Finite Group Databasebeta

← C73×#23035 #32932439

Subgroups — C73×#23035 #32932439

Order 18688.

998 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C73C211yesmaximal, characteristic
2C2×C4×SD16×C73C211yesmaximal, characteristic, complemented
3C2×#428×C73C211yesmaximal, characteristic, complemented
4C73×#2363C211yesmaximal, characteristic
5C73×#2360C211yesmaximal, characteristic, complemented
6C73×#1973C211yesmaximal, characteristic, complemented
7C73×#1942C211yesmaximal, characteristic, complemented
8C73×#1927C211yesmaximal, characteristic, complemented
9C73×#1925C211yesmaximal, characteristic, complemented
10C73×#1874C211yesmaximal, characteristic
11C73×#1873C211yesmaximal, characteristic, complemented
12C73×#1864C211yesmaximal, characteristic, complemented
13C73×#1863C211yesmaximal, characteristic, complemented
14C73×#1776C211yesmaximal, characteristic, complemented
15C73×#1753C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C2×C22⋊Q8×C73C2211yescharacteristic
19C2×#121×C73C2211yescharacteristic
20C2×C4×Q8×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22C2×#117×C73C2211yescharacteristic
23C22×C4⋊C4×C73C2211yescharacteristic
24#468×C73C418yescomplemented
25C4×SD16×C73—24no—
26#428×C73—24no—
27C2×#107×C73C2211yescharacteristic
28C2×#107×C73C2211yescharacteristic
29C2×#107×C73C2211yescharacteristic
30C2×#106×C73C2211yescharacteristic
31C2×#106×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×#97×C73C2211yescharacteristic
40C2×C4×C8×C73C2211yescharacteristic
41#391×C73C2211yescharacteristic
42#390×C73—21no—
43#390×C73C2211yescharacteristic
44#389×C73—21no—
45#389×C73C2211yescharacteristic
46#389×C73C2211yescharacteristic
47#388×C73—21no—
48#387×C73—21no—
49#386×C73—21no—
50#385×C73—21no—
51C4×C4⋊C4×C73C2211yescharacteristic
52C4×C4⋊C4×C73C2211yescharacteristic
53C4×C22⋊C4×C73—21no—
54C4×C22⋊C4×C73—21no—
55C4×C22⋊C4×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62C22×Q8×C73C2311yescharacteristic
63C22×D4×C73—21no—
64C22×D4×C73C2311yescharacteristic
65C23×C4×C73—21no—
66C23×C4×C73—21no—
67C23×C4×C73C2311yescharacteristic
68C2×SD16×C73—22no—
69C2×SD16×C73—22no—
70C2×SD16×C73C2×C414yescomplemented
71C2×M16×C73—22no—
72C2×M16×C73—22no—
73C2×M16×C73C2×C414yescomplemented
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77C22×C8×C73C2311yescharacteristic
78C22⋊Q8×C73—22no—
79C22⋊Q8×C73C2×C414yescomplemented
80#121×C73—22no—
81#121×C73C2×C414yes—
82C4×Q8×C73—22no—
83C4×Q8×C73—41no—
84C4×D4×C73—22no—
85C4×D4×C73—41no—
86#117×C73—22no—
87#117×C73—41no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73—22no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—41no—
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C22⋊C4×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73D411yescharacteristic
108C2×C22⋊C4×C73D411yescharacteristic
109C2×C42×C73—21no—
110C2×C42×C73—21no—
111C2×C42×C73—21no—
112C2×C42×C73—21no—
113C2×C42×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115#107×C73—22no—
116#107×C73—22no—
117#107×C73C2×C414yescomplemented
118#106×C73—22no—
119#106×C73D414yescomplemented
120#103×C73—22no—
121#103×C73—41no—
122#103×C73C2×C414yescomplemented
123#102×C73—22no—
124#102×C73—41no—
125#102×C73C2×C414yescomplemented
126C22⋊C8×C73—22no—
127#97×C73—22no—
128C4×C8×C73—22no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73D411yescharacteristic
136#95×C73D411yescharacteristic
137C24×C73—21no—
138C24×C73C2×D411yescharacteristic
139C2×Q8×C73—21no—
140C2×Q8×C73—21no—
141C2×Q8×C73—21no—
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73C22×C412yes—
145C2×D4×C73—24no—
146C2×D4×C73—21no—
147C2×D4×C73—21no—
148C2×D4×C73—21no—
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—81no—
152C2×D4×C73—81no—
153C2×D4×C73C22×C412yes—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—42no—
166C22×C4×C73—42no—
167C22×C4×C73—42no—
168C22×C4×C73—42no—
169C22×C4×C73—81no—
170C22×C4×C73—81no—
171C22×C4×C73C22×C412yes—
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73#4112yes—
178C22×C4×C73C2411yescharacteristic
179SD16×C73—28no—
180M16×C73—28no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73C22×C412yes—
190C2×C8×C73C22×C412yes—
191C2×C8×C73C2×D412yes—
192C2×C8×C73#4112yes—
193C4⋊C4×C73—24no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—42no—
203C4⋊C4×C73—42no—
204C4⋊C4×C73—81no—
205C4⋊C4×C73—81no—
206C4⋊C4×C73C22×C412yes—
207C4⋊C4×C73C22×C412yes—
208C4⋊C4×C73C2×D412yes—
209C4⋊C4×C73C2×D412yes—
210C22⋊C4×C73—24no—
211C22⋊C4×C73—24no—
212C22⋊C4×C73—22no—
213C22⋊C4×C73—41no—
214C22⋊C4×C73—42no—
215C22⋊C4×C73—42no—
216C22⋊C4×C73—42no—
217C22⋊C4×C73—81no—
218C42×C73—21no—
219C42×C73—21no—
220C42×C73—21no—
221C42×C73—21no—
222C42×C73—42no—
223C42×C73—42no—
224C42×C73—81no—
225C42×C73—81no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—22no—
233C23×C73—41no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73C4×D412yes—
240C23×C73C22×D411yescharacteristic
241Q8×C73—22no—
242Q8×C73—22no—
243Q8×C73—41no—
244Q8×C73—41no—
245D4×C73—22no—
246D4×C73—22no—
247D4×C73—41no—
248D4×C73—41no—
249D4×C73—84no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—22no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—22no—
261C2×C4×C73—21no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—84no—
289C2×C4×C73—84no—
290C2×C4×C73C4×D412yes—
291C2×C4×C73#13712yes—
292C2×C4×C73C23×C411yescharacteristic
293C2×C4×C73C22×D411yescharacteristic
294C2×C4×C73C2×#4111yescharacteristic
295C2×C4×C73C2×#4111yescharacteristic
296C2×C4×C73H(5,𝔽2)11yescharacteristic
297C2×C4×C732−1+411yescharacteristic
298C8×C73—22no—
299C8×C73—41no—
300C8×C73—41no—
301C8×C73C4×D414yes—
302C22×C73—22no—
303C22×C73—22no—
304C22×C73—22no—
305C22×C73—41no—
306C22×C73—41no—
307C22×C73—41no—
308C22×C73—41no—
309C22×C73—42no—
310C22×C73—42no—
311C22×C73—42no—
312C22×C73—81no—
313C22×C73—81no—
314C22×C73—81no—
315C22×C73—81no—
316C22×C73C2×C4×D411yescharacteristic
317C22×C73D4211yescharacteristic
318C22×C73#54711yescharacteristic
319C22×C73C2×#13711yescharacteristic
320C22×C73#57511yescharacteristic
321C22×C73#57611yescharacteristic
322C22×C73#57711yescharacteristic
323C4×C73—22no—
324C4×C73—22no—
325C4×C73—41no—
326C4×C73—41no—
327C4×C73—42no—
328C4×C73—42no—
329C4×C73—42no—
330C4×C73—42no—
331C4×C73—41no—
332C4×C73—42no—
333C4×C73—81no—
334C4×C73—81no—
335C4×C73C2×C4×D411yescharacteristic
336C4×C73#52011yescharacteristic
337C4×C73#54811yescharacteristic
338C4×C73#55311yescharacteristic
339#23035C7311yesmaximal, characteristic, direct product factor, Sylow
340C2×C73—42no—
341C2×C73—82no—
342C2×C73#236111yescharacteristic
343C2×C73C4×#13711yescharacteristic
344C2×C73#294611yescharacteristic
345C2×C73#326611yescharacteristic
346C2×C73#326811yescharacteristic
347C2×C73#335111yescharacteristic
348C2×C73#335711yescharacteristic
349C2×#468C2×C7311yescharacteristic
350C2×C4×SD16C2×C7311yescharacteristic, complemented
351C2×#428C2×C7311yescharacteristic, complemented
352#2363C2×C7311yescharacteristic
353#2360C2×C7311yescharacteristic, complemented
354#1973C2×C7311yescharacteristic, complemented
355#1942C2×C7311yescharacteristic, complemented
356#1927C2×C7311yescharacteristic, complemented
357#1925C2×C7311yescharacteristic, complemented
358#1874C2×C7311yescharacteristic
359#1873C2×C7311yescharacteristic, complemented
360#1864C2×C7311yescharacteristic, complemented
361#1863C2×C7311yescharacteristic, complemented
362#1776C2×C7311yescharacteristic, complemented
363#1753C2×C7311yescharacteristic, complemented
364C73#2303511yescharacteristic, direct product factor, Sylow
365C22×SD16C22×C7311yescharacteristic
366C22×M16C22×C7311yescharacteristic
367C2×C22⋊Q8C22×C7311yescharacteristic
368C2×#121C22×C7311yescharacteristic
369C2×C4×Q8C22×C7311yescharacteristic
370C2×C4×D4C22×C7311yescharacteristic
371C2×#117C22×C7311yescharacteristic
372C22×C4⋊C4C22×C7311yescharacteristic
373#468C4×C7318yescomplemented
374C4×SD16—24no—
375#428—24no—
376C2×#107C22×C7311yescharacteristic
377C2×#107C22×C7311yescharacteristic
378C2×#107C22×C7311yescharacteristic
379C2×#106C22×C7311yescharacteristic
380C2×#106C22×C7311yescharacteristic
381C2×#103C22×C7311yescharacteristic
382C2×#103C22×C7311yescharacteristic
383C2×#103C22×C7311yescharacteristic
384C2×#102C22×C7311yescharacteristic
385C2×#102C22×C7311yescharacteristic
386C2×#102C22×C7311yescharacteristic
387C2×C22⋊C8C22×C7311yescharacteristic
388C2×#97C22×C7311yescharacteristic
389C2×C4×C8C22×C7311yescharacteristic
390#391C22×C7311yescharacteristic
391#390—21no—
392#390C22×C7311yescharacteristic
393#389—21no—
394#389C22×C7311yescharacteristic
395#389C22×C7311yescharacteristic
396#388—21no—
397#387—21no—
398#386—21no—
399#385—21no—
400C4×C4⋊C4C22×C7311yescharacteristic
401C4×C4⋊C4C22×C7311yescharacteristic
402C4×C22⋊C4—21no—
403C4×C22⋊C4—21no—
404C4×C22⋊C4C22×C7311yescharacteristic
405#340C22×C7311yescharacteristic
406#340C22×C7311yescharacteristic
407#340C22×C7311yescharacteristic
408#340C22×C7311yescharacteristic
409#336C22×C7311yescharacteristic
410#336C22×C7311yescharacteristic
411C22×Q8C23×C7311yescharacteristic
412C22×D4—21no—
413C22×D4C23×C7311yescharacteristic
414C23×C4—21no—
415C23×C4—21no—
416C23×C4C23×C7311yescharacteristic
417C2×SD16—22no—
418C2×SD16—22no—
419C2×SD16C2×C4×C7314yescomplemented
420C2×M16—22no—
421C2×M16—22no—
422C2×M16C2×C4×C7314yescomplemented
423C22×C8C23×C7311yescharacteristic
424C22×C8C23×C7311yescharacteristic
425C22×C8C23×C7311yescharacteristic
426C22×C8C23×C7311yescharacteristic
427C22⋊Q8—22no—
428C22⋊Q8C2×C4×C7314yescomplemented
429#121—22no—
430#121C2×C4×C7314yes—
431C4×Q8—22no—
432C4×Q8—41no—
433C4×D4—22no—
434C4×D4—41no—
435#117—22no—
436#117—41no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4C23×C7311yescharacteristic
445C2×C4⋊C4C23×C7311yescharacteristic
446C2×C4⋊C4C23×C7311yescharacteristic
447C2×C4⋊C4C23×C7311yescharacteristic
448C2×C4⋊C4C23×C7311yescharacteristic
449C2×C4⋊C4C23×C7311yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4D4×C7311yescharacteristic
457C2×C22⋊C4D4×C7311yescharacteristic
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C23×C7311yescharacteristic
463C2×C42C23×C7311yescharacteristic
464#107—22no—
465#107—22no—
466#107C2×C4×C7314yescomplemented
467#106—22no—
468#106D4×C7314yescomplemented
469#103—22no—
470#103—41no—
471#103C2×C4×C7314yescomplemented
472#102—22no—
473#102—41no—
474#102C2×C4×C7314yescomplemented
475C22⋊C8—22no—
476#97—22no—
477C4×C8—22no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95D4×C7311yescharacteristic
485#95D4×C7311yescharacteristic
486C24—21no—
487C24C2×D4×C7311yescharacteristic
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8C22×C4×C7312yes—
494C2×D4—24no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—81no—
501C2×D4—81no—
502C2×D4C22×C4×C7312yes—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—81no—
519C22×C4—81no—
520C22×C4C22×C4×C7312yes—
521C22×C4C2×D4×C7311yescharacteristic
522C22×C4C2×D4×C7311yescharacteristic
523C22×C4C2×D4×C7311yescharacteristic
524C22×C4C2×D4×C7311yescharacteristic
525C22×C4C2×D4×C7311yescharacteristic
526C22×C4#41×C7312yes—
527C22×C4C24×C7311yescharacteristic
528SD16—28no—
529M16—28no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8C22×C4×C7312yes—
539C2×C8C22×C4×C7312yes—
540C2×C8C2×D4×C7312yes—
541C2×C8#41×C7312yes—
542C4⋊C4—24no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—81no—
554C4⋊C4—81no—
555C4⋊C4C22×C4×C7312yes—
556C4⋊C4C22×C4×C7312yes—
557C4⋊C4C2×D4×C7312yes—
558C4⋊C4C2×D4×C7312yes—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—22no—
562C22⋊C4—41no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—42no—
573C42—81no—
574C42—81no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—22no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23C4×D4×C7312yes—
589C23C22×D4×C7311yescharacteristic
590Q8—22no—
591Q8—22no—
592Q8—41no—
593Q8—41no—
594D4—22no—
595D4—22no—
596D4—41no—
597D4—41no—
598D4—84no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—84no—
638C2×C4—84no—
639C2×C4C4×D4×C7312yes—
640C2×C4#137×C7312yes—
641C2×C4C23×C4×C7311yescharacteristic
642C2×C4C22×D4×C7311yescharacteristic
643C2×C4C2×#41×C7311yescharacteristic
644C2×C4C2×#41×C7311yescharacteristic
645C2×C4H(5,𝔽2)×C7311yescharacteristic
646C2×C42−1+4×C7311yescharacteristic
647C8—22no—
648C8—41no—
649C8—41no—
650C8C4×D4×C7314yes—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22C2×C4×D4×C7311yescharacteristic
666C22D42×C7311yescharacteristic
667C22#547×C7311yescharacteristic
668C22C2×#137×C7311yescharacteristic
669C22#575×C7311yescharacteristic
670C22#576×C7311yescharacteristic
671C22#577×C7311yescharacteristic
672C4—22no—
673C4—22no—
674C4—42no—
675C4—41no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—42no—
680C4—42no—
681C4—42no—
682C4—81no—
683C4—81no—
684C4C2×C4×D4×C7311yescharacteristic
685C4#520×C7311yescharacteristic
686C4#548×C7311yescharacteristic
687C4#553×C7311yescharacteristic
688C2—42no—
689C2—82no—
690C2C73×#236111yescharacteristic
691C2C4×#137×C7311yescharacteristic
692C2C73×#294611yescharacteristic
693C2C73×#326611yescharacteristic
694C2C73×#326811yescharacteristic
695C2C73×#335111yescharacteristic
696C2C73×#335711yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC2×#121×C73C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C73C2semidirect
3. C2×#428×C73C2semidirect
5. C73×#2360C2semidirect
6. C73×#1973C2semidirect
7. C73×#1942C2semidirect
8. C73×#1927C2semidirect
9. C73×#1925C2semidirect
11. C73×#1873C2semidirect
12. C73×#1864C2semidirect
13. C73×#1863C2semidirect
14. C73×#1776C2semidirect
15. C73×#1753C2semidirect
24. #468×C73C4semidirect
70. C2×SD16×C73C2×C4semidirect
73. C2×M16×C73C2×C4semidirect
79. C22⋊Q8×C73C2×C4semidirect
117. #107×C73C2×C4semidirect
119. #106×C73D4semidirect
122. #103×C73C2×C4semidirect
125. #102×C73C2×C4semidirect
339. #23035C73direct (N × H)
350. C2×C4×SD16C2×C73semidirect
351. C2×#428C2×C73semidirect
353. #2360C2×C73semidirect
354. #1973C2×C73semidirect
355. #1942C2×C73semidirect
356. #1927C2×C73semidirect
357. #1925C2×C73semidirect
359. #1873C2×C73semidirect
360. #1864C2×C73semidirect
361. #1863C2×C73semidirect
362. #1776C2×C73semidirect
363. #1753C2×C73semidirect
364. C73#23035direct (N × H)
373. #468C4×C73semidirect
419. C2×SD16C2×C4×C73semidirect
422. C2×M16C2×C4×C73semidirect
428. C22⋊Q8C2×C4×C73semidirect
466. #107C2×C4×C73semidirect
468. #106D4×C73semidirect
471. #103C2×C4×C73semidirect
474. #102C2×C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C732
C2×C4×SD16×C732
C2×#428×C732
C73×#23632
C73×#23602
C73×#19732
C73×#19422
C73×#19272
C73×#19252
C73×#18742
C73×#18732
C73×#18642
C73×#18632
C73×#17762
C73×#17532
#2303573