacteristic, complemented
400#2035C2×C10711yescharacteristic, complemented
401#2033C2×C10711yescharacteristic, complemented
402#2001C2×C10711yescharacteristic, complemented
403#2000C2×C10711yescharacteristic, complemented
404#1958C2×C10711yescharacteristic, complemented
405#1949C2×C10711yescharacteristic, complemented
406#1893C2×C10711yescharacteristic, complemented
407#1892C2×C10711yescharacteristic, complemented
408C4×#103C2×C10711yescharacteristic, complemented
409C107#2538911yescharacteristic, direct product factor, Sylow
410C22×Q16C22×C10711yescharacteristic
411C22×SD16C22×C10711yescharacteristic
412C23×C8C22×C10711yescharacteristic
413C23×C8C22×C10711yescharacteristic
414C2×#124C22×C10711yescharacteristic
415C2×C22⋊Q8C22×C10711yescharacteristic
416C2×C22⋊Q8C22×C10711yescharacteristic
417C2×C22⋊Q8C22×C10711yescharacteristic
418C2×C22⋊Q8C22×C10711yescharacteristic
419C2×#121C22×C10711yescharacteristic
420C2×#121C22×C10711yescharacteristic
421C2×C4×Q8C22×C10711yescharacteristic
422C2×C4×D4C22×C10711yescharacteristic
423#467—24no—
424#465—24no—
425#464—24no—
426C8×D4—24no—
427C2×#107C22×C10711yescharacteristic
428C2×#106C22×C10711yescharacteristic
429C2×C4⋊C8C22×C10711yescharacteristic
430C2×#103C22×C10711yescharacteristic
431C2×#103C22×C10711yescharacteristic
432C2×#103C22×C10711yescharacteristic
433C2×#103C22×C10711yescharacteristic
434C2×#103C22×C10711yescharacteristic
435C2×#102C22×C10711yescharacteristic
436C2×#102C22×C10711yescharacteristic
437C2×#102C22×C10711yescharacteristic
438C2×C22⋊C8C22×C10711yescharacteristic
439C2×C22⋊C8C22×C10711yescharacteristic
440C2×C4×C8C22×C10711yescharacteristic
441#399—21no—
442#398—21no—
443#394—21no—
444#392—21no—
445#390—21no—
446#390—21no—
447#388—21no—
448#388—21no—
449#382C22×C10711yescharacteristic
450#380C22×C10711yescharacteristic
451#380C22×C10711yescharacteristic
452C4×C4⋊C4C22×C10711yescharacteristic
453#340C22×C10711yescharacteristic
454#340C22×C10711yescharacteristic
455#340C22×C10711yescharacteristic
456#340C22×C10711yescharacteristic
457C22×Q8C23×C10711yescharacteristic
458C22×Q8C23×C10711yescharacteristic
459C22×D4—21no—
460C22×D4—21no—
461C22×D4D4×C10711yescharacteristic
462C22×D4C23×C10711yescharacteristic
463C23×C4C23×C10711yescharacteristic
464C23×C4C23×C10711yescharacteristic
465C2×Q16—22no—
466C2×Q16—22no—
467C2×Q16—41no—
468C2×SD16—22no—
469C2×SD16—22no—
470C2×SD16—41no—
471C22×C8—22no—
472C22×C8—22no—
473C22×C8—22no—
474C22×C8—22no—
475C22×C8—41no—
476C22×C8—41no—
477C22×C8C23×C10711yescharacteristic
478C22×C8C23×C10711yescharacteristic
479C22×C8C23×C10711yescharacteristic
480C22×C8C23×C10711yescharacteristic
481#124—22no—
482#124—22no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—41no—
488C22⋊Q8—41no—
489C22⋊Q8—41no—
490C22⋊Q8—41no—
491#121—22no—
492#121—22no—
493#121—41no—
494#121—41no—
495C4×Q8—22no—
496C4×Q8—22no—
497C4×D4—22no—
498C4×D4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4D4×C10711yescharacteristic
505C2×C4⋊C4C23×C10711yescharacteristic
506C2×C4⋊C4C23×C10711yescharacteristic
507C2×C4⋊C4C23×C10711yescharacteristic
508C2×C4⋊C4C23×C10711yescharacteristic
509C2×C4⋊C4C23×C10711yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4D4×C10711yescharacteristic
521C2×C22⋊C4D4×C10711yescharacteristic
522C2×C42—21no—
523C2×C42—21no—
524C2×C42C23×C10711yescharacteristic
525#107—22no—
526#106—22no—
527C4⋊C8D4×C10714yescomplemented
528#103—22no—
529#103—22no—
530#103—22no—
531#103—41no—
532#103D4×C10714yescomplemented
533#102—22no—
534#102—22no—
535#102—41no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C4×C8—22no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C24—21no—
545C24C2×D4×C10711yescharacteristic
546C24C2×D4×C10711yescharacteristic
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8C2×D4×C10712yes—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—81no—
573C2×D4—81no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4C2×D4×C10711yescharacteristic
594C22×C4C2×D4×C10711yescharacteristic
595C22×C4C2×D4×C10711yescharacteristic
596C22×C4C2×D4×C10711yescharacteristic
597C22×C4C24×C10711yescharacteristic
598Q16—44no—
599SD16—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—44no—
610C2×C8—44no—
611C2×C8C2×D4×C10712yes—
612C2×C8C2×D4×C10712yes—
613C2×C8C2×D4×C10712yes—
614C4⋊C4—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4C2×D4×C10712yes—
629C4⋊C4#41×C10712yes—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C42—42no—
643C42—81no—
644C42C2×D4×C10712yes—
645C42#41×C10712yes—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23#135×C10712yes—
666C23#135×C10712yes—
667C23C22×D4×C10711yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676D4—28no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—84no—
682D4—84no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4#121×C10712yes—
723C2×C4#121×C10712yes—
724C2×C4C22×D4×C10711yescharacteristic
725C2×C4C22×D4×C10711yescharacteristic
726C2×C4C2×#41×C10711yescharacteristic
727C2×C4C2×#41×C10711yescharacteristic
728C2×C4H(5,𝔽2)×C10711yescharacteristic
729C2×C4H(5,𝔽2)×C10711yescharacteristic
730C8—22no—
731C8—22no—
732C8—22no—
733C8—41no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22C2×#121×C10711yescharacteristic
756C22D42×C10711yescharacteristic
757C22#546×C10711yescharacteristic
758C22C2×#135×C10711yescharacteristic
759C22C2×#135×C10711yescharacteristic
760C22#577×C10711yescharacteristic
761C22#578×C10711yescharacteristic
762C4—22no—
763C4—22no—
764C4—41no—
765C4—41no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—81no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4#532×C10711yescharacteristic
774C4#540×C10711yescharacteristic
775C4D42×C10711yescharacteristic
776C4#550×C10711yescharacteristic
777C2—42no—
778C2—42no—
779C2—161no—
780C2C107×#242811yescharacteristic
781C2C107×#305011yescharacteristic
782C2C107×#306311yescharacteristic
783C2C107×#328211yescharacteristic
784C2C107×#328511yescharacteristic
785C2C107×#329611yescharacteristic
786C2C107×#330011yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#2540C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C4×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#467×C107C2semidirect
2. C2×#465×C107C2semidirect
3. C2×#464×C107C2semidirect
4. C2×C8×D4×C107C2semidirect
6. C107×#2536C2semidirect
7. C107×#2035C2semidirect
8. C107×#2033C2semidirect
9. C107×#2001C2semidirect
10. C107×#2000C2semidirect
11. C107×#1958C2semidirect
12. C107×#1949C2semidirect
13. C107×#1893C2semidirect
14. C107×#1892C2semidirect
15. C4×#103×C107C2semidirect
133. C4⋊C8×C107D4semidirect
138. #103×C107D4semidirect
383. #25389C107direct (N × H)
394. C2×#467C2×C107semidirect
395. C2×#465C2×C107semidirect
396. C2×#464C2×C107semidirect
397. C2×C8×D4C2×C107semidirect
399. #2536C2×C107semidirect
400. #2035C2×C107semidirect
401. #2033C2×C107semidirect
402. #2001C2×C107semidirect
403. #2000C2×C107semidirect
404. #1958C2×C107semidirect
405. #1949C2×C107semidirect
406. #1893C2×C107semidirect
407. #1892C2×C107semidirect
408. C4×#103C2×C107semidirect
409. C107#25389direct (N × H)
527. C4⋊C8D4×C107semidirect
532. #103D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#467×C1072
C2×#465×C1072
C2×#464×C1072
C2×C8×D4×C1072
C107×#25402
C107×#25362
C107×#20352
C107×#20332
C107×#20012
C107×#20002
C107×#19582
C107×#19492
C107×#18932
C107×#18922
C4×#103×C1072
#25389107