Finite Group Databasebeta

← #33007693

Subgroups — #33007693

Order 18688.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556547C211yesmaximal, characteristic
2C2×C4⋊C4×Dic73C211yesmaximal, characteristic, complemented
3C2×#17988438C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic73C211yesmaximal, characteristic
5C2×C22⋊C4×Dic73C211yesmaximal, characteristic
6#22608195C211yesmaximal, characteristic, complemented
7#22608194C211yesmaximal, characteristic, complemented
8#22608189C211yesmaximal, characteristic, complemented
9#22608186C211yesmaximal, characteristic, complemented
10#22608176C211yesmaximal, characteristic
11#22608174C211yesmaximal, characteristic
12#22608174C211yesmaximal, characteristic
13#95×Dic73C211yesmaximal, characteristic, complemented
14#95×Dic73C211yesmaximal, characteristic, complemented
15C73×#1439C211yesmaximal, characteristic
16C24×Dic73C2211yescharacteristic
17C2×#14556547—24no—
18C2×#14556547—24no—
19C2×#14556547—24no—
20C22×C4⋊Dic73C2211yescharacteristic
21C22×#11924007C2211yescharacteristic
22C22×#11924007C2211yescharacteristic
23C22×#11924007C2211yescharacteristic
24C22×#11924007C2211yescharacteristic
25C22×C22⋊Dic73C2211yescharacteristic
26C22×C22⋊Dic73C2211yescharacteristic
27C22×C22⋊Dic73C2211yescharacteristic
28C22×C4×Dic73C2211yescharacteristic
29C22×C4×Dic73C2211yescharacteristic
30C22×C4×Dic73C2211yescharacteristic
31C22×C4×Dic73C2211yescharacteristic
32C22×C4×Dic73C2211yescharacteristic
33C22×C4×Dic73C2211yescharacteristic
34C4⋊C4×Dic73—24no—
35#17988438—24no—
36C22⋊C4×Dic73—24no—
37C22⋊C4×Dic73C418yescomplemented
38C2×#14556498C2211yescharacteristic
39C2×#14556498C2211yescharacteristic
40C2×#14556498C2211yescharacteristic
41C2×#14556498C2211yescharacteristic
42C2×#14556498C2211yescharacteristic
43C2×#14556498C2211yescharacteristic
44C2×#14556498C2211yescharacteristic
45C2×#14556498C2211yescharacteristic
46C2×#14556498C2211yescharacteristic
47C2×#14556498C2211yescharacteristic
48C2×#14556498C2211yescharacteristic
49C2×#14556498C2211yescharacteristic
50C2×#14556498C2211yescharacteristic
51C22×C4⋊C4×C73C2211yescharacteristic
52C22×C22⋊C4×C73C2211yescharacteristic
53C22×C22⋊C4×C73C2211yescharacteristic
54C22×C22⋊C4×C73C2211yescharacteristic
55C2×#95×C73C2211yescharacteristic
56C2×#95×C73C2211yescharacteristic
57C2×#95×C73C2211yescharacteristic
58C23×Dic73—22no—
59C23×Dic73—22no—
60C23×Dic73—22no—
61C23×Dic73—22no—
62C23×Dic73C2×C414yes—
63C23×Dic73D414yes—
64C23×Dic73Q814yes—
65C23×Dic73C2311yescharacteristic
66C23×Dic73C2311yescharacteristic
67C23×Dic73C2311yescharacteristic
68C23×Dic73C2311yescharacteristic
69C23×Dic73C2311yescharacteristic
70C23×Dic73C2311yescharacteristic
71C23×Dic73C2311yescharacteristic
72C23×Dic73C2311yescharacteristic
73#14556547—232no—
74C2×C4⋊Dic73—22no—
75C2×C4⋊Dic73—22no—
76C2×C4⋊Dic73—22no—
77C2×#11924007—22no—
78C2×#11924007—22no—
79C2×#11924007—22no—
80C2×#11924007—22no—
81C2×#11924007—22no—
82C2×#11924007—22no—
83C2×#11924007—22no—
84C2×#11924007—22no—
85C2×#11924007—22no—
86C2×#11924007—22no—
87C2×#11924007—22no—
88C2×#11924007—22no—
89C2×C22⋊Dic73—22no—
90C2×C22⋊Dic73—22no—
91C2×C22⋊Dic73—22no—
92C2×C22⋊Dic73—22no—
93C2×C22⋊Dic73—22no—
94C2×C22⋊Dic73—22no—
95C2×C22⋊Dic73—22no—
96C2×C22⋊Dic73—22no—
97C2×C22⋊Dic73C2×C414yes—
98C2×C4×Dic73—22no—
99C2×C4×Dic73—22no—
100C2×C4×Dic73—22no—
101C2×C4×Dic73—22no—
102C2×C4×Dic73—22no—
103C2×C4×Dic73—22no—
104C2×C4×Dic73—22no—
105C2×C4×Dic73—22no—
106C2×C4×Dic73—22no—
107C2×C4×Dic73—22no—
108C2×C4×Dic73—22no—
109C2×C4×Dic73—22no—
110C2×C4×Dic73—22no—
111C2×C4×Dic73—22no—
112C2×C4×Dic73C2×C414yes—
113C2×C4×Dic73C2×C414yes—
114C2×C4×Dic73D414yes—
115C2×C4×Dic73D414yes—
116#14556498—22no—
117#14556498—22no—
118#14556498—22no—
119#14556498—22no—
120#14556498—22no—
121#14556498—22no—
122#14556498—22no—
123#14556498—22no—
124#14556498—22no—
125#14556498—22no—
126#14556498—22no—
127#14556498C2×C414yes—
128#14556498C2×C414yes—
129C25×C73C2311yescharacteristic
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C23×C4×C73C2311yescharacteristic
135C23×C4×C73C2311yescharacteristic
136C2×C4⋊C4×C73—22no—
137C2×C4⋊C4×C73—22no—
138C2×C4⋊C4×C73—22no—
139C2×C22⋊C4×C73—22no—
140C2×C22⋊C4×C73—22no—
141C2×C22⋊C4×C73—22no—
142C2×C22⋊C4×C73—22no—
143C2×C22⋊C4×C73—22no—
144C2×C22⋊C4×C73—22no—
145C2×C22⋊C4×C73—22no—
146C2×C22⋊C4×C73—22no—
147C2×C22⋊C4×C73C2×C414yes—
148#95×C73—22no—
149#95×C73—22no—
150#95×C73—22no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73—21no—
154C22×Dic73—21no—
155C22×Dic73—21no—
156C22×Dic73—21no—
157C22×Dic73—21no—
158C22×Dic73—21no—
159C22×Dic73—28no—
160C22×Dic73—28no—
161C22×Dic73—28no—
162C22×Dic73—28no—
163C22×Dic73—28no—
164C22×Dic73—28no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73—21no—
170C22×Dic73—21no—
171C22×Dic73—21no—
172C22×Dic73—21no—
173C22×Dic73—21no—
174C22×Dic73—21no—
175C22×Dic73—21no—
176C22×Dic73—21no—
177C22×Dic73—21no—
178C22×Dic73—21no—
179C22×Dic73—21no—
180C22×Dic73—21no—
181C22×Dic73—21no—
182C22×Dic73—21no—
183C22×Dic73—21no—
184C22×Dic73—21no—
185C22×Dic73—21no—
186C22×Dic73—21no—
187C22×Dic73—21no—
188C22×Dic73—21no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73C4⋊C4116yescomplemented
196C22×Dic73C22×C412yes—
197C22×Dic73C22×C412yes—
198C22×Dic73C22×C412yes—
199C22×Dic73C22×C412yes—
200C22×Dic73C2×D412yes—
201C22×Dic73C2×D412yes—
202C22×Dic73C2×D412yes—
203C22×Dic73C2×D412yes—
204C22×Dic73C2×D412yes—
205C22×Dic73C2×D412yes—
206C22×Dic73C2×Q812yes—
207C22×Dic73C2×Q812yes—
208C22×Dic73#4112yes—
209C22×Dic73#4112yes—
210C22×Dic73#4112yes—
211C22×Dic73#4112yes—
212C22×Dic73#4112yes—
213C22×Dic73#4112yes—
214C4⋊Dic73—28no—
215#11924007—28no—
216#11924007—28no—
217#11924007—28no—
218#11924007—28no—
219C22⋊Dic73—28no—
220C22⋊Dic73—28no—
221C22⋊Dic73—28no—
222C4×Dic73—28no—
223C4×Dic73—28no—
224C4×Dic73—28no—
225C4×Dic73—28no—
226C4×Dic73—44no—
227C4×Dic73—44no—
228C24×C73—21no—
229C24×C73—21no—
230C24×C73—21no—
231C24×C73—21no—
232C24×C73—21no—
233C24×C73—21no—
234C24×C73—21no—
235C24×C73—21no—
236C24×C73—21no—
237C24×C73—21no—
238C24×C73—21no—
239C24×C73—21no—
240C24×C73C22×C412yes—
241C24×C73C2×D412yes—
242C24×C73C2×Q812yes—
243C24×C73C2411yescharacteristic
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—21no—
276C22×C4×C73—21no—
277C22×C4×C73—21no—
278C22×C4×C73C22×C412yes—
279C22×C4×C73C22×C412yes—
280C22×C4×C73C2×D412yes—
281C22×C4×C73C2×D412yes—
282C22×C4×C73#4112yes—
283C22×C4×C73#4112yes—
284C22×C4×C73#4112yes—
285C22×C4×C73#4112yes—
286C4⋊C4×C73—28no—
287C22⋊C4×C73—28no—
288C22⋊C4×C73—28no—
289C22⋊C4×C73—28no—
290C23×C73—22no—
291C23×C73—22no—
292C23×C73—22no—
293C23×C73—22no—
294C23×C73—22no—
295C23×C73—22no—
296C23×C73—22no—
297C23×C73—22no—
298C23×C73—22no—
299C23×C73—22no—
300C23×C73—22no—
301C23×C73—22no—
302C23×C73—22no—
303C23×C73—22no—
304C23×C73—22no—
305C23×C73—22no—
306C23×C73—22no—
307C23×C73—22no—
308C23×C73—41no—
309C23×C73—41no—
310C23×C73—41no—
311C23×C73—41no—
312C23×C73—41no—
313C23×C73—41no—
314C23×C73—41no—
315C23×C73—41no—
316C23×C73—41no—
317C23×C73—41no—
318C23×C73—41no—
319C23×C73—41no—
320C23×C73—41no—
321C23×C73—41no—
322C23×C73—41no—
323C23×C73—41no—
324C23×C73C2×C4⋊C414yes—
325C23×C73C23×C411yescharacteristic
326C23×C73C22×D411yescharacteristic
327C23×C73C22×D411yescharacteristic
328C23×C73C22×D411yescharacteristic
329C23×C73C22×Q811yescharacteristic
330C23×C73C2×#4111yescharacteristic
331C23×C73C2×#4111yescharacteristic
332C23×C73C2×#4111yescharacteristic
333C23×C73C2×#4111yescharacteristic
334C23×C73C2×#4111yescharacteristic
335C23×C73C2×#4111yescharacteristic
336C23×C73C2×#4111yescharacteristic
337C23×C73C2×#4111yescharacteristic
338C23×C73C2×#4111yescharacteristic
339C23×C73C2×#4111yescharacteristic
340C2×C4×C73—22no—
341C2×C4×C73—22no—
342C2×C4×C73—22no—
343C2×C4×C73—22no—
344C2×C4×C73—22no—
345C2×C4×C73—22no—
346C2×C4×C73—22no—
347C2×C4×C73—22no—
348C2×C4×C73—22no—
349C2×C4×C73—22no—
350C2×C4×C73—22no—
351C2×C4×C73—22no—
352C2×C4×C73—22no—
353C2×C4×C73—22no—
354C2×C4×C73—22no—
355C2×C4×C73—22no—
356C2×C4×C73—22no—
357C2×C4×C73—22no—
358C2×C4×C73—22no—
359C2×C4×C73—22no—
360C2×C4×C73—22no—
361C2×C4×C73—41no—
362C2×C4×C73—41no—
363C2×C4×C73—41no—
364C2×C4×C73—41no—
365C2×C4×C73—41no—
366C2×C4×C73—41no—
367C2×C4×C73—41no—
368C2×C4×C73—41no—
369C2×C4×C73—41no—
370C2×C4×C73—41no—
371C2×C4×C73—41no—
372C2×C4×C73—41no—
373C2×C4×C73—41no—
374C2×C4×C73—41no—
375C2×C4×C73—41no—
376C2×C4×C73—41no—
377C2×C4×C73—41no—
378C2×C4×C73—41no—
379C2×C4×C73—41no—
380C2×C4×C73—41no—
381C2×C4×C73#11714yescomplemented
382C2×Dic73—22no—
383C2×Dic73—22no—
384C2×Dic73—22no—
385C2×Dic73—22no—
386C2×Dic73—22no—
387C2×Dic73—22no—
388C2×Dic73—22no—
389C2×Dic73—22no—
390C2×Dic73—22no—
391C2×Dic73—22no—
392C2×Dic73—22no—
393C2×Dic73—22no—
394C2×Dic73—232no—
395C2×Dic73—22no—
396C2×Dic73—22no—
397C2×Dic73—22no—
398C2×Dic73—22no—
399C2×Dic73—22no—
400C2×Dic73—22no—
401C2×Dic73—22no—
402C2×Dic73—22no—
403C2×Dic73—22no—
404C2×Dic73—22no—
405C2×Dic73—22no—
406C2×Dic73—22no—
407C2×Dic73—22no—
408C2×Dic73—22no—
409C2×Dic73—22no—
410C2×Dic73—41no—
411C2×Dic73—41no—
412C2×Dic73—41no—
413C2×Dic73—41no—
414C2×Dic73—41no—
415C2×Dic73—41no—
416C2×Dic73—41no—
417C2×Dic73—41no—
418C2×Dic73—41no—
419C2×Dic73—41no—
420C2×Dic73—41no—
421C2×Dic73—41no—
422C2×Dic73—41no—
423C2×Dic73—41no—
424C2×Dic73—41no—
425C2×Dic73—41no—
426C2×Dic73—41no—
427C2×Dic73—41no—
428C2×Dic73—41no—
429C2×Dic73—41no—
430C2×Dic73C2×C4⋊C414yes—
431C2×Dic73C2×C4⋊C414yes—
432C2×Dic73#11714yescomplemented
433C2×Dic73C4×D414yes—
434C2×Dic73C4×D414yes—
435C2×Dic73#12014yes—
436C2×Dic73C22⋊Q814yes—
437C2×Dic73C22⋊Q814yes—
438C2×Dic73#12314yes—
439C22×C73—24no—
440C22×C73—24no—
441C22×C73—24no—
442C22×C73—42no—
443C22×C73—42no—
444C22×C73—42no—
445C22×C73—42no—
446C22×C73—42no—
447C22×C73—42no—
448C22×C73—42no—
449C22×C73—42no—
450C22×C73—42no—
451C22×C73—42no—
452C22×C73—42no—
453C22×C73—42no—
454C22×C73C22×C4⋊C411yescharacteristic
455C22×C73C2×#11711yescharacteristic
456C22×C73C2×#11711yescharacteristic
457C22×C73C2×C4×D411yescharacteristic
458C22×C73C2×C4×D411yescharacteristic
459C22×C73C4×#4111yescharacteristic
460C22×C73C4×#4111yescharacteristic
461C22×C73C2×#12011yescharacteristic
462C22×C73C2×C22⋊Q811yescharacteristic
463C22×C73C2×C22⋊Q811yescharacteristic
464C22×C73C2×#12311yescharacteristic
465C22×C73#52511yescharacteristic
466C22×C73#52511yescharacteristic
467C22×C73#52511yescharacteristic
468C22×C73#52511yescharacteristic
469C22×C73#52511yescharacteristic
470C22×C73#52511yescharacteristic
471C22×C73#52911yescharacteristic
472C22×C73#52911yescharacteristic
473C22×C73#52911yescharacteristic
474C22×C73#52911yescharacteristic
475C22×C73#52911yescharacteristic
476C22×C73#52911yescharacteristic
477C22×C73#52911yescharacteristic
478C22×C73#52911yescharacteristic
479C22×C73#53211yescharacteristic
480C22×C73#53211yescharacteristic
481C22×C73#53211yescharacteristic
482C22×C73#53211yescharacteristic
483C22×C73#53211yescharacteristic
484C22×C73#53211yescharacteristic
485C22×C73#53311yescharacteristic
486C22×C73#53311yescharacteristic
487C22×C73#53311yescharacteristic
488C22×C73#53311yescharacteristic
489C4×C73—24no—
490C4×C73—42no—
491C4×C73—42no—
492C4×C73—42no—
493C4×C73—42no—
494C4×C73—42no—
495Dic73—24no—
496Dic73—24no—
497Dic73—42no—
498Dic73—42no—
499Dic73—42no—
500Dic73—42no—
501Dic73—42no—
502Dic73#38518yes—
503#13844—731nomaximal, Sylow
504C2×C73—44no—
505C2×C73#228511yescharacteristic
506C2×C73C2×#38511yescharacteristic
507C2×C73#229011yescharacteristic
508C2×C73#229011yescharacteristic
509C2×C73#229311yescharacteristic
510C2×C73#229311yescharacteristic
511C2×C73#229611yescharacteristic
512C2×C73#238811yescharacteristic
513C2×C73#238811yescharacteristic
514C2×C73#239511yescharacteristic
515C2×C73#239511yescharacteristic
516C2×C73#239611yescharacteristic
517C2×C73#239611yescharacteristic
518C2×C73#239611yescharacteristic
519C2×C73#239611yescharacteristic
520C22×#117—731no—
521C2×C4×C4⋊C4—731no—
522C2×C4×C4⋊C4—731no—
523C2×C4×C22⋊C4—731no—
524C2×C4×C22⋊C4—731no—
525#1444—731no—
526#1444—731no—
527#1442—731no—
528#1442—731no—
529#1439—731no—
530#1439—731no—
531#1439—731no—
532#1439D7311yescharacteristic
533C4×#95—731no—
534C4×#95—731no—
535C73#1384411yescharacteristic, complemented, Sylow
536C24×C4—731no—
537C2×#117—1464no—
538C2×#117—1464no—
539C2×#117—1464no—
540C22×C4⋊C4—731no—
541C22×C4⋊C4—731no—
542C22×C4⋊C4—731no—
543C22×C4⋊C4—731no—
544C22×C4⋊C4—731no—
545C22×C4⋊C4C2×D7311yescharacteristic
546C22×C22⋊C4—731no—
547C22×C22⋊C4—731no—
548C22×C22⋊C4—731no—
549C22×C22⋊C4C2×D7311yescharacteristic
550C22×C22⋊C4C2×D7311yescharacteristic
551C22×C22⋊C4C2×D7311yescharacteristic
552C22×C42—731no—
553C22×C42—731no—
554C22×C42—731no—
555C22×C42—731no—
556C22×C42—731no—
557C22×C42—731no—
558C4×C4⋊C4—1464no—
559C4×C4⋊C4—1464no—
560C4×C22⋊C4—738no—
561C4×C22⋊C4—1464no—
562C2×#95—731no—
563C2×#95—731no—
564C2×#95—731no—
565C2×#95—731no—
566C2×#95—731no—
567C2×#95—731no—
568C2×#95—731no—
569C2×#95—731no—
570C2×#95—731no—
571C2×#95—731no—
572C2×#95—731no—
573C2×#95—731no—
574C2×#95—731no—
575C2×#95C2×D7311yescharacteristic
576C2×#95C2×D7311yescharacteristic
577C2×#95C2×D7311yescharacteristic
578C25C22×D7311yescharacteristic
579C23×C4—731no—
580C23×C4—734no—
581C23×C4—734no—
582C23×C4—734no—
583C23×C4—731no—
584C23×C4—731no—
585C23×C4—731no—
586C23×C4—731no—
587C23×C4—731no—
588C23×C4—731no—
589C23×C4—731no—
590C23×C4—1462no—
591C23×C4—1462no—
592C23×C4—1462no—
593C23×C4—1462no—
594C23×C4C22×D7311yescharacteristic
595C23×C4C22×D7311yescharacteristic
596C23×C4C22×D7311yescharacteristic
597C23×C4C22×D7311yescharacteristic
598C23×C4C22×D7311yescharacteristic
599C23×C4C22×D7311yescharacteristic
600#117—14632no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—1462no—
605C2×C4⋊C4—1462no—
606C2×C4⋊C4—1462no—
607C2×C4⋊C4—1462no—
608C2×C4⋊C4—1462no—
609C2×C4⋊C4—1462no—
610C2×C4⋊C4—1462no—
611C2×C4⋊C4—1462no—
612C2×C4⋊C4—1462no—
613C2×C4⋊C4—1462no—
614C2×C4⋊C4—1462no—
615C2×C4⋊C4—1462no—
616C2×C4⋊C4—1462no—
617C2×C4⋊C4—1462no—
618C2×C4⋊C4—1462no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—22no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—734no—
628C2×C22⋊C4—1462no—
629C2×C22⋊C4—1462no—
630C2×C22⋊C4—1462no—
631C2×C22⋊C4—1462no—
632C2×C22⋊C4—1462no—
633C2×C22⋊C4—1462no—
634C2×C22⋊C4—1462no—
635C2×C22⋊C4—1462no—
636C2×C22⋊C4C4×D7314yes—
637C2×C42—734no—
638C2×C42—734no—
639C2×C42—734no—
640C2×C42—734no—
641C2×C42—1462no—
642C2×C42—1462no—
643C2×C42—1462no—
644C2×C42—1462no—
645C2×C42—1462no—
646C2×C42—1462no—
647C2×C42—1462no—
648C2×C42—1462no—
649C2×C42—1462no—
650C2×C42—1462no—
651C2×C42—1462no—
652C2×C42—1462no—
653C2×C42—1462no—
654C2×C42—1462no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—734no—
659#95—734no—
660#95—1462no—
661#95—1462no—
662#95—1462no—
663#95—1462no—
664#95—1462no—
665#95—1462no—
666#95—1462no—
667#95—1462no—
668#95—1462no—
669#95—1462no—
670#95—1462no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24C2×C4×D7312yes—
684C24D4×D7312yes—
685C24Q8×D7312yes—
686C24C23×D7311yescharacteristic
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—732no—
722C22×C4—732no—
723C22×C4—732no—
724C22×C4—732no—
725C22×C4—732no—
726C22×C4—732no—
727C22×C4—732no—
728C22×C4—7316no—
729C22×C4—732no—
730C22×C4—732no—
731C22×C4—732no—
732C22×C4—732no—
733C22×C4—732no—
734C22×C4—732no—
735C22×C4—732no—
736C22×C4—732no—
737C22×C4—732no—
738C22×C4—732no—
739C22×C4—732no—
740C22×C4—1461no—
741C22×C4—1461no—
742C22×C4—1461no—
743C22×C4—1461no—
744C22×C4—1461no—
745C22×C4—1461no—
746C22×C4—1461no—
747C22×C4—1461no—
748C22×C4—1461no—
749C22×C4—1461no—
750C22×C4—1461no—
751C22×C4—1461no—
752C22×C4—1461no—
753C22×C4—1461no—
754C22×C4—1461no—
755C22×C4—1461no—
756C22×C4—1461no—
757C22×C4—1461no—
758C22×C4—1461no—
759C22×C4—1461no—
760C22×C4—1461no—
761C22×C4—1461no—
762C22×C4—1461no—
763C22×C4—1461no—
764C22×C4—1461no—
765C22×C4—1461no—
766C22×C4—1461no—
767C22×C4—1461no—
768C22×C4—1461no—
769C22×C4—1461no—
770C22×C4—1468no—
771C22×C4—1468no—
772C22×C4—1468no—
773C22×C4—1468no—
774C22×C4—1468no—
775C22×C4—1468no—
776C22×C4—1461no—
777C22×C4—1461no—
778C22×C4—1461no—
779C22×C4—1461no—
780C22×C4—1461no—
781C22×C4—1461no—
782C22×C4—1461no—
783C22×C4—1461no—
784C22×C4C2×C4×D7312yes—
785C22×C4C2×C4×D7312yes—
786C22×C4D4×D7312yes—
787C22×C4D4×D7312yes—
788C22×C4#1192402712yes—
789C22×C4#1192402712yes—
790C22×C4#1192402712yes—
791C22×C4#1192402712yes—
792C4⋊C4—28no—
793C4⋊C4—1468no—
794C4⋊C4—1468no—
795C4⋊C4—1468no—
796C4⋊C4—1468no—
797C4⋊C4—1468no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—1468no—
802C22⋊C4—1468no—
803C22⋊C4—1468no—
804C42—2924no—
805C42—2924no—
806C42—1468no—
807C42—1468no—
808C42—1468no—
809C42—1468no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23C4⋊C4×D7314yes—
845C23C22×C4×D7311yescharacteristic
846C23C2×D4×D7311yescharacteristic
847C23C2×D4×D7311yescharacteristic
848C23C2×D4×D7311yescharacteristic
849C23C2×Q8×D7311yescharacteristic
850C23#41×D7311yescharacteristic
851C23#41×D7311yescharacteristic
852C23#41×D7311yescharacteristic
853C23#41×D7311yescharacteristic
854C23#41×D7311yescharacteristic
855C23#41×D7311yescharacteristic
856C23C2×#1192402711yescharacteristic
857C23C2×#1192402711yescharacteristic
858C23C2×#1192402711yescharacteristic
859C23C2×#1192402711yescharacteristic
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—2921no—
902C2×C4—2921no—
903C2×C4—2921no—
904C2×C4—2921no—
905C2×C4—2921no—
906C2×C4—2921no—
907C2×C4—2921no—
908C2×C4—2921no—
909C2×C4—2921no—
910C2×C4—2921no—
911C2×C4—2921no—
912C2×C4—2921no—
913C2×C4—2921no—
914C2×C4—2921no—
915C2×C4—2921no—
916C2×C4—2921no—
917C2×C4—2921no—
918C2×C4—2921no—
919C2×C4—2921no—
920C2×C4—2921no—
921C2×C4—734no—
922C2×C4—734no—
923C2×C4—734no—
924C2×C4—734no—
925C2×C4—734no—
926C2×C4—734no—
927C2×C4—734no—
928C2×C4—734no—
929C2×C4—734no—
930C2×C4—1462no—
931C2×C4—1462no—
932C2×C4—1462no—
933C2×C4—1462no—
934C2×C4—1462no—
935C2×C4—1462no—
936C2×C4—1462no—
937C2×C4—1462no—
938C2×C4—1462no—
939C2×C4—1462no—
940C2×C4—1462no—
941C2×C4—1462no—
942C2×C4—1462no—
943C2×C4—1462no—
944C2×C4—1462no—
945C2×C4—14632no—
946C2×C4—1462no—
947C2×C4—1462no—
948C2×C4—1462no—
949C2×C4—1462no—
950C2×C4—1462no—
951C2×C4—1462no—
952C2×C4—1462no—
953C2×C4—1462no—
954C2×C4—1462no—
955C2×C4—1462no—
956C2×C4—1462no—
957C2×C4—1462no—
958C2×C4#1455654714yescomplemented
959C22—24no—
960C22—24no—
961C22—24no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22C2×C4⋊C4×D7311yescharacteristic
975C22#117×D7311yescharacteristic
976C22C2×#1455654711yescharacteristic
977C22C4×D4×D7311yescharacteristic
978C22C4×D4×D7311yescharacteristic
979C22C4×#1192402711yescharacteristic
980C22C4×#1192402711yescharacteristic
981C22#120×D7311yescharacteristic
982C22C22⋊Q8×D7311yescharacteristic
983C22C22⋊Q8×D7311yescharacteristic
984C22#123×D7311yescharacteristic
985C22#1798909311yescharacteristic
986C22#1798909311yescharacteristic
987C22#1798909511yescharacteristic
988C22#1798909511yescharacteristic
989C22#1798909711yescharacteristic
990C22#1798909711yescharacteristic
991C22#1798911411yescharacteristic
992C22#1798911411yescharacteristic
993C22#1798911611yescharacteristic
994C22#1798911611yescharacteristic
995C22#1798911811yescharacteristic
996C22#1798911811yescharacteristic
997C22#1798912011yescharacteristic
998C22#1798912011yescharacteristic
999C22#1798913211yescharacteristic
1000C22#1798913211yescharacteristic
1001C22#1798913211yescharacteristic
1002C22#1798913211yescharacteristic
1003C22#1798913511yescharacteristic
1004C22#1798913611yescharacteristic
1005C22#1798913911yescharacteristic
1006C22#1798913911yescharacteristic
1007C22#1798913911yescharacteristic
1008C22#1798913911yescharacteristic
1009C4—24no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—2922no—
1016C4—2922no—
1017C4—2922no—
1018C4—2922no—
1019C4—2922no—
1020C4—738no—
1021C4—1464no—
1022C4—1464no—
1023C2—44no—
1024C2#2261233311yescharacteristic
1025C2#385×D7311yescharacteristic
1026C2#2261237111yescharacteristic
1027C2#2261237311yescharacteristic
1028C2#2261239111yescharacteristic
1029C2#2261239311yescharacteristic
1030C2#2261241011yescharacteristic
1031C2#2261314311yescharacteristic
1032C2#2261314511yescharacteristic
1033C2#2261318711yescharacteristic
1034C2#2261318911yescharacteristic
1035C2#2261319811yescharacteristic
1036C2#2261320011yescharacteristic
1037C2#2261320611yescharacteristic
1038C2#2261320611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×#1439C2
socle, cosocleC24×C73C24
prime radicalC25×C73C23
hypercenter#1439D73
hypocenterC73#13844
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic73C2semidirect
3. C2×#17988438C2semidirect
6. #22608195C2semidirect
7. #22608194C2semidirect
8. #22608189C2semidirect
9. #22608186C2semidirect
13. #95×Dic73C2semidirect
14. #95×Dic73C2semidirect
37. C22⋊C4×Dic73C4semidirect
195. C22×Dic73C4⋊C4semidirect
381. C2×C4×C73#117semidirect
432. C2×Dic73#117semidirect
535. C73#13844semidirect
958. C2×C4#14556547semidirect

Maximal subgroups

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

subgroupindex
C22×#145565472
C2×C4⋊C4×Dic732
C2×#179884382
C2×C22⋊C4×Dic732
#226081952
#226081942
#226081892
#226081862
#226081762
#226081742
#95×Dic732
C73×#14392
#1384473