Finite Group Databasebeta

← C73×#25971 #32935375

Subgroups — C73×#25971 #32935375

Order 18688.

928 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#475×C73C211yesmaximal, characteristic, complemented
2C2×#419×C73C211yesmaximal, characteristic
3C73×#2439C211yesmaximal, characteristic
4Q8×C22⋊C4×C73C211yesmaximal, characteristic
5C73×#2097C211yesmaximal, characteristic, complemented
6C73×#2068C211yesmaximal, characteristic, complemented
7C73×#2066C211yesmaximal, characteristic, complemented
8C73×#2024C211yesmaximal, characteristic, complemented
9C73×#1863C211yesmaximal, characteristic, complemented
10C73×#1863C211yesmaximal, characteristic, complemented
11C73×#1854C211yesmaximal, characteristic
12C73×#1851C211yesmaximal, characteristic
13C73×#1809C211yesmaximal, characteristic
14C73×#1805C211yesmaximal, characteristic, complemented
15C73×#1787C211yesmaximal, characteristic
16C23×Q8×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C2×C4⋊Q8×C73C2211yescharacteristic
19C2×C4×Q8×C73C2211yescharacteristic
20C2×C4×Q8×C73C2211yescharacteristic
21C2×#117×C73C2211yescharacteristic
22#475×C73—24no—
23C2×#107×C73C2211yescharacteristic
24C2×#107×C73C2211yescharacteristic
25C2×#106×C73C2211yescharacteristic
26C2×#106×C73C2211yescharacteristic
27C2×C4⋊C8×C73C2211yescharacteristic
28C2×C4⋊C8×C73C2211yescharacteristic
29#419×C73—24no—
30C2×#103×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×#103×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39#396×C73—21no—
40#393×C73—21no—
41#391×C73—21no—
42#391×C73—21no—
43#391×C73—21no—
44#391×C73C2211yescharacteristic
45#391×C73C2211yescharacteristic
46#389×C73C2211yescharacteristic
47#389×C73C2211yescharacteristic
48#387×C73—21no—
49#382×C73C2211yescharacteristic
50#380×C73—21no—
51#380×C73C2211yescharacteristic
52#380×C73C2211yescharacteristic
53C4×C22⋊C4×C73—21no—
54C4×C22⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73—21no—
62C22×Q8×C73—21no—
63C22×Q8×C73—22no—
64C22×Q8×C73—22no—
65C22×Q8×C73—22no—
66C22×Q8×C73—41no—
67C22×Q8×C73—41no—
68C22×Q8×C73Q814yescomplemented
69C22×Q8×C73C2311yescharacteristic
70C22×Q8×C73C2311yescharacteristic
71C23×C4×C73—21no—
72C23×C4×C73C2311yescharacteristic
73C2×M16×C73—22no—
74C2×M16×C73—22no—
75C2×M16×C73—41no—
76C22×C8×C73C2311yescharacteristic
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C4⋊Q8×C73—22no—
81C4⋊Q8×C73—41no—
82C4×Q8×C73—22no—
83C4×Q8×C73—22no—
84C4×Q8×C73—41no—
85C4×Q8×C73—41no—
86#117×C73—22no—
87#117×C73—41no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C22⋊C4×C73—21no—
100C2×C22⋊C4×C73—21no—
101C2×C22⋊C4×C73—21no—
102C2×C22⋊C4×C73D411yescharacteristic
103C2×C22⋊C4×C73D411yescharacteristic
104C2×C42×C73—21no—
105C2×C42×C73—21no—
106C2×C42×C73—21no—
107C2×C42×C73C2311yescharacteristic
108C2×C42×C73C2311yescharacteristic
109#107×C73—41no—
110#107×C73—41no—
111#106×C73—22no—
112#106×C73—22no—
113C4⋊C8×C73—22no—
114C4⋊C8×C73—41no—
115#103×C73—22no—
116#103×C73—22no—
117#103×C73—22no—
118#103×C73—22no—
119#103×C73—22no—
120#103×C73—41no—
121#103×C73—41no—
122#103×C73D414yes—
123C22⋊C8×C73—22no—
124#95×C73—21no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73D411yescharacteristic
135#95×C73D411yescharacteristic
136C24×C73C2×D411yescharacteristic
137C2×Q8×C73—24no—
138C2×Q8×C73—21no—
139C2×Q8×C73—21no—
140C2×Q8×C73—21no—
141C2×Q8×C73—21no—
142C2×Q8×C73—28no—
143C2×Q8×C73—21no—
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—42no—
148C2×Q8×C73—42no—
149C2×Q8×C73—42no—
150C2×Q8×C73—44no—
151C2×Q8×C73—44no—
152C2×Q8×C73—44no—
153C2×Q8×C73—42no—
154C2×Q8×C73—81no—
155C2×Q8×C73C2×D412yes—
156C2×Q8×C73C2×Q812yes—
157C2×Q8×C73C2×Q812yes—
158C2×Q8×C73#4112yes—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—24no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—42no—
173C22×C4×C73—42no—
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×Q812yes—
180C22×C4×C73#4112yes—
181C22×C4×C73C2411yescharacteristic
182M16×C73—44no—
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×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73C2×D412yes—
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—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—42no—
207C4⋊C4×C73—42no—
208C4⋊C4×C73—42no—
209C4⋊C4×C73—42no—
210C4⋊C4×C73—81no—
211C4⋊C4×C73C2×D412yes—
212C22⋊C4×C73—22no—
213C22⋊C4×C73—41no—
214C22⋊C4×C73—42no—
215C22⋊C4×C73—42no—
216C22⋊C4×C73—81no—
217C42×C73—21no—
218C42×C73—21no—
219C42×C73—21no—
220C42×C73—21no—
221C42×C73—42no—
222C42×C73—42no—
223C42×C73—42no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73C22⋊Q812yes—
231C23×C73C22×D411yescharacteristic
232Q8×C73—22no—
233Q8×C73—22no—
234Q8×C73—22no—
235Q8×C73—22no—
236Q8×C73—22no—
237Q8×C73—48no—
238Q8×C73—41no—
239Q8×C73—41no—
240Q8×C73—84no—
241Q8×C73C22⋊Q814yes—
242C2×C4×C73—22no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—22no—
246C2×C4×C73—22no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—22no—
250C2×C4×C73—22no—
251C2×C4×C73—22no—
252C2×C4×C73—22no—
253C2×C4×C73—22no—
254C2×C4×C73—21no—
255C2×C4×C73—22no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—48no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
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×C73C22⋊Q812yes—
285C2×C4×C73#13712yes—
286C2×C4×C73C22×D411yescharacteristic
287C2×C4×C73C22×Q811yescharacteristic
288C2×C4×C73C2×#4111yescharacteristic
289C2×C4×C73C2×#4111yescharacteristic
290C2×C4×C73H(5,𝔽2)11yescharacteristic
291C2×C4×C73H(5,𝔽2)11yescharacteristic
292C8×C73—22no—
293C8×C73—41no—
294C8×C73—41no—
295C8×C73—41no—
296C22×C73—22no—
297C22×C73—22no—
298C22×C73—22no—
299C22×C73—41no—
300C22×C73—41no—
301C22×C73—41no—
302C22×C73—41no—
303C22×C73C2×C22⋊Q811yescharacteristic
304C22×C73D4211yescharacteristic
305C22×C73#54611yescharacteristic
306C22×C73C2×#13711yescharacteristic
307C22×C73#57511yescharacteristic
308C22×C73#57711yescharacteristic
309C22×C73#57811yescharacteristic
310C4×C73—22no—
311C4×C73—24no—
312C4×C73—22no—
313C4×C73—41no—
314C4×C73—42no—
315C4×C73—42no—
316C4×C73—41no—
317C4×C73—41no—
318C4×C73—81no—
319C4×C73—81no—
320C4×C73—81no—
321C4×C73—81no—
322C4×C73—81no—
323C4×C73C2×C22⋊Q811yescharacteristic
324C4×C73#54311yescharacteristic
325C4×C73#54611yescharacteristic
326C4×C73#55111yescharacteristic
327#25971C7311yesmaximal, characteristic, direct product factor, Sylow
328C2×C73—42no—
329C2×C73#243711yescharacteristic
330C2×C73#307811yescharacteristic
331C2×C73#308211yescharacteristic
332C2×C73#326611yescharacteristic
333C2×C73#327711yescharacteristic
334C2×C73#332111yescharacteristic
335C2×C73#332811yescharacteristic
336C2×#475C2×C7311yescharacteristic, complemented
337C2×#419C2×C7311yescharacteristic
338#2439C2×C7311yescharacteristic
339Q8×C22⋊C4C2×C7311yescharacteristic
340#2097C2×C7311yescharacteristic, complemented
341#2068C2×C7311yescharacteristic, complemented
342#2066C2×C7311yescharacteristic, complemented
343#2024C2×C7311yescharacteristic, complemented
344#1863C2×C7311yescharacteristic, complemented
345#1863C2×C7311yescharacteristic, complemented
346#1854C2×C7311yescharacteristic
347#1851C2×C7311yescharacteristic
348#1809C2×C7311yescharacteristic
349#1805C2×C7311yescharacteristic, complemented
350#1787C2×C7311yescharacteristic
351C73#2597111yescharacteristic, direct product factor, Sylow
352C23×Q8C22×C7311yescharacteristic
353C22×M16C22×C7311yescharacteristic
354C2×C4⋊Q8C22×C7311yescharacteristic
355C2×C4×Q8C22×C7311yescharacteristic
356C2×C4×Q8C22×C7311yescharacteristic
357C2×#117C22×C7311yescharacteristic
358#475—24no—
359C2×#107C22×C7311yescharacteristic
360C2×#107C22×C7311yescharacteristic
361C2×#106C22×C7311yescharacteristic
362C2×#106C22×C7311yescharacteristic
363C2×C4⋊C8C22×C7311yescharacteristic
364C2×C4⋊C8C22×C7311yescharacteristic
365#419—24no—
366C2×#103C22×C7311yescharacteristic
367C2×#103C22×C7311yescharacteristic
368C2×#103C22×C7311yescharacteristic
369C2×#103C22×C7311yescharacteristic
370C2×#103C22×C7311yescharacteristic
371C2×#103C22×C7311yescharacteristic
372C2×#103C22×C7311yescharacteristic
373C2×#103C22×C7311yescharacteristic
374C2×C22⋊C8C22×C7311yescharacteristic
375#396—21no—
376#393—21no—
377#391—21no—
378#391—21no—
379#391—21no—
380#391C22×C7311yescharacteristic
381#391C22×C7311yescharacteristic
382#389C22×C7311yescharacteristic
383#389C22×C7311yescharacteristic
384#387—21no—
385#382C22×C7311yescharacteristic
386#380—21no—
387#380C22×C7311yescharacteristic
388#380C22×C7311yescharacteristic
389C4×C22⋊C4—21no—
390C4×C22⋊C4C22×C7311yescharacteristic
391#340C22×C7311yescharacteristic
392#340C22×C7311yescharacteristic
393#340C22×C7311yescharacteristic
394#340C22×C7311yescharacteristic
395#336C22×C7311yescharacteristic
396#336C22×C7311yescharacteristic
397C22×Q8—21no—
398C22×Q8—21no—
399C22×Q8—22no—
400C22×Q8—22no—
401C22×Q8—22no—
402C22×Q8—41no—
403C22×Q8—41no—
404C22×Q8Q8×C7314yescomplemented
405C22×Q8C23×C7311yescharacteristic
406C22×Q8C23×C7311yescharacteristic
407C23×C4—21no—
408C23×C4C23×C7311yescharacteristic
409C2×M16—22no—
410C2×M16—22no—
411C2×M16—41no—
412C22×C8C23×C7311yescharacteristic
413C22×C8C23×C7311yescharacteristic
414C22×C8C23×C7311yescharacteristic
415C22×C8C23×C7311yescharacteristic
416C4⋊Q8—22no—
417C4⋊Q8—41no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8—41no—
421C4×Q8—41no—
422#117—22no—
423#117—41no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4C23×C7311yescharacteristic
430C2×C4⋊C4C23×C7311yescharacteristic
431C2×C4⋊C4C23×C7311yescharacteristic
432C2×C4⋊C4C23×C7311yescharacteristic
433C2×C4⋊C4C23×C7311yescharacteristic
434C2×C4⋊C4C23×C7311yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4D4×C7311yescharacteristic
439C2×C22⋊C4D4×C7311yescharacteristic
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C7311yescharacteristic
444C2×C42C23×C7311yescharacteristic
445#107—41no—
446#107—41no—
447#106—22no—
448#106—22no—
449C4⋊C8—22no—
450C4⋊C8—41no—
451#103—22no—
452#103—22no—
453#103—22no—
454#103—22no—
455#103—22no—
456#103—41no—
457#103—41no—
458#103D4×C7314yes—
459C22⋊C8—22no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95D4×C7311yescharacteristic
471#95D4×C7311yescharacteristic
472C24C2×D4×C7311yescharacteristic
473C2×Q8—24no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—28no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—42no—
490C2×Q8—81no—
491C2×Q8C2×D4×C7312yes—
492C2×Q8C2×Q8×C7312yes—
493C2×Q8C2×Q8×C7312yes—
494C2×Q8#41×C7312yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—24no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4C2×D4×C7311yescharacteristic
511C22×C4C2×D4×C7311yescharacteristic
512C22×C4C2×D4×C7311yescharacteristic
513C22×C4C2×D4×C7311yescharacteristic
514C22×C4C2×D4×C7311yescharacteristic
515C22×C4C2×Q8×C7312yes—
516C22×C4#41×C7312yes—
517C22×C4C24×C7311yescharacteristic
518M16—44no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8C2×D4×C7312yes—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—81no—
547C4⋊C4C2×D4×C7312yes—
548C22⋊C4—22no—
549C22⋊C4—41no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—81no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—42no—
558C42—42no—
559C42—42no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23C22⋊Q8×C7312yes—
567C23C22×D4×C7311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8—48no—
574Q8—41no—
575Q8—41no—
576Q8—84no—
577Q8C22⋊Q8×C7314yes—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—48no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4C22⋊Q8×C7312yes—
621C2×C4#137×C7312yes—
622C2×C4C22×D4×C7311yescharacteristic
623C2×C4C22×Q8×C7311yescharacteristic
624C2×C4C2×#41×C7311yescharacteristic
625C2×C4C2×#41×C7311yescharacteristic
626C2×C4H(5,𝔽2)×C7311yescharacteristic
627C2×C4H(5,𝔽2)×C7311yescharacteristic
628C8—22no—
629C8—41no—
630C8—41no—
631C8—41no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C2×C22⋊Q8×C7311yescharacteristic
640C22D42×C7311yescharacteristic
641C22#546×C7311yescharacteristic
642C22C2×#137×C7311yescharacteristic
643C22#575×C7311yescharacteristic
644C22#577×C7311yescharacteristic
645C22#578×C7311yescharacteristic
646C4—22no—
647C4—22no—
648C4—24no—
649C4—42no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4C2×C22⋊Q8×C7311yescharacteristic
660C4#543×C7311yescharacteristic
661C4#546×C7311yescharacteristic
662C4#551×C7311yescharacteristic
663C2—42no—
664C2C73×#243711yescharacteristic
665C2C73×#307811yescharacteristic
666C2C73×#308211yescharacteristic
667C2C73×#326611yescharacteristic
668C2C73×#327711yescharacteristic
669C2C73×#332111yescharacteristic
670C2C73×#332811yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC24×C73C2×D4
LCSG ▷ C22×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
1. C2×#475×C73C2semidirect
5. C73×#2097C2semidirect
6. C73×#2068C2semidirect
7. C73×#2066C2semidirect
8. C73×#2024C2semidirect
9. C73×#1863C2semidirect
10. C73×#1863C2semidirect
14. C73×#1805C2semidirect
68. C22×Q8×C73Q8semidirect
327. #25971C73direct (N × H)
336. C2×#475C2×C73semidirect
340. #2097C2×C73semidirect
341. #2068C2×C73semidirect
342. #2066C2×C73semidirect
343. #2024C2×C73semidirect
344. #1863C2×C73semidirect
345. #1863C2×C73semidirect
349. #1805C2×C73semidirect
351. C73#25971direct (N × H)
404. C22×Q8Q8×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#475×C732
C2×#419×C732
C73×#24392
Q8×C22⋊C4×C732
C73×#20972
C73×#20682
C73×#20662
C73×#20242
C73×#18632
C73×#18542
C73×#18512
C73×#18092
C73×#18052
C73×#17872
#2597173