Finite Group Databasebeta

← #13514830

Subgroups — #13514830

Order 1792.

5050 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6551C211yesmaximal, characteristic
2C2×#90263C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D7C211yesmaximal, characteristic, complemented
4C7×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
5Q8×C22⋊Dic7C211yesmaximal, characteristic, complemented
6#11739902C211yesmaximal, characteristic, complemented
7#11739902C211yesmaximal, characteristic, complemented
8#11734059C213yesmaximal, complemented
9#11734059C213yesmaximal, complemented
10#11733927C213yesmaximal, complemented
11#11733923C213yesmaximal, complemented
12#11731448C213yesmaximal, complemented
13#11731322C213yesmaximal, complemented
14#11731008C213yesmaximal, complemented
15#11730899C213yesmaximal, complemented
16C23×C7×Q8C2211yescharacteristic
17C2×#6551—28no—
18C2×#6551—28no—
19C2×#6551C4116yescomplemented
20C22×#1161C2213yes—
21C22×#1161C2211yescharacteristic
22C22×Q8×D7C2213yes—
23C22×Q8×D7C2211yescharacteristic
24C22×#1157C2213yes—
25C22×#1157C2213yes—
26C2×C4×C7×Q8C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×Q8×Dic7C2211yescharacteristic
29C2×Q8×Dic7C2211yescharacteristic
30#90263—28no—
31C4×Q8×D7—28no—
32C2×#6455C2213yes—
33C2×D7×C4⋊C4C2213yes—
34C2×#6450C2213yes—
35C2×#6450C2213yes—
36C2×#6435C2213yes—
37C2×C42×D7C2213yes—
38C2×C4×Dic14C2213yes—
39C2×C4×Dic14C2213yes—
40C7×#391C2213yes—
41C7×#391C2213yes—
42C7×#380C2213yes—
43C4×C7×C22⋊C4C2213yes—
44#90002C2213yes—
45#90002C2213yes—
46#89984C2213yes—
47C4×C22⋊Dic7C2213yes—
48#89760C2213yes—
49#89760C2213yes—
50#89759C2213yes—
51#89759C2213yes—
52#89729C2213yes—
53#89729C2213yes—
54#89729C2216yes—
55#89728C2211yescharacteristic
56#89728C2213yes—
57#89711C2213yes—
58#89711C2213yes—
59C4×(C2×D7)⋊C4C2213yes—
60C4×(C2×D7)⋊C4C2213yes—
61#89439C2216yes—
62#89439C2216yes—
63#89438C2216yes—
64#89438C2216yes—
65#89437C2213yes—
66#89437C2213yes—
67#89437C2216yes—
68#89418C2213yes—
69#89418C2213yes—
70#89418C2216yes—
71#34257—71nomaximal, Sylow
72C22×C7×Q8—24no—
73C22×C7×Q8—24no—
74C22×C7×Q8C2×C418yescomplemented
75C22×C7×Q8C2313yes—
76C22×C7×Q8C2311yescharacteristic
77C23×C4×C7C2313yes—
78C22×C22⋊D7C2311yescharacteristic
79C22×C22⋊D7C2313yes—
80#6551—2128no—
81C2×#1161—24no—
82C2×#1161—24no—
83C2×#1161—212no—
84C2×#1161—212no—
85C2×#1161C2×C4124yes—
86C2×#1161C2×C418yescomplemented
87C2×Q8×D7—212no—
88C2×Q8×D7—212no—
89C2×Q8×D7C2×C418yes—
90C2×Q8×D7C2×C4124yescomplemented
91C2×Q8×D7D418yes—
92C2×Q8×D7D418yes—
93C2×#1157—212no—
94C2×#1157—212no—
95C2×#1157—212no—
96C2×#1157—212no—
97C2×#1157C2×C4124yes—
98C2×#1157C2×C4124yescomplemented
99C22×D28C2313yes—
100C22×D28C2313yes—
101C22×C4×D7C2311yescharacteristic
102C22×C4×D7C2316yes—
103C22×C4×D7C2313yes—
104C22×C4×D7C2313yes—
105C22×C4×D7C2313yes—
106C22×Dic14C2313yes—
107C22×Dic14C2313yes—
108C4×C7×Q8—24no—
109C4×C7×Q8—24no—
110C2×C7×C4⋊C4C2313yes—
111C2×C7×C4⋊C4C2313yes—
112C2×C7×C22⋊C4C2311yescharacteristic
113C2×C7×C22⋊C4C2313yes—
114C2×C42×C7C2313yes—
115C2×C42×C7C2313yes—
116C2×C22⋊Dic7C2311yescharacteristic
117C2×C22⋊Dic7C2313yes—
118Q8×Dic7—24no—
119Q8×Dic7—24no—
120C2×(C2×D7)⋊C4C2311yescharacteristic
121C2×(C2×D7)⋊C4C2313yes—
122C2×(C2×D7)⋊C4C2313yes—
123C2×(C2×D7)⋊C4C2313yes—
124C2×(C2×D7)⋊C4C2316yes—
125C2×(C2×D7)⋊C4C2316yes—
126C2×(C2×D7)⋊C4C2313yes—
127C2×(C2×D7)⋊C4C2313yes—
128C2×C4⋊Dic7C2313yes—
129C2×C4⋊Dic7C2313yes—
130C2×Dic7⋊C4C2313yes—
131C2×Dic7⋊C4C2316yes—
132C2×Dic7⋊C4C2313yes—
133C2×C4×Dic7C2313yes—
134C2×C4×Dic7C2316yes—
135C2×C4×Dic7C2313yes—
136C2×C4×Dic7C2313yes—
137C2×C4×Dic7C2313yes—
138#6455—212no—
139D7×C4⋊C4—212no—
140#6450—212no—
141#6450—212no—
142#6435—212no—
143C42×D7—212no—
144C4×Dic14—212no—
145C4×Dic14—212no—
146C7×#95C2313yes—
147C7×#95C2316yes—
148C7×#95C2313yes—
149C7⋊#95C2311yescharacteristic
150C7⋊#95C2311yescharacteristic
151C7⋊#95C2313yes—
152C7⋊#95C2313yes—
153C7⋊#95C2313yes—
154C7⋊#95C2316yes—
155C7⋊#95C2313yes—
156C22×2−1+4—71no—
157C2×#519—71no—
158C22×C4×Q8—71no—
159#2341—73no—
160#2341—73no—
161#2341—71no—
162#2341—71no—
163Q8×C22⋊C4—73no—
164Q8×C22⋊C4—73no—
165Q8×C22⋊C4—71no—
166Q8×C22⋊C4D711yescharacteristic, complemented
167#2311—73no—
168#2311—73no—
169#2297—73no—
170#2297—73no—
171C24×C7C2411yescharacteristic
172C23×D7C2413yes—
173C23×D7C2411yescharacteristic
174C2×C7×Q8—232no—
175C2×C7×Q8—26no—
176C2×C7×Q8—26no—
177C2×C7×Q8C22×C4112yes—
178C2×C7×Q8C22×C414yes—
179C2×C7×Q8C2×D414yes—
180C2×C7×Q8C2×D414yes—
181C22×C4×C7—26no—
182C22×C4×C7—26no—
183C22×C4×C7C22×C4112yes—
184C22×C4×C7C2413yes—
185C22×C4×C7C2413yes—
186C22×C4×C7C2411yescharacteristic
187C22×C4×C7C2413yes—
188C22×C4×C7C2411yescharacteristic
189C22×C4×C7C2413yes—
190C2×C22⋊D7—22no—
191C2×C22⋊D7—22no—
192C2×C22⋊D7—26no—
193C2×C22⋊D7—26no—
194C2×C22⋊D7C22×C414yes—
195C2×C22⋊D7C22×C4112yes—
196C22×Dic7C2411yescharacteristic
197C22×Dic7C2413yes—
198C22×Dic7C2413yes—
199C22×Dic7C2411yescharacteristic
200C22×Dic7C2411yescharacteristic
201C22×Dic7C2413yes—
202#1161—232no—
203#1161—296no—
204Q8×D7—296no—
205Q8×D7C22⋊C4164yescomplemented
206#1157—296no—
207#1157—296no—
208C2×D28—26no—
209C2×D28—26no—
210C2×D28—26no—
211C2×D28—26no—
212C2×D28C22×C4112yes—
213C2×D28C22×C4112yes—
214C2×C4×D7—22no—
215C2×C4×D7—26no—
216C2×C4×D7—26no—
217C2×C4×D7—22no—
218C2×C4×D7—212no—
219C2×C4×D7—212no—
220C2×C4×D7—22no—
221C2×C4×D7—26no—
222C2×C4×D7—43no—
223C2×C4×D7—43no—
224C2×C4×D7C22×C4112yes—
225C2×C4×D7C22×C4124yes—
226C2×C4×D7C22×C4112yes—
227C2×C4×D7C2×D4112yes—
228C2×C4×D7C2×D4112yes—
229C2×Dic14—26no—
230C2×Dic14—26no—
231C2×Dic14C22×C4112yes—
232C2×Dic14C22×C4112yes—
233C2×Dic14C2×D4112yes—
234C2×Dic14C2×D4112yes—
235C7×C4⋊C4—26no—
236C7×C4⋊C4—26no—
237C7×C22⋊C4—22no—
238C7×C22⋊C4—43no—
239C42×C7—26no—
240C42×C7—26no—
241C22⋊Dic7—22no—
242C22⋊Dic7—43no—
243(C2×D7)⋊C4—22no—
244(C2×D7)⋊C4—26no—
245(C2×D7)⋊C4—26no—
246(C2×D7)⋊C4—26no—
247(C2×D7)⋊C4—43no—
248(C2×D7)⋊C4—46no—
249(C2×D7)⋊C4—46no—
250(C2×D7)⋊C4—43no—
251C4⋊Dic7—26no—
252C4⋊Dic7—26no—
253Dic7⋊C4—26no—
254Dic7⋊C4—212no—
255Dic7⋊C4—26no—
256C4×Dic7—26no—
257C4×Dic7—26no—
258C4×Dic7—26no—
259C4×Dic7—212no—
260C4×Dic7—26no—
261C2×2−1+4—716no—
262C2×2−1+4—148no—
263C2×2−1+4—148no—
264C22×#41—73no—
265C22×#41—71no—
266C22×#41—73no—
267C22×#41—73no—
268C23×Q8—71no—
269C23×Q8—73no—
270C23×Q8C2×D711yescharacteristic
271#519—148no—
272C2×C4×Q8—71no—
273C2×C4×Q8—71no—
274C2×C4×Q8—73no—
275C2×C4×Q8—73no—
276C2×C4×Q8—73no—
277C2×C4×Q8—73no—
278C2×C4×Q8—148no—
279C2×C4×Q8C2×D711yescharacteristic
280C2×C4×Q8C2×D711yescharacteristic
281C2×#117—73no—
282C2×#117—73no—
283C22×C4⋊C4—73no—
284C22×C42—73no—
285#391—73no—
286#391—73no—
287#391—76no—
288#391—73no—
289#391—73no—
290#391C2×D713yes—
291#391C2×D713yes—
292#390—73no—
293#390—73no—
294#390—76no—
295#390—73no—
296#390—73no—
297#390—73no—
298#390—73no—
299#386—73no—
300#386—71no—
301#386—76no—
302#386—73no—
303#386—73no—
304#380—73no—
305#380—73no—
306#380—73no—
307#380—76no—
308#380—76no—
309#380C2×D713yes—
310C4×C22⋊C4—73no—
311C4×C22⋊C4—73no—
312C4×C22⋊C4—73no—
313C4×C22⋊C4—76no—
314C4×C22⋊C4—76no—
315C4×C22⋊C4C2×D713yes—
316C23×C7—21no—
317C23×C7—21no—
318C23×C7—21no—
319C23×C7—21no—
320C23×C7—21no—
321C23×C7—21no—
322C23×C7C23×C412yes—
323C23×C7C2511yescharacteristic
324C22×D7—21no—
325C22×D7—21no—
326C22×D7—21no—
327C22×D7—21no—
328C22×D7—23no—
329C22×D7—23no—
330C22×D7—23no—
331C22×D7—23no—
332C22×D7—23no—
333C22×D7—23no—
334C22×D7C23×C416yes—
335C22×D7C23×C412yes—
336C22×D7C22×D412yes—
337C22×D7C22×D412yes—
338C7×Q8—224no—
339C7×Q8C2×C22⋊C4116yes—
340C2×C4×C7—21no—
341C2×C4×C7—23no—
342C2×C4×C7—23no—
343C2×C4×C7—21no—
344C2×C4×C7—224no—
345C2×C4×C7—23no—
346C2×C4×C7—23no—
347C2×C4×C7—21no—
348C2×C4×C7—23no—
349C2×C4×C7—21no—
350C2×C4×C7—21no—
351C2×C4×C7—23no—
352C2×C4×C7—23no—
353C2×C4×C7—23no—
354C2×C4×C7C23×C416yes—
355C2×C4×C7C23×C416yes—
356C2×C4×C7C22×D416yes—
357C2×C4×C7C22×D416yes—
358C2×C4×C72−1+412yescomplemented
359C22⋊D7—28no—
360C22⋊D7—224no—
361C2×Dic7—21no—
362C2×Dic7—21no—
363C2×Dic7—21no—
364C2×Dic7—21no—
365C2×Dic7—21no—
366C2×Dic7—23no—
367C2×Dic7—23no—
368C2×Dic7—23no—
369C2×Dic7—21no—
370C2×Dic7—21no—
371C2×Dic7—23no—
372C2×Dic7—23no—
373C2×Dic7—23no—
374C2×Dic7C23×C412yes—
375C2×Dic7C23×C416yes—
376C2×Dic7C22×D416yes—
377C2×Dic7C22×D416yes—
378C2×Dic72−1+412yescomplemented
379D28—224no—
380D28—224no—
381C4×D7—28no—
382C4×D7—224no—
383C4×D7—248no—
384C4×D7—412no—
385C4×D7C2×C22⋊C4148yes—
386Dic14—224no—
387Dic14C2×C22⋊C4148yes—
3882−1+4—14128no—
389C2×#41—724no—
390C2×#41—78no—
391C2×#41—724no—
392C2×#41—724no—
393C2×#41—1412no—
394C2×#41—1412no—
395C2×#41—1412no—
396C2×#41—1412no—
397C2×#41—1412no—
398C2×#41—1412no—
399C2×#41—144no—
400C2×#41—144no—
401C22×Q8—24no—
402C22×Q8—24no—
403C22×Q8—78no—
404C22×Q8—78no—
405C22×Q8—78no—
406C22×Q8—724no—
407C22×Q8—73no—
408C22×Q8—73no—
409C22×Q8—1412no—
410C22×Q8—1412no—
411C22×Q8C4×D718yescomplemented
412C22×Q8C22×D713yes—
413C22×Q8C22×D711yescharacteristic
414C22×D4—71no—
415C22×D4—73no—
416C22×D4—73no—
417C22×D4—73no—
418C23×C4—73no—
419C23×C4—76no—
420C23×C4—73no—
421C23×C4—71no—
422C23×C4—73no—
423C23×C4C22×D713yes—
424C4×Q8—24no—
425C4×Q8—24no—
426C4×Q8—1412no—
427C4×Q8—1412no—
428C4×Q8—1412no—
429C4×Q8—1412no—
430C4×Q8—144no—
431C4×Q8—144no—
432#117—1412no—
433#117—1412no—
434C2×C4⋊C4—76no—
435C2×C4⋊C4—73no—
436C2×C4⋊C4—73no—
437C2×C4⋊C4—73no—
438C2×C4⋊C4—73no—
439C2×C4⋊C4—1412no—
440C2×C4⋊C4C22×D713yes—
441C2×C4⋊C4C22×D713yes—
442C2×C22⋊C4—71no—
443C2×C22⋊C4—73no—
444C2×C22⋊C4—71no—
445C2×C22⋊C4—73no—
446C2×C22⋊C4—73no—
447C2×C22⋊C4—73no—
448C2×C22⋊C4—76no—
449C2×C22⋊C4—73no—
450C2×C22⋊C4—76no—
451C2×C22⋊C4—73no—
452C2×C22⋊C4C22×D711yescharacteristic
453C2×C22⋊C4C22×D713yes—
454C2×C42—76no—
455C2×C42—73no—
456C2×C42—73no—
457C2×C42—73no—
458C2×C42—73no—
459C2×C42—1412no—
460C2×C42C22×D713yes—
461C2×C42C22×D713yes—
462#95—71no—
463#95—71no—
464#95—73no—
465#95—73no—
466#95—73no—
467#95—76no—
468#95—73no—
469#95C22×D713yes—
470#95C22×D716yes—
471#95C22×D713yes—
472C22×C7—22no—
473C22×C7—22no—
474C22×C7—22no—
475C22×C7—41no—
476C22×C7—41no—
477C22×C7—41no—
478C22×C7—41no—
479C22×C7C24×C411yescharacteristic
480C22×C7C23×D411yescharacteristic
481C22×C7C23×D411yescharacteristic
482C22×C7C2×2−1+411yescharacteristic
483C22×C7C2×2−1+411yescharacteristic
484C22×C7#58511yescharacteristic
485C22×C7#58511yescharacteristic
486C2×D7—22no—
487C2×D7—22no—
488C2×D7—22no—
489C2×D7—22no—
490C2×D7—22no—
491C2×D7—22no—
492C2×D7—26no—
493C2×D7—26no—
494C2×D7—26no—
495C2×D7—43no—
496C2×D7—43no—
497C2×D7—43no—
498C2×D7—43no—
499C2×D7C22×C22⋊C414yes—
500C4×C7—26no—
501C4×C7—22no—
502C4×C7—43no—
503C4×C7—43no—
504C4×C7—41no—
505C4×C7C22×C22⋊C4112yes—
506Dic7—22no—
507Dic7—22no—
508Dic7—43no—
509Dic7—41no—
510Dic7—43no—
511Dic7C22×C22⋊C4112yes—
512C24—71no—
513C24—73no—
514C24C23×D711yescharacteristic
515#41—1496no—
516#41—1496no—
517#41—1496no—
518#41—1432no—
519C2×Q8—232no—
520C2×Q8—26no—
521C2×Q8—26no—
522C2×Q8—764no—
523C2×Q8—712no—
524C2×Q8—712no—
525C2×Q8—712no—
526C2×Q8—712no—
527C2×Q8—146no—
528C2×Q8—146no—
529C2×Q8—1496no—
530C2×Q8C2×C4×D7112yes—
531C2×Q8C2×C4×D714yes—
532C2×Q8D4×D714yes—
533C2×Q8D4×D714yes—
534C2×D4—712no—
535C2×D4—74no—
536C2×D4—712no—
537C2×D4—712no—
538C2×D4—146no—
539C2×D4—146no—
540C2×D4—146no—
541C2×D4—146no—
542C2×D4—142no—
543C2×D4—142no—
544C2×D4—146no—
545C2×D4—146no—
546C22×C4—26no—
547C22×C4—26no—
548C22×C4—73no—
549C22×C4—712no—
550C22×C4—712no—
551C22×C4—712no—
552C22×C4—71no—
553C22×C4—71no—
554C22×C4—724no—
555C22×C4—712no—
556C22×C4—73no—
557C22×C4—71no—
558C22×C4—73no—
559C22×C4—142no—
560C22×C4—1412no—
561C22×C4—1412no—
562C22×C4—142no—
563C22×C4—146no—
564C22×C4—146no—
565C22×C4—146no—
566C22×C4—142no—
567C22×C4—283no—
568C22×C4—283no—
569C22×C4C2×C4×D7112yes—
570C22×C4C23×D713yes—
571C22×C4C23×D713yes—
572C22×C4C23×D711yescharacteristic
573C22×C4C23×D713yes—
574C22×C4C23×D711yescharacteristic
575C22×C4C23×D713yes—
576C4⋊C4—26no—
577C4⋊C4—26no—
578C4⋊C4—1412no—
579C4⋊C4—146no—
580C4⋊C4—146no—
581C4⋊C4—146no—
582C4⋊C4—146no—
583C22⋊C4—22no—
584C22⋊C4—43no—
585C22⋊C4—146no—
586C22⋊C4—142no—
587C22⋊C4—146no—
588C22⋊C4—142no—
589C22⋊C4—146no—
590C22⋊C4—286no—
591C22⋊C4—283no—
592C22⋊C4—283no—
593C22⋊C4—286no—
594C22⋊C4—283no—
595C42—26no—
596C42—26no—
597C42—146no—
598C42—146no—
599C42—1412no—
600C42—146no—
601C42—146no—
602C2×C7—42no—
603C2×C7C23×C22⋊C411yescharacteristic
604C2×C7C4×2−1+411yescharacteristic
605C2×C7C4×2−1+411yescharacteristic
606C2×C7#348611yescharacteristic
607C2×C7#348711yescharacteristic
608C2×C7#349711yescharacteristic
609C2×C7#349711yescharacteristic
610D7—24no—
611D7—46no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—72no—
619C23—72no—
620C23—72no—
621C23—76no—
622C23—141no—
623C23—141no—
624C23—141no—
625C23—141no—
626C23—143no—
627C23—143no—
628C23—143no—
629C23—143no—
630C23—143no—
631C23—143no—
632C23C22×C4×D712yes—
633C23C24×D711yescharacteristic
634Q8—224no—
635Q8—748no—
636Q8—1424no—
637Q8D7×C22⋊C4116yes—
638D4—1424no—
639D4—1424no—
640D4—148no—
641D4—1424no—
642C2×C4—21no—
643C2×C4—23no—
644C2×C4—23no—
645C2×C4—21no—
646C2×C4—224no—
647C2×C4—21no—
648C2×C4—23no—
649C2×C4—23no—
650C2×C4—21no—
651C2×C4—23no—
652C2×C4—23no—
653C2×C4—23no—
654C2×C4—21no—
655C2×C4—23no—
656C2×C4—76no—
657C2×C4—76no—
658C2×C4—76no—
659C2×C4—748no—
660C2×C4—72no—
661C2×C4—72no—
662C2×C4—1448no—
663C2×C4—148no—
664C2×C4—141no—
665C2×C4—141no—
666C2×C4—141no—
667C2×C4—141no—
668C2×C4—1424no—
669C2×C4—141no—
670C2×C4—143no—
671C2×C4—143no—
672C2×C4—143no—
673C2×C4—141no—
674C2×C4—143no—
675C2×C4—141no—
676C2×C4—143no—
677C2×C4—143no—
678C2×C4—2812no—
679C2×C4C22×C4×D716yes—
680C2×C4C22×C4×D716yes—
681C2×C4C2×D4×D716yes—
682C2×C4C2×D4×D716yes—
683C2×C4#655112yescomplemented
684C7#3425711yescharacteristic, complemented, Sylow
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—74no—
693C22—142no—
694C22—142no—
695C22—142no—
696C22—142no—
697C22—142no—
698C22—142no—
699C22—146no—
700C22—146no—
701C22—146no—
702C22—283no—
703C22—283no—
704C22—283no—
705C22—283no—
706C22C23×C4×D711yescharacteristic
707C22C22×D4×D711yescharacteristic
708C22C22×D4×D711yescharacteristic
709C22C2×#655111yescharacteristic
710C22#9061611yescharacteristic
711C22D7×2−1+411yescharacteristic
712C22#9062011yescharacteristic
713C4—26no—
714C4—22no—
715C4—43no—
716C4—43no—
717C4—41no—
718C4—712no—
719C4—142no—
720C4—142no—
721C4—283no—
722C4—281no—
723C4—283no—
724C4C2×D7×C22⋊C4112yes—
725C2—42no—
726C2—144no—
727C2—286no—
728C2C22×D7×C22⋊C411yescharacteristic
729C2C4×#655111yescharacteristic
730C2#1174294111yescharacteristic
731C2#1174380411yescharacteristic
732C2#1174380511yescharacteristic
733C2#1174382711yescharacteristic
734C2#1174382811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutatorC22×C7C24×C4
FittingC7×Q8×C22⋊C4C2
socle, cosocleC23×C7C25
prime radicalC22×#6551C2
hypercenterQ8×C22⋊C4D7
hypocenterC7#34257
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#90263C2semidirect
3. C2×C4×Q8×D7C2semidirect
4. C7×Q8×C22⋊C4C2semidirect
5. Q8×C22⋊Dic7C2semidirect
6. #11739902C2semidirect
7. #11739902C2semidirect
8. #11734059C2semidirect
9. #11734059C2semidirect
10. #11733927C2semidirect
11. #11733923C2semidirect
12. #11731448C2semidirect
13. #11731322C2semidirect
14. #11731008C2semidirect
15. #11730899C2semidirect
19. C2×#6551C4semidirect
74. C22×C7×Q8C2×C4semidirect
86. C2×#1161C2×C4semidirect
90. C2×Q8×D7C2×C4semidirect
98. C2×#1157C2×C4semidirect
166. Q8×C22⋊C4D7semidirect
205. Q8×D7C22⋊C4semidirect
358. C2×C4×C72−1+4semidirect
378. C2×Dic72−1+4semidirect
411. C22×Q8C4×D7semidirect
683. C2×C4#6551semidirect
684. C7#34257semidirect

Maximal subgroups

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

subgroupindex
C22×#65512
C2×#902632
C2×C4×Q8×D72
C7×Q8×C22⋊C42
Q8×C22⋊Dic72
#117399022
#117340592
#117339272
#117339232
#117314482
#117313222
#117310082
#117308992
#342577