Finite Group Databasebeta

← C103×#22059 #39927334

Subgroups — C103×#22059 #39927334

Order 26368.

968 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#452×C103C211yesmaximal, characteristic
2C103×#2323C211yesmaximal, characteristic, complemented
3C103×#2311C211yesmaximal, characteristic
4C103×#1971C211yesmaximal, characteristic, complemented
5C103×#1968C211yesmaximal, characteristic, complemented
6C103×#1936C211yesmaximal, characteristic, complemented
7C103×#1933C211yesmaximal, characteristic, complemented
8C103×#1927C211yesmaximal, characteristic, complemented
9C103×#1926C211yesmaximal, characteristic, complemented
10C103×#1880C211yesmaximal, characteristic, complemented
11C103×#1878C211yesmaximal, characteristic, complemented
12C103×#1872C211yesmaximal, characteristic, complemented
13C103×#1853C211yesmaximal, characteristic, complemented
14C103×#1788C211yesmaximal, characteristic
15C103×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C22×Q16×C103C2211yescharacteristic
18C22×SD16×C103C2211yescharacteristic
19C2×C22⋊Q8×C103C2211yescharacteristic
20C2×C4×Q8×C103C2211yescharacteristic
21C2×#117×C103C2211yescharacteristic
22C22×C4⋊C4×C103C2211yescharacteristic
23#452×C103C418yescomplemented
24C2×#106×C103C2211yescharacteristic
25C2×#106×C103C2211yescharacteristic
26C2×#103×C103C2211yescharacteristic
27C2×#103×C103C2211yescharacteristic
28C2×#103×C103C2211yescharacteristic
29C2×#103×C103C2211yescharacteristic
30C2×#103×C103C2211yescharacteristic
31C2×#102×C103C2211yescharacteristic
32C2×#102×C103C2211yescharacteristic
33C2×#102×C103C2211yescharacteristic
34C2×C22⋊C8×C103C2211yescharacteristic
35C2×C22⋊C8×C103C2211yescharacteristic
36C2×#97×C103C2211yescharacteristic
37C2×C4×C8×C103C2211yescharacteristic
38#391×C103C2211yescharacteristic
39#391×C103C2211yescharacteristic
40#391×C103C2211yescharacteristic
41#390×C103C2211yescharacteristic
42#390×C103C2211yescharacteristic
43#389×C103—21no—
44#389×C103C2211yescharacteristic
45#388×C103—21no—
46#388×C103—21no—
47#387×C103—21no—
48#386×C103—21no—
49#386×C103—21no—
50#380×C103—21no—
51#380×C103—21no—
52#380×C103C2211yescharacteristic
53C4×C4⋊C4×C103C2211yescharacteristic
54#340×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#340×C103C2211yescharacteristic
58#336×C103C2211yescharacteristic
59#336×C103C2211yescharacteristic
60C2×#41×C103—22no—
61C2×#41×C103—41no—
62C2×#41×C103—41no—
63C2×#41×C103—41no—
64C2×#41×C103—41no—
65C2×#41×C103C2×C414yes—
66C22×Q8×C103C2311yescharacteristic
67C22×Q8×C103C2311yescharacteristic
68C22×D4×C103—21no—
69C22×D4×C103C2311yescharacteristic
70C23×C4×C103—21no—
71C23×C4×C103—21no—
72C23×C4×C103C2311yescharacteristic
73C2×Q16×C103—41no—
74C2×Q16×C103—41no—
75C2×Q16×C103C2×C414yescomplemented
76C2×SD16×C103—41no—
77C2×SD16×C103—41no—
78C2×SD16×C103C2×C414yescomplemented
79C22×C8×C103C2311yescharacteristic
80C22×C8×C103C2311yescharacteristic
81C22×C8×C103C2311yescharacteristic
82C22×C8×C103C2311yescharacteristic
83C22⋊Q8×C103—22no—
84C22⋊Q8×C103C2×C414yes—
85C4×Q8×C103—41no—
86C4×Q8×C103—41no—
87#117×C103—41no—
88#117×C103—41no—
89C2×C4⋊C4×C103—21no—
90C2×C4⋊C4×C103—21no—
91C2×C4⋊C4×C103—21no—
92C2×C4⋊C4×C103—21no—
93C2×C4⋊C4×C103—41no—
94C2×C4⋊C4×C103—41no—
95C2×C4⋊C4×C103D411yescharacteristic
96C2×C4⋊C4×C103D411yescharacteristic
97C2×C4⋊C4×C103C2311yescharacteristic
98C2×C4⋊C4×C103C2311yescharacteristic
99C2×C4⋊C4×C103C2311yescharacteristic
100C2×C4⋊C4×C103C2311yescharacteristic
101C2×C4⋊C4×C103C2311yescharacteristic
102C2×C22⋊C4×C103—21no—
103C2×C22⋊C4×C103—21no—
104C2×C22⋊C4×C103—21no—
105C2×C22⋊C4×C103—21no—
106C2×C22⋊C4×C103—21no—
107C2×C22⋊C4×C103—21no—
108C2×C22⋊C4×C103D411yescharacteristic
109C2×C22⋊C4×C103D411yescharacteristic
110C2×C42×C103—21no—
111C2×C42×C103—21no—
112C2×C42×C103C2311yescharacteristic
113C2×C42×C103C2311yescharacteristic
114#106×C103—41no—
115#106×C103—41no—
116#103×C103—41no—
117#103×C103—41no—
118#103×C103—41no—
119#103×C103—41no—
120#103×C103C2×C414yescomplemented
121#102×C103—41no—
122#102×C103—41no—
123#102×C103C2×C414yescomplemented
124C22⋊C8×C103—22no—
125C22⋊C8×C103C2×C414yes—
126#97×C103—41no—
127C4×C8×C103—41no—
128#95×C103—21no—
129#95×C103—21no—
130#95×C103—21no—
131#95×C103—21no—
132#95×C103—21no—
133#95×C103—21no—
134#95×C103—21no—
135#95×C103—21no—
136#95×C103—21no—
137C24×C103—21no—
138C24×C103C2×D411yescharacteristic
139#41×C103—44no—
140#41×C103—44no—
141#41×C103—44no—
142#41×C103—44no—
143C2×Q8×C103—21no—
144C2×Q8×C103—21no—
145C2×Q8×C103—21no—
146C2×Q8×C103—21no—
147C2×Q8×C103—21no—
148C2×Q8×C103—21no—
149C2×Q8×C103—21no—
150C2×Q8×C103—21no—
151C2×Q8×C103—21no—
152C2×Q8×C103—21no—
153C2×Q8×C103C22×C412yes—
154C2×Q8×C103C22×C412yes—
155C2×D4×C103—24no—
156C2×D4×C103—21no—
157C2×D4×C103—21no—
158C2×D4×C103—21no—
159C2×D4×C103—21no—
160C2×D4×C103—21no—
161C2×D4×C103—42no—
162C2×D4×C103—42no—
163C2×D4×C103C22×C412yes—
164C22×C4×C103—21no—
165C22×C4×C103—21no—
166C22×C4×C103—21no—
167C22×C4×C103—21no—
168C22×C4×C103—21no—
169C22×C4×C103—21no—
170C22×C4×C103—21no—
171C22×C4×C103—24no—
172C22×C4×C103—21no—
173C22×C4×C103—21no—
174C22×C4×C103—21no—
175C22×C4×C103—21no—
176C22×C4×C103—42no—
177C22×C4×C103—42no—
178C22×C4×C103—42no—
179C22×C4×C103—81no—
180C22×C4×C103—81no—
181C22×C4×C103C22×C412yes—
182C22×C4×C103C2×D411yescharacteristic
183C22×C4×C103C2×D411yescharacteristic
184C22×C4×C103C2×D411yescharacteristic
185C22×C4×C103C2×D411yescharacteristic
186C22×C4×C103C2×D411yescharacteristic
187C22×C4×C103#4112yes—
188C22×C4×C103C2411yescharacteristic
189Q16×C103—44no—
190SD16×C103—44no—
191C2×C8×C103—21no—
192C2×C8×C103—21no—
193C2×C8×C103—21no—
194C2×C8×C103—21no—
195C2×C8×C103—21no—
196C2×C8×C103—21no—
197C2×C8×C103—21no—
198C2×C8×C103—21no—
199C2×C8×C103—21no—
200C2×C8×C103—21no—
201C2×C8×C103C22×C412yes—
202C2×C8×C103C22×C412yes—
203C4⋊C4×C103—24no—
204C4⋊C4×C103—21no—
205C4⋊C4×C103—21no—
206C4⋊C4×C103—21no—
207C4⋊C4×C103—21no—
208C4⋊C4×C103—21no—
209C4⋊C4×C103—21no—
210C4⋊C4×C103—21no—
211C4⋊C4×C103—21no—
212C4⋊C4×C103—21no—
213C4⋊C4×C103—41no—
214C4⋊C4×C103—41no—
215C4⋊C4×C103—42no—
216C4⋊C4×C103—42no—
217C4⋊C4×C103—81no—
218C4⋊C4×C103C22×C412yes—
219C22⋊C4×C103—24no—
220C22⋊C4×C103—41no—
221C22⋊C4×C103—41no—
222C22⋊C4×C103—81no—
223C22⋊C4×C103—81no—
224C22⋊C4×C103—81no—
225C22⋊C4×C103—81no—
226C22⋊C4×C103—81no—
227C42×C103—21no—
228C42×C103—21no—
229C42×C103—21no—
230C42×C103—21no—
231C42×C103—42no—
232C42×C103—81no—
233C23×C103—21no—
234C23×C103—21no—
235C23×C103—21no—
236C23×C103—21no—
237C23×C103—21no—
238C23×C103—21no—
239C23×C103—22no—
240C23×C103—41no—
241C23×C103—41no—
242C23×C103—41no—
243C23×C103—41no—
244C23×C103—41no—
245C23×C103—41no—
246C23×C103C4×D412yes—
247C23×C103C22×D411yescharacteristic
248Q8×C103—22no—
249Q8×C103—22no—
250Q8×C103—22no—
251Q8×C103—22no—
252Q8×C103—41no—
253Q8×C103—41no—
254Q8×C103—41no—
255Q8×C103—41no—
256D4×C103—22no—
257D4×C103—22no—
258D4×C103—48no—
259D4×C103—41no—
260D4×C103—41no—
261C2×C4×C103—21no—
262C2×C4×C103—21no—
263C2×C4×C103—22no—
264C2×C4×C103—22no—
265C2×C4×C103—22no—
266C2×C4×C103—22no—
267C2×C4×C103—22no—
268C2×C4×C103—22no—
269C2×C4×C103—22no—
270C2×C4×C103—21no—
271C2×C4×C103—21no—
272C2×C4×C103—21no—
273C2×C4×C103—21no—
274C2×C4×C103—21no—
275C2×C4×C103—21no—
276C2×C4×C103—21no—
277C2×C4×C103—21no—
278C2×C4×C103—21no—
279C2×C4×C103—21no—
280C2×C4×C103—21no—
281C2×C4×C103—21no—
282C2×C4×C103—48no—
283C2×C4×C103—41no—
284C2×C4×C103—41no—
285C2×C4×C103—41no—
286C2×C4×C103—41no—
287C2×C4×C103—41no—
288C2×C4×C103—41no—
289C2×C4×C103—41no—
290C2×C4×C103—41no—
291C2×C4×C103—41no—
292C2×C4×C103—41no—
293C2×C4×C103—41no—
294C2×C4×C103—41no—
295C2×C4×C103—41no—
296C2×C4×C103—41no—
297C2×C4×C103—41no—
298C2×C4×C103—41no—
299C2×C4×C103—41no—
300C2×C4×C103—41no—
301C2×C4×C103—84no—
302C2×C4×C103C4×D412yes—
303C2×C4×C103C23×C411yescharacteristic
304C2×C4×C103C2×#4111yescharacteristic
305C2×C4×C103H(5,𝔽2)11yescharacteristic
306C2×C4×C103H(5,𝔽2)11yescharacteristic
307C2×C4×C103H(5,𝔽2)11yescharacteristic
308C2×C4×C103H(5,𝔽2)11yescharacteristic
309C8×C103—22no—
310C8×C103—22no—
311C8×C103—41no—
312C8×C103—41no—
313C22×C103—22no—
314C22×C103—22no—
315C22×C103—22no—
316C22×C103—41no—
317C22×C103—41no—
318C22×C103—41no—
319C22×C103—41no—
320C22×C103—42no—
321C22×C103—42no—
322C22×C103—42no—
323C22×C103—81no—
324C22×C103—81no—
325C22×C103—81no—
326C22×C103—81no—
327C22×C103C2×C4×D411yescharacteristic
328C22×C103#53411yescharacteristic
329C22×C103#53511yescharacteristic
330C22×C103#57711yescharacteristic
331C22×C103#57711yescharacteristic
332C22×C103#57711yescharacteristic
333C22×C103#57811yescharacteristic
334C4×C103—22no—
335C4×C103—42no—
336C4×C103—42no—
337C4×C103—41no—
338C4×C103—41no—
339C4×C103—41no—
340C4×C103—41no—
341C4×C103—42no—
342C4×C103—81no—
343C4×C103—81no—
344C4×C103—81no—
345C4×C103—81no—
346C4×C103#51811yescharacteristic
347C4×C103#51811yescharacteristic
348C4×C103#53811yescharacteristic
349C4×C103#53811yescharacteristic
350#22059C10311yesmaximal, characteristic, direct product factor, Sylow
351C2×C103—42no—
352C2×C103—82no—
353C2×C103#232111yescharacteristic
354C2×C103#294711yescharacteristic
355C2×C103#295211yescharacteristic
356C2×C103#320111yescharacteristic
357C2×C103#320411yescharacteristic
358C2×C103#322211yescharacteristic
359C2×C103#322511yescharacteristic
360C2×#452C2×C10311yescharacteristic
361#2323C2×C10311yescharacteristic, complemented
362#2311C2×C10311yescharacteristic
363#1971C2×C10311yescharacteristic, complemented
364#1968C2×C10311yescharacteristic, complemented
365#1936C2×C10311yescharacteristic, complemented
366#1933C2×C10311yescharacteristic, complemented
367#1927C2×C10311yescharacteristic, complemented
368#1926C2×C10311yescharacteristic, complemented
369#1880C2×C10311yescharacteristic, complemented
370#1878C2×C10311yescharacteristic, complemented
371#1872C2×C10311yescharacteristic, complemented
372#1853C2×C10311yescharacteristic, complemented
373#1788C2×C10311yescharacteristic
374#1750C2×C10311yescharacteristic, complemented
375C103#2205911yescharacteristic, direct product factor, Sylow
376C22×#41C22×C10311yescharacteristic
377C22×Q16C22×C10311yescharacteristic
378C22×SD16C22×C10311yescharacteristic
379C2×C22⋊Q8C22×C10311yescharacteristic
380C2×C4×Q8C22×C10311yescharacteristic
381C2×#117C22×C10311yescharacteristic
382C22×C4⋊C4C22×C10311yescharacteristic
383#452C4×C10318yescomplemented
384C2×#106C22×C10311yescharacteristic
385C2×#106C22×C10311yescharacteristic
386C2×#103C22×C10311yescharacteristic
387C2×#103C22×C10311yescharacteristic
388C2×#103C22×C10311yescharacteristic
389C2×#103C22×C10311yescharacteristic
390C2×#103C22×C10311yescharacteristic
391C2×#102C22×C10311yescharacteristic
392C2×#102C22×C10311yescharacteristic
393C2×#102C22×C10311yescharacteristic
394C2×C22⋊C8C22×C10311yescharacteristic
395C2×C22⋊C8C22×C10311yescharacteristic
396C2×#97C22×C10311yescharacteristic
397C2×C4×C8C22×C10311yescharacteristic
398#391C22×C10311yescharacteristic
399#391C22×C10311yescharacteristic
400#391C22×C10311yescharacteristic
401#390C22×C10311yescharacteristic
402#390C22×C10311yescharacteristic
403#389—21no—
404#389C22×C10311yescharacteristic
405#388—21no—
406#388—21no—
407#387—21no—
408#386—21no—
409#386—21no—
410#380—21no—
411#380—21no—
412#380C22×C10311yescharacteristic
413C4×C4⋊C4C22×C10311yescharacteristic
414#340C22×C10311yescharacteristic
415#340C22×C10311yescharacteristic
416#340C22×C10311yescharacteristic
417#340C22×C10311yescharacteristic
418#336C22×C10311yescharacteristic
419#336C22×C10311yescharacteristic
420C2×#41—22no—
421C2×#41—41no—
422C2×#41—41no—
423C2×#41—41no—
424C2×#41—41no—
425C2×#41C2×C4×C10314yes—
426C22×Q8C23×C10311yescharacteristic
427C22×Q8C23×C10311yescharacteristic
428C22×D4—21no—
429C22×D4C23×C10311yescharacteristic
430C23×C4—21no—
431C23×C4—21no—
432C23×C4C23×C10311yescharacteristic
433C2×Q16—41no—
434C2×Q16—41no—
435C2×Q16C2×C4×C10314yescomplemented
436C2×SD16—41no—
437C2×SD16—41no—
438C2×SD16C2×C4×C10314yescomplemented
439C22×C8C23×C10311yescharacteristic
440C22×C8C23×C10311yescharacteristic
441C22×C8C23×C10311yescharacteristic
442C22×C8C23×C10311yescharacteristic
443C22⋊Q8—22no—
444C22⋊Q8C2×C4×C10314yes—
445C4×Q8—41no—
446C4×Q8—41no—
447#117—41no—
448#117—41no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4D4×C10311yescharacteristic
456C2×C4⋊C4D4×C10311yescharacteristic
457C2×C4⋊C4C23×C10311yescharacteristic
458C2×C4⋊C4C23×C10311yescharacteristic
459C2×C4⋊C4C23×C10311yescharacteristic
460C2×C4⋊C4C23×C10311yescharacteristic
461C2×C4⋊C4C23×C10311yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4D4×C10311yescharacteristic
469C2×C22⋊C4D4×C10311yescharacteristic
470C2×C42—21no—
471C2×C42—21no—
472C2×C42C23×C10311yescharacteristic
473C2×C42C23×C10311yescharacteristic
474#106—41no—
475#106—41no—
476#103—41no—
477#103—41no—
478#103—41no—
479#103—41no—
480#103C2×C4×C10314yescomplemented
481#102—41no—
482#102—41no—
483#102C2×C4×C10314yescomplemented
484C22⋊C8—22no—
485C22⋊C8C2×C4×C10314yes—
486#97—41no—
487C4×C8—41no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C24—21no—
498C24C2×D4×C10311yescharacteristic
499#41—44no—
500#41—44no—
501#41—44no—
502#41—44no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8C22×C4×C10312yes—
514C2×Q8C22×C4×C10312yes—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4C22×C4×C10312yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4C22×C4×C10312yes—
542C22×C4C2×D4×C10311yescharacteristic
543C22×C4C2×D4×C10311yescharacteristic
544C22×C4C2×D4×C10311yescharacteristic
545C22×C4C2×D4×C10311yescharacteristic
546C22×C4C2×D4×C10311yescharacteristic
547C22×C4#41×C10312yes—
548C22×C4C24×C10311yescharacteristic
549Q16—44no—
550SD16—44no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8C22×C4×C10312yes—
562C2×C8C22×C4×C10312yes—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—81no—
578C4⋊C4C22×C4×C10312yes—
579C22⋊C4—24no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C22⋊C4—81no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—42no—
592C42—81no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—22no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23C4×D4×C10312yes—
607C23C22×D4×C10311yescharacteristic
608Q8—22no—
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616D4—22no—
617D4—22no—
618D4—48no—
619D4—41no—
620D4—41no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—48no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4C4×D4×C10312yes—
663C2×C4C23×C4×C10311yescharacteristic
664C2×C4C2×#41×C10311yescharacteristic
665C2×C4H(5,𝔽2)×C10311yescharacteristic
666C2×C4H(5,𝔽2)×C10311yescharacteristic
667C2×C4H(5,𝔽2)×C10311yescharacteristic
668C2×C4H(5,𝔽2)×C10311yescharacteristic
669C8—22no—
670C8—22no—
671C8—41no—
672C8—41no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22C2×C4×D4×C10311yescharacteristic
688C22#534×C10311yescharacteristic
689C22#535×C10311yescharacteristic
690C22#577×C10311yescharacteristic
691C22#577×C10311yescharacteristic
692C22#577×C10311yescharacteristic
693C22#578×C10311yescharacteristic
694C4—22no—
695C4—42no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—41no—
701C4—42no—
702C4—81no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4#518×C10311yescharacteristic
707C4#518×C10311yescharacteristic
708C4#538×C10311yescharacteristic
709C4#538×C10311yescharacteristic
710C2—42no—
711C2—82no—
712C2C103×#232111yescharacteristic
713C2C103×#294711yescharacteristic
714C2C103×#295211yescharacteristic
715C2C103×#320111yescharacteristic
716C2C103×#320411yescharacteristic
717C2C103×#322211yescharacteristic
718C2C103×#322511yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
prime radicalC22×#41×C103C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×#117×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2323C2semidirect
4. C103×#1971C2semidirect
5. C103×#1968C2semidirect
6. C103×#1936C2semidirect
7. C103×#1933C2semidirect
8. C103×#1927C2semidirect
9. C103×#1926C2semidirect
10. C103×#1880C2semidirect
11. C103×#1878C2semidirect
12. C103×#1872C2semidirect
13. C103×#1853C2semidirect
15. C103×#1750C2semidirect
23. #452×C103C4semidirect
75. C2×Q16×C103C2×C4semidirect
78. C2×SD16×C103C2×C4semidirect
120. #103×C103C2×C4semidirect
123. #102×C103C2×C4semidirect
350. #22059C103direct (N × H)
361. #2323C2×C103semidirect
363. #1971C2×C103semidirect
364. #1968C2×C103semidirect
365. #1936C2×C103semidirect
366. #1933C2×C103semidirect
367. #1927C2×C103semidirect
368. #1926C2×C103semidirect
369. #1880C2×C103semidirect
370. #1878C2×C103semidirect
371. #1872C2×C103semidirect
372. #1853C2×C103semidirect
374. #1750C2×C103semidirect
375. C103#22059direct (N × H)
383. #452C4×C103semidirect
435. C2×Q16C2×C4×C103semidirect
438. C2×SD16C2×C4×C103semidirect
480. #103C2×C4×C103semidirect
483. #102C2×C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#452×C1032
C103×#23232
C103×#23112
C103×#19712
C103×#19682
C103×#19362
C103×#19332
C103×#19272
C103×#19262
C103×#18802
C103×#18782
C103×#18722
C103×#18532
C103×#17882
C103×#17502
#22059103